Home

ILOG CPLEX 8.1 Getting Started

1. 111 Building and Solving a Small LP Model 111 Complete Program ie ai eari hh hrs 113 Reading a Problem from File Example 2 122 Complete Program Led ade Se RUNE CERE ENSE RERO eR ee 124 Adding Rows to a Problem Example 131 Complete Programs c sob eem Tab a dete ed a ire 132 Performing Sensitivity Analysis 138 141 ILOG CPLEX 8 1 GETTING STARTED 9 TABLE OF CONTENTS 10 ILOG CPLEX 8 1 GETTING STARTED Introducing ILOG CPLEX This preface introduces ILOG CPLEX 8 1 It includes sections on What Is ILOG CPLEX Solving an LP with CPLEX Technology What You Need to Know Manual Organization Notation in this Manual Related Documentation 5 9 9 For More Information ILOG CPLEX 8 1 GETTING STARTED 11 WHAT IS ILOG CPLEX What Is ILOG CPLEX ILOG CPLEX is a tool for solving linear optimization problems commonly referred to as Linear Programming LP problems of the form Maximize or Minimize subject to 11 1 12 2 1 2 b Q5jX 22 2 t b gt Amn jX AnyXy Dn with these bounds lj lt lt 1 Sy lt
2. 54 Adding Constraints and Bounds 55 Changing a Problem ce cee eee eee eee ee ee 56 Changing Constraint or Variable 57 Changing Sense red ree eed a eee 57 Changing Bounds sed hace dg Aiea lng awed eta es 58 Removing BOurnds ace eos ire BVA ie Gai RA EG NET ae eet dy 58 Changing Coefficients cette teeta 58 Deleting aes ied eae ed a E ak thd e EE 59 Executing Operating System Commands 60 Quitting ILOG CPLEX Rae ay Saw ge ae ale ee 61 Concert Technology Tutorial for C Users 63 The Design of CPLEX in Concert Technology 64 Compiling and Linking CPLEX in Concert Technology Applications 65 Testing Your Installation on UNIX 0 0 IH HI 65 Testing Your Installation on Windows 65 In Case of Problems x gem fur ROUEN HERES BU 66 The Anatomy of a Concert Technology Application 66 Constructing the Environment 66 Creating a Model 67 Solving the Model lloC
3. IloRange 93 IloRange class 68 69 73 79 setCoef member function 74 IloRange setExpr 98 lloS IloSemiContVar class 79 1105051 class 79 1105052 class 79 continued importModel member function IloCplex class 79 81 infeasible 95 installing CPLEX 25 to 29 testing installation 28 integer parameter 86 integer variable optimizer used 110 representing in model 68 Interactive Optimizer 31 to 61 GETTING STARTED command formats 32 commands 33 description 13 example model 15 quitting 61 starting 32 invalid encrypted key 91 iteration log 43 44 J Java Native Interface 89 Java Virtual Machine 90 javamake 90 JNI 89 JVM 90 L libformat 90 licensing CPLEX 28 linear optimization 12 link Concert Technology library files 29 CPLEX library files 29 linker error messages 66 using with CPLEX 65 linking applications 29 Callable Library applications 104 Concert Technology applications 65 log file adding to 54 cplex log44 creating 44 iteration log 43 44 LP creating a model 15 node 80 problem format 12 root 80 solving a model 15 solving pure 80 ILOG CPLEX 8 1 INDEX LP file reading 51 writing 49 LP file format 35 1 1 138 LPex1 java 95 LPMETHOD parameter 42 makefile 90 maximization in LP problem 35 memory management by environment object 67 MIN file format 48 minimization in LP problem 35 MIP description 12 solving 80 MIP optimizer availability
4. CPLEX 8 1 Getting Started December 2002 Copyright 2001 2002 by ILOG This document and the software described in this document are the property of ILOG and are protected as ILOG trade secrets They are furnished under a license or non disclosure agreement and may be used or copied only within the terms of such license or non disclosure agreement No part of this work may be reproduced or disseminated in any form or by any means without the prior written permission of ILOG S A Printed in France Preface Chapter 1 Table of Contents Introducing ILOG 11 What Is ILOG CPLEX coe pie Ee m ace RR Romx eR erm n E 12 ILOG CPLEX Technologies 0 0 0 cece eee 13 Optimizer Options 2 os ee he Dae RP ed ii we a e deg hdmi es 13 Data Entry Options o stre oet esed x BOR Ga ae a alee 14 Solving an LP with CPLEX Technology 15 Using the Interactive 15 Concert Technology for C 16 Concert Technology for Java 00 cece cette tenets 18 Using the Callable 18 What You Need to KNOW 1 0 eee eee eee eee n hh hh hh 21 Manual Organization lesse n RR n 21 Notation in this Manual
5. lt switch argv 1 1 case r populatebyrow model var con break case c populatebycolumn model var con break case n populatebynonzero model var con break IloCplex cplex model Optimize the problem and obtain solution if cplex solve env error Failed to optimize LP endl throw 1 ILOG CPLEX 8 1 GETTING STARTED 75 BUILDING AND SOLVING A SMALL LP MODEL IN IloNumArray vals env env out lt lt Solution status lt lt cplex getStatus lt lt endl env out lt lt Solution value lt lt cplex getObjValue lt lt endl cplex getValues vals var env out Values lt lt vals lt lt endl cplex getSlacks vals con env out lt lt Slacks lt lt vals lt lt endl cplex getDuals vals con env out lt lt Duals lt lt vals lt lt endl cplex getReducedCosts vals var env out lt lt Reduced Costs lt lt vals lt lt endl cplex exportModel 1 1 1 catch IloException amp e cerr Concert exception caught e endl gateh st cerr Unknown exception caught endl env end return 0 END main static void usage const char progname cerr lt lt Usage lt lt progname lt lt X lt lt endl cerr lt lt where X is one of the following options lt lt endl cerr lt lt
6. 104 Building CPLEX Callable Library Applications on UNIX Platforms 105 ILOG CPLEX 8 1 GETTING STARTED TABLE OF CONTENTS Building CPLEX Callable Library Applications on Win32 Platforms 105 Building Applications that Use the CPLEX Parallel 106 How ILOG CPLEX Works ae Mile ee E ete 106 Opening the ILOG CPLEX 106 Instantiating the Problem 107 Populating the Problem Object 107 Changing the Problem 107 Creating a Successful Callable Library 108 Prototype the Model bored Sig ea ek Ae A pie ie as d RIT HE 108 Identify the Routines to be Called 108 Test Procedures in the Application 109 Assemble the Data he A doe bo 109 Choose an Optimizer hh rn 110 Observe Good Programming 110 Debug Your Program case cc eee eee ee ee Pe mel ee ed eed ies 110 Test Your Application oem ORE ae Sat Aes aie A 111 Use the Examples occa baer
7. if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON ILOG CPLEX 8 1 GETTING STARTED 125 D aqe READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C 126 if lp Tf status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Create the problem using the filename as the problem name CPXcreateprob env amp status argv 1 A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX PARAM SCRIND causes the error message to appear on stdout Note that most CPLEX routines return an error code to indicate the reason for failure 1 NULL fprintf stderr Failed to create LP n goto TERMINATE Now read the file and copy the data into the created lp Status CPXreadcopyprob env lp argv 1 NULL if status fprintf stderr Failed to read and copy the problem data n goto TERMINATE Optimize the problem and obtain solution swit
8. 0 0 000 cece RR n hh hh hh hn 21 Related Documentation 2 00 c cee eee eee n n nn nnn 22 For More Information 00 00 cece eee hh hh hn 23 Customer Supports 2x em ete nok aed Enea eats vind RENS 23 Web Site She eb cee es uo pee ee eh ew ee 23 Setting Up CPLEX Michie dete ie ad eet 25 Installing CPLEX dacs we GN RR wae ace f CR 26 Setting Up Licensing 2 me Rr ERI E LEER I eere re er ete 28 ILOG CPLEX 8 1 GETTING STARTED 5 TABLE OF CONTENTS Chapter 2 Using the Component Libraries 00 cece eee 28 Interactive Optimizer 31 Starting ILOG CPLEX eee lle pl e eee eel ee 32 Using Help usas xr x nae ala ed ital ei 32 Entering a Problem eee cece eee eee ee hh hh hm hm hn 34 Entering the Example Problem 34 Using the LP Format nr Ee DR E esce eec lex wwe yea doles 35 Entering Data eso Bae ae fy CERIS OE RE ERREUR 37 Displaying a Problem 2 0 0 cece RR hh hh htt 38 Displaying Problem Statistics llle es 39 Specifying Item mr 40 Displaying Variable or Constraint Names 40 Ordering Variables E DE e er UU RR TUE es 41 Displayirig Constraints Ee eic ecu uo e ee e irae n 41 D
9. fprintf stderr CPXfreeprob failed error code d n status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX_PARAM_SCRIND indicator is set to CPX_ON if status char errmsg 1024 fprintf stderr Could not close CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr Ss errmsg return status END main This simple routine frees up the pointer ptr and sets ptr to NULL static void free_and_null char ptr if ptr NULL free ptr ptr NULL END free_and_null static void usage char progname fprintf stderr Usage s filename algorithm n progname fprintf stderr where filename is a file with extension n fprintf stderr MPS SAV or LP lower case is allowed Nn fprintf stderr and algorithm is one of the letters n default n primal simplex n fprintf stderr fprintf stderr dual simplex n network simplex n fprintf stderr fprintf stderr O 130 ILOG CPLEX 8 1 GETTING STARTED ADDING ROWS TO A PROBLEM EXAMPLE 1 fprintf stderr barrier n fprintf stderr barrier with crossover n fprintf stderr s
10. where 2 or and the upper bounds and lower bounds may be positive infinity negative infinity or any real number The elements of data you provide as input for this LP are Objective function coefficients Constraint coefficients Ay gt Any Ami Am2 Amn Right hand sides by bz Dm Upper and lower bounds Uj Uy U and lj b L The optimal solution that CPLEX computes and returns is Variables Xp X75 00 CPLEX also can solve several extensions to LP Network Flow problems a special case of LP that CPLEX can solve much faster by exploiting the problem structure Quadratic Programming QP problems where the LP objective function is expanded to include quadratic terms Mixed Integer Programming MIP problems where any or all of the LP or QP variables are further restricted to take integer values in the optimal solution and where MIP itself is extended to include constructs like Special Ordered Sets SOS and semi continuous variables 12 ILOG CPLEX 8 1 GETTING STARTED WHAT IS ILOG CPLEX ILOG CPLEX Technologies CPLEX comes in three forms to meet a wide range of users needs The CPLEX Interactive Optimizer is an executable program that can read a problem interactively or from files in certain standard formats solve the problem and deliver the solution interactively or into text files The program consists o
11. GETTING STARTED DISPLAYING A PROBLEM The default names obj c1 c2 are provided by ILOG CPLEX If that is what you want you are ready to solve the problem If there is a mistake you must use the change command to modify the problem The change command is described in Changing a Problem on page 56 Summary Display problem characteristics by entering the command display problem Displaying Problem Statistics When the problem is as small as our example it is easy to display it on the screen however many real problems are far too large to display For these problems the st at s option of the display problem command is helpful When you select stat s information about the attributes of the problem appears but not the entire problem itself These attributes include the number and type of constraints variables JOZIWNdO 1 nonzero constraint coefficients Try this feature by typing display problem stats For our example the following information appears Problem Name example Constraints 2 Less 2 Variables 3 Nneg 2 Box 1 Constraint nonzeros 6 Objective nonzeros 3 RHS nonzeros 2 This information tells us that in the example there are two constraints three variables and six nonzero constraint coefficients The two constraints are both of the type less than or equal to Two of the three variables have the default nonnegativity bounds 0 x lt
12. The SOS format specifies the special ordered sets of a model The TRE format saves the branch and bound tree for restart purposes The VEC format saves the solution to a pure barrier solution as a restart to a later crossover step Reminder All these file formats are described in more detail in the CPLEX Reference Manual Writing LP Files When you enter the write command the following message appears Name of file to write Enter the problem name example and CPLEX will ask you to select from a list of options For this example choose LP CPLEX displays a confirmation message like this Problem written to file example If you would like to save the file with a different name you can simply use the write command with the new file name as an argument Try this using the name examp1e2 This time we avoid intermediate prompts by specifying an LP problem type like this write example2 lp Another way of avoiding the prompt for a file format is by specifying the file type explicitly in the file name extension Try the following as an example write example lp Using a file extension to indicate the file type is the recommended naming convention This makes it easier to keep track of your problem and solution files When the file type is specified by the file name extension ILOG CPLEX ignores subsequent file type information issued within the write command For example ILOG CPLEX responds to the following comma
13. 1 0 obj 1 2 0 obj 2 3 0 lb 0 0 0 lb 1 0 0 lb 2 0 0 m ub 0 40 0 ub 1 CPX INFBOUND ub 2 CPX INFBOUND colname 0 x1 colname 1 x2 colname 2 x3 gt status CPXnewcols env lp NUMCOLS obj lb ub NULL colname lt ILOG CPLEX 8 1 GETTING STARTED 121 READING PROBLEM FROM FILE EXAMPLE LPEX2 C if status goto TERMINATE Now create the list of coefficients rowlist 0 0 collist 0 0 vallist 0 1 0 rowlist 1 0 collist 1 1 vallist 1 1 0 rowlist 2 0 collist 2 2 vallist 2 1 0 rowlist 3 1 collist 3 0 vallist 3 1 0 rowlist 4 1 collist 4 1 vallist 4 3 0 rowlist 5 1 collist 5 2 vallist 5 1 0 Status CPXchgcoeflist env lp 6 rowlist collist vallist if status goto TERMINATE TERMINATE return status END populatebynonzero Reading a Problem from a File Example lpex2 c The previous example 1pex1 c shows a way to copy problem data into CPLEX problem object as part of an application that calls routines from the ILOG CPLEX Callable Library Frequently however a file already exists containing a linear programming problem in the industry standard MPS format the ILOG CPLEX LP format or the ILOG CPLEX binary SAV format In example 1pex2 c ILOG CPLEX file reading and optimization routines read such a file to solve the problem Example
14. 9 and one is restricted to a certain range a box variable In addition to a constraint matrix nonzero count there is a count of nonzero coefficients in the objective function and on the right hand side Such statistics can help to identify errors in a problem without displaying it in its entirety Another way to avoid displaying an entire problem is to display a specific part of it by using one of the following three options of the display problem command names described in Displaying Variable or Constraint Names on page 40 can be used to display a specified set of variable or constraint names ILOG CPLEX 8 1 GETTING STARTED 39 DISPLAYING A PROBLEM 40 constraints described in Displaying Constraints on page 41 can be used to display a specified set of constraints bounds described in Displaying Bounds on page 42 can be used to display a specified set of bounds Specifying Item Ranges For some options of the display command you must specify the item or range of items you want to see Whenever input defining a range of items is required ILOG CPLEX expects two indices separated by a hyphen the range character The indices can be names or matrix index numbers You simply enter the starting name or index number a hyphen and finally the ending name or index number CPLEX automatically sets the default upper and lower limits defining any range to be the highest and lowest possible values
15. Monitoring the Iteration Log Next an iteration log appears on the screen ILOG CPLEX reports its progress as it solves the problem The solution process involves two stages during Phase I ILOG CPLEX searches for a feasible solution in Phase II ILOG CPLEX searches for the optimal feasible solution The iteration log periodically displays the current iteration number and either the current scaled infeasibility during Phase I or the objective function value during Phase II Once the optimal solution has been found the objective function value solution time and iteration count total with Phase I in parentheses are displayed This information can be useful for monitoring the rate of progress The iteration log display can be modified by the set simplex display command to display differing amounts of data while the problem is being solved Reporting the Solution After it finds the optimal solution ILOG CPLEX reports JOZIWNdO the objective function value the problem solution time in seconds the total iteration count the Phase I iteration count in parentheses Optimizing our example problem produces a report like the following one although the solution times vary with each computer Tried aggregator 1 time No presolve or aggregator reductions Presolve Time 0 00 sec Iteration Log Iteration 1 Dual infeasibility 0 000000 Iteration 2 Dual objective
16. 1 2 x3 lt 20 The part x1 2 x3 lt 20 creates an object of class IloRange that is immediately added to the model by passing it to the method 1 1 Again if a reference to the IloRange object is needed later an IloRange handle object must be stored for it Concert Technology provides flexible array classes for storing data such as these IloRange objects As with variables Concert Technology provides a variety of constructors that help create range constraints While the above examples use expressions with modeling variables directly for modeling it should be pointed out that such expressions are themselves represented by yet another Concert Technology class 11oExpr Like most Concert Technology objects IloExpr objects are handles Consequently method end must be called when the object is no longer needed The only exceptions are implicit expressions where the user does not create an IloExpr object such as when writing for example x1 2 x2 For such implicit expressions method end should not be called The importance of the class IloExpr becomes clear when expressions can no longer be fully spelled out in the source code but need instead to be built up in a loop Operators like provide an efficient way to do this Solving the Model lloCplex Once the optimization problem has been created in an IloMode1 object it is time to create the IloCplex object for solving the pr
17. 15 then called to supply the constraints The routine populatebycolumn first calls CPXnewrows to specify the row based problem data such as the right hand side values and sense of constraints The routine CPXaddcols is then called to supply the columns of the matrix and the associated column bounds names and objective coefficients The routine populatebynonzero calls both CPXnewrows and CPXnewcols to supply all the problem data except the actual constraint matrix At this point the rows and columns are well defined but the constraint matrix remains empty The routine CPXchgcoeflist is then called to fill in the nonzero entries in the matrix Once the problem has been specified the application optimizes it by calling the routine 1 Its default behavior is to use ILOG CPLEX Dual Simplex Optimizer If this routine returns a nonzero result then an error occurred If no error occurred the application allocates arrays for solution values of the primal variables dual variables slack variables and reduced costs then it obtains the solution information by calling the routine CPXsolution This routine returns the status of the problem whether optimal infeasible or unbounded and whether a time limit or iteration limit was reached the objective value and the solution vectors The application then displays this information on the screen ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING A SMALL
18. SOS file format 49 sparse matrix 86 starting CPLEX 32 from previous basis 87 Interactive Optimizer 32 new problem 34 string parameter 86 structure of a CPLEX application 92 Supported Platforms 90 System out 96 T technical support 23 tranopt Interactive Optimizer command 44 TRE file format 49 True 94 TXT file format 48 U unbounded 94 UNIX building Callable Library applications 105 executing commands 61 installation directory 26 installing CPLEX 26 testing CPLEX in Concert Technology 65 verifying installation 28 UnsatisfiedLinkError 91 V variable boolean 68 box 39 changing bounds 58 changing names 57 continuous 68 creating 79 deleting 59 displaying 39 displaying names 40 GETTING STARTED entering bounds 36 entering names 35 integer 68 name limitations 35 ordering 41 removing bounds 58 representing in model 68 variables modeling 93 VEC solution File format 49 Web site 23 Windows building Callable Library applications 105 dynamic loading 106 installing CPLEX 26 Microsoft Visual C compiler 105 Microsoft Visual C IDE 105 testing CPLEX in Concert Technology 65 verifying installation 29 write Interactive Optimizer command 47 48 49 file type options 48 syntax 50 writing basis files 50 file format for 48 LP files 49 model to file 79 problem files 47 solution files 47 X xecute Interactive Optimizer command 60 syntax 61 xxx file format 50 ILOG CPLEX 8 1 GETTING ST
19. can be used to change or turn off the OutputStream that will be used If the solve method finds a solution for the active model it returns t rue and we enter the section of code that accesses the solution The method cplex getValues var 0 returns an array of primal solution values for all the variables This array is stored as double x The values in x are ordered such that x j is the primal solution value for variable var 0 j Similarly the reduced costs duals and slack values are queried and stored in arrays dj pi and slack respectively Finally the solution status of the active model and the objective value of the solution are queried with the methods IloCplex getStatus and IloCplex getObjValue respectively The program then concludes by printing the values that have been obtained in the previous steps and terminates after calling cplex end to free the memory used by the model object the catch method of IloException provides screen output in case of any error conditions along the way The remainder of the example source code is devoted to the details of populating the model object mentioned above and the following three sections provide details on how the methods work ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING SMALL LP MODEL IN JAVA Modeling by Rows The method populateByRow creates the model by adding the finished constraints and objective function to the active model one by one
20. constraints delete range of constraints variables delete range of variables equality delete range of equality constraints greater than delete range of greater than constraints less than delete range of less than constraints At the first prompt specify that you want to delete a constraint Deletion to make constraints ILOG CPLEX 8 1 GETTING STARTED 59 EXECUTING OPERATING SYSTEM COMMANDS At the next prompt enter a constraint name or number or a range as you did when you used the display command Since the constraint we want to delete is named new3 we enter that name Delete which constraint s new3 Constraint 3 deleted Check to be sure that the correct range or number is specified when you perform this operation since constraints are permanently removed from the problem Indices of any constraints that appeared after a deleted constraint will be decremented to reflect the removal of that constraint The last message indicates that the operation is complete The problem can now be checked to see if it has been changed back to its original form display problem all Maximize obj sl 4 2 x2 4 3 X3 Subject To 2 x3 lt 20 cz x1 3 x2 x3 lt 30 Bounds lt 1 lt 40 All other variables are gt 0 When you remove a constraint with the delete option that constraint no longer exists in memory however variables that appear in the deleted constraint are not removed from memory If a
21. env 1p x doubl d doub doub slack dj pi slack dj pi status fprintf goto TE C statu status if fprintf goto TE Write t CN S printf printf 116 ILOG CPLEX 8 1 e malloc cur numcols sizeof double ouble malloc cur numrows sizeof double le malloc cur numcols sizeof double le malloc cur numrows sizeof double NULL NULL NULL NULL CPXERR NO MEMORY stderr Could not allocate memory for solution n RMINATE PXsolution env lp amp solstat amp objval x pi slack dj stderr Failed to obtain solution n RMINATE he output to the screen nSolution status d n solstat olution value f n n objval GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL for i 0 i lt cur_numrows i printf Row d Slack 10f 10f n i slack il 1 for j 0 j lt cur numcols j printf Column d Value 10f Reduced cost 10f n 9 xl31 43131 Finally write a copy of the problem to a file status CPXwriteprob env lp lpexl lp NULL if status 4 fprintf stderr Failed to write LP to disk n goto TERMINATE TERMINATE Free up the solution free_and_null char amp free_and_null char amp slack free and null char amp dj free and null char amp pi Free up the problem a
22. goto TERMINATE Status CPXgetx env lp x 0 cur numcols 1 if status fprintf stderr Failed to obtain primal solution n goto TERMINATE ILOG CPLEX 8 1 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C Write out the solution for j 0 j lt cur numcols j printf Column Sd Value 17 10g j 1 if cstat NULL switch cstat j case CPX_AT_LOWER basismsg Nonbasic at lower bound break case CPX_BASIC basismsg Basic break case CPX_AT_UPPER basismsg Nonbasic at upper bound break case CPX_FREE_SUPER basismsg Superbasic or free variable at zero break default basismsg Bad basis status break printf s basismsg printf Xn Display the maximum bound violation status CPXgetdblquality env lp amp maxviol CPX MAX PRIMAL INFEAS if status y 1 fprintf stderr Failed to obtain bound violation Mn goto TERMINATE printf Maximum bound violation 17 10g n maxviol TERMINATE Free up the basis and solution free and null char amp cstat free and null char amp rstat free and null char amp x Free up the problem if necessary D if lp NULL status CPXfreeprob env amp 1 aqe ILOG CPLEX 8 1 GETTING STARTED 129 READING A PROBLEM FROM FILE EXAMPLE LPEX2 C if status
23. goto TERMINATE lp CPXcreateprob env amp status 1 1 if lp NULL fprintf stderr Failed to create LP n goto TERMINATE CPXchgobjsen env lp CPX MAX obj 0 1 0 obj 1 2 0 obj 2 3 0 IBIOI 0 0 ip 1 0 0 ip 2 0 0 ub 0 40 0 ub 1 CPX_INFBOUND ub 2 CPX_INFBOUND status CPXnewcols env lp NUMCOLS obj lb ub NULL NULL if status fprintf stderr Failed to populate problem n goto TERMINATE ILOG CPLEX 8 1 GETTING STARTED 19 SOLVING AN LP WITH CPLEX TECHNOLOGY 20 rmatbeg 0 rmatind 0 rmatval 0 rmatbeg 1 rmatind 3 rmatval 3 0 0 rmatind 1 1 rmatind 2 2 sense 0 L 1 0 rmatval 1 1 0 rmatval 2 1 0 rhs 0 20 0 3 0 rmatind 4 1 rmatind 5 2 sense 1 L 1 0 rmatval 4 3 0 rmatval 5 1 0 rhs 1 30 0 Status CPXaddrows env lp 0 NUMROWS NUMNZ rhs sense rmatbeg if statu fprintf goto TE status C it statu fprintf goto TE status C if statu fprintf goto TE printf printf S printf S TERMINATE if lp status it st fpri if env status if GE char fpri CPXg fpri return st END mai rmatind rmatval NULL NULL 5 stderr Failed to populate problem n RMINATE PXlpopt env 1 stderr Failed to optimize LP n RMINATE PXsolution env lp amp solstat amp objval x
24. while assembling the arrays in memory may be a useful enhancement for a production version ILOG CPLEX 8 1 GETTING STARTED 109 D CREATING SUCCESSFUL CALLABLE LIBRARY APPLICATION 110 Choose an Optimizer Once a problem object has been instantiated and populated it can be solved using one of the optimizers provided by the ILOG CPLEX Callable Library The choice of optimizer depends on the problem type LP and QP problems can be solved by e the primal simplex optimizer e the dual simplex optimizer and e the barrier optimizer LP problems can also be solved by e the sifting optimizer and e the concurrent optimizer LP problems with a substantial network can also be solved by a special network optimizer Ifthe problem includes integer variables branch amp cut must be used There are also many different possible parameter settings for each optimizer The default values will usually be the best for linear programs Integer programming problems are more sensitive to specific settings so additional experimentation will often be useful Choosing the best way to solve the problem can dramatically improve performance For more information refer to the sections about tuning LP performance and trouble shooting MIP performance in the ILOG CPLEX User s Manual Observe Good Programming Practices Using good programming practices will save development time and ma
25. 202 500000 Dual simplex Optimal Objective 2 0250000000 02 Solution Time 0 00 sec Iterations 2 1 CPLEX gt In our example ILOG CPLEX finds an optimal solution with an objective value of 202 5 in two iterations For this simple problem 1 Phase I iteration was required Summary To solve an LP problem use the command optimize ILOG CPLEX 8 1 GETTING STARTED 43 SOLVING A PROBLEM 44 Solution Options We describe here some of the basic options in solving linear programming problems Although the tutorial example does not make use of these options you will find them useful when handling larger more realistic problems The topics are Filing Iteration Logs Re Solving Using Alternative Optimizers Interrupting the Optimization Process For detailed information on performance options refer to the ILOG CPLEX User s Manual Filing Iteration Logs Every time ILOG CPLEX solves a problem much of the information appearing on the screen is also directed into a log file This file is automatically created by ILOG CPLEX with the name cplex 10g If there is an existing cplex 1og file in the directory where ILOG CPLEX is launched ILOG CPLEX will append the current session data to the existing file If you want to keep a unique log file of a problem session you can change the default name with the set logfile command See CPLEX User s Manual The log file is written in standard ASCII format a
26. 44 mipopt Interactive Optimizer command 44 Model creating 67 model adding constraints 86 creating ILoMode1 67 extracting 72 modifying 85 reading from file 79 81 solving 81 writing to file 79 model object creating 72 model column 98 modeling by column 73 by nonzerows 74 objects 64 modeling by columns 97 Modeling by Columns 72 modeling by columns 95 GETTING STARTED 147 INDEX Modeling by Nonzero Elements 72 modeling by nonzeros 95 98 Modeling by Rows 72 modeling by rows 73 95 97 modeling variables 93 modifying problem object 107 monitoring iteration log 43 MPS file format 52 MST file format 48 multiple algorithms selecting 80 N NET file format 49 netopt Interactive Optimizer command 44 network description 12 flow 86 network optimizer availability 44 selecting 80 solving with 86 Nmake 90 no license found 91 NoClassDefFoundError 91 node LP solving 80 nonzeros modeling by 74 notation in this manual 21 notification 85 numeric parameter 86 numVar 98 numVarArray 97 objective function accessing value 45 adding to model 69 changing coefficient 59 changing sense 58 148 ILOG CPLEX 8 1 creating 73 79 default name 36 displaying 41 entering 36 entering in LP format 35 name 36 representing in model 68 sensitivity analysis 46 138 operator 73 operator 73 optimal solution 94 optimization interrupting 44 optimization model creating 67 defining extr
27. 85 Setting CPLEX cect tee ena 86 Modifying an Optimization 86 Starting from Previous Basis cette tees 87 Complete Program s i desee ean dae vg e e Pa Sabie eua eee aie de eA 87 Concert Technology for Java 89 Compiling CPLEX Applications in Concert Technology 89 In Case Problems 90 The Design of CPLEX in Concert Technology 91 The Anatomy of a Concert Technology 92 Create the ccc cette rh 93 Solve the Model 59222 cob chain Bs ee eU ee 94 Query He Results nrbe red oer TC GT d 95 Building and Solving a Small LP Model 95 Modeling by ROWS pe IERI Rea 97 Modeling by Columns dec Boa eet se kee is E pe aA 97 Modeling 26 wee Ik sede lene ae a eon nd 98 Complete Code of LPex1 java 0 0 cece eee n nn nnn 98 Callable Library 103 The Design of the ILOG CPLEX Callable Library 103 Compiling and Linking Callable Library Applications
28. A as the complicating constraints and the constraints with H as the simple problem The idea is to solve the simple problem first and then add the constraints for the complicating constraints and solve with dual ILOG CPLEX 8 1 GETTING STARTED 87 MODIFYING AN OPTIMIZATION PROBLEM EXAMPLE 11 include lt ilcplex ilocplex h gt ILOSTLBEGIN int main IloEnv env try IloModel model env chvatal IloNumVarArray x env 8 0 50 model add IloMinimize env 9 x 0 x 1 4 x 2 2 x 3 e8 x 4 2 xI5 S xl6 model add x 0 x 2 x 4 model add x 0 x 1 x 3 model add x 1 2 x 5 x 6 model add x 3 x 5 x 7 model add x 4 x 6 7 IloCplex cplex model cplex setParam IloCplex SimDisplay 2 cplex setParam IloCplex RootAlg IloCplex Network cplex solve cplex out After network optimization objective is lt lt cplex getObjValue lt lt endl model add 2 x 0 1 x 1 2 x Z2 1 x 3 2 x 4 1 x 5 2 x 6 3 x 7 4 model add 1 x 0 3 x 1 2 x 2 3 x 3 1 x 4 2 x 5 1 x 6 1 x 7 2 cplex setParam IloCplex RootAlg IloCplex Dual cplex solve IloNumArray vals env cplex getValues vals x cplex out Solution status cplex getStatus endl cplex out lt lt Objective value lt lt cplex getObjValue lt lt endl cple
29. ILOG CPLEX issues a message indicating that the process was stopped and displays progress information If you issue another optimization command in the same session ILOG CPLEX will resume optimization from where it was interrupted Displaying Post Solution Information Once an optimal solution is found ILOG CPLEX can provide many different kinds of information for viewing and analyzing the results This information is accessed via the display command and via some write commands Information about the following is available with the display solution command objective function value solution values slack values reduced costs dual values shadow prices JOZIWNdO 5 99 basic rows and columns For information on the write commands see Writing Problem and Solution Files on page 47 Sensitivity analysis can also be performed in analyzing results as described in Performing Sensitivity Analysis on page 46 For example to view the optimal value of each variable enter the command display solution variables In response the list of variable names with the solution value for each variable is displayed like this Variable Name Solution Value x1 40 000000 x2 17 500000 x3 42 500000 To view the slack values of each constraint enter the command display solution slacks The resulting message indicates that for this problem the slack variables are all zero All s
30. In order to see a list of change options type change ILOG CPLEX 8 1 GETTING STARTED CHANGING A PROBLEM The elements that can be changed are displayed like this Change options bounds change bounds on a variable coefficient change a coefficient delete delete some part of the problem name change a constraint or variable name objective change objective function value problem change problem type qpterm change a quadratic objective term rhs change a right hand side or network supply demand value sense change objective function or a constraint sense type change variable type Change to make Changing Constraint or Variable Names Enter name at the Change to make prompt to change the name of a constraint Change to make name FEAT eg e EST The present name of the constraint is c3 In the example you can change the name to new3 to differentiate it from the other constraints using the following entries Change a constraint or variable name c Present name of constraint c3 New name of constraint new3 The constraint c3 now has name new3 Or The name of the constraint has been changed The problem can be checked with a display command for example display problem constraints new3 to confirm that the change was made This same technique can also be used to change the name of a variable Changing Sense Next change the sense of the new3 constraint fr
31. It does so by first creating the variables with the method cplex numVarArray Then the minimization objective function is created and added to the active model with the method I1oCplex addMinimize The expression that defines the objective function is created by a method IloCplex scalProd that forms a scalar product using an array of objective coefficients times the array of variables Finally each of the two constraints of the model are created and added to the active model with the method 11oCplex addLe For building the constraint expression the methods 11o0Cplex sum and IloCplex prod are used as a contrast to the approach used in constructing the objective function Modeling by Columns While for many examples population by rows may seem most straightforward and natural there are some models where population by columns is a more natural or more efficient approach to implement For example problems with network structure typically lend themselves well to modeling by column Readers familiar with matrix algebra may view the method populateByColumn as the transpose of populateByRow Range objects are created for modeling by column with only their lower and upper bound No expressions are given building them at this point would be impossible since the variables have not been created yet Similarly the objective function is created only with its intended optimization sense and without any expression Next the variable
32. LP MODEL IN JAVA 96 exception triggers the printing of a line stating Concert exception caught where e is the specific exception We first create the model object cplex by executing the statement IloCplex 1 new IloCplex At this point the cplex object represents an empty model that is a model with no variables constraints or other content The model is then populated in one of several ways depending on the command line argument The possible choices are implemented in the methods e populateByRow e populateByColumn e populateByNonzero All these methods pass the same three arguments The first argument is the cplex object to be populated The second and third arguments correspond to the variables var and range constraints rng respectively the methods will write to var 0 and rng 0 an array of all the variables and constraints in the model for later access After the model has been created in the cplex object it is ready to be solved by calling cplex solve The solution log will be output to the screen this is because IloCplex prints all logging information to the OutputStream cplex out which by default is initialized to System out You can change this by calling the method cplex setOut In particular you can turn off logging by setting the output stream to nu11 i e by calling cplex setOut null Similarly 11o0Cplex issues warning messages to cplex warning and cplex setWarning
33. NULL NULL NULL stderr Failed to obtain solution n RMINATE nSolution status d n solstat olution value f n objval olution f f x 0 1 x 2 NULL CPXfreeprob env amp lp atus ntf stderr CPXfreeprob failed error code NULL CPXcloseCPLEX amp env atus errmsg 1024 ntf stderr Could not close CPLEX environment eterrorstring env status errmsg ntf stderr s errmsg atus mot ILOG CPLEX 8 1 GETTING STARTED n status in WHAT YOU NEED KNOW What You Need to Know In order to use ILOG CPLEX effectively you need to be familiar with your operating system whether Unix or Windows This manual assumes you already know how to create and manage files In addition if you are building an application that uses the Component Libraries this manual assumes that you know how to compile link and execute programs written in a high level language The Callable Library is written in the C programming language while Concert Technology is written in C and Java This manual also assumes that you already know how to program in the appropriate language and that you will consult a programming guide when you have questions in that area Manual Organization Chapter 1 Setting Up CPLEX tells how to install CPLEX Chapter 2 Interactive Optimizer Tutorial describes step by step how to use the Interactive Optimize
34. adding rows to a problem 131 entering a problem 34 entering and optimizing a problem 111 ilolpex2 cpp 80 ilolpex3 cpp 85 1 1 111 lpex2 c 122 lpex3 c 131 modifying an optimization problem 85 reading a problem file 122 reading a problem from a file 80 running Callable Library 105 running Component Libraries 28 running Concert Technology 65 running from standard distribution 105 solving a problem 42 exception handling 71 executing operating system commands 60 exportModel member function IloCplex class 79 expression column 73 F False 94 feasible solution 94 file format read options 51 write options 48 file name extension 49 52 79 G getCplexStatus 95 getCplexStatus member function IloCplex class 70 getDuals member function IloCplex class 73 getObjValue member function ILOG CPLEX 8 1 INDEX IloCplex class 70 getReducedCosts member function IloCplex class 73 getSlacks member function IloCplex class 73 getStatus 94 getStatus member function IloCplex class 70 78 getValue member function IloCplex class 70 getValues member function IloCplex class 73 greater than equal to constraints add to a model 94 H handle class definition 67 empty handle 68 handling errors 71 110 exceptions 71 help Interactive Optimizer command 32 syntax 33 IIS file format 48 IloAddNumVar class 73 IloAlgorithm Exception class 71 IloAlgorithm Status enumeration 73 IloColumn and 9
35. controlled within the application Figure 3 1 shows a picture of an application using CPLEX with Concert Technology to solve optimization problems User Written Application lloCplex object Concert Technology modeling objects E CPLEX database Figure 3 1 View of CPLEX with Concert Technology The CPLEX database includes the computing environment its communication channels and your problem objects In this chapter we give a brief tutorial illustrating the modeling and solution classes provided by Concert Technology and CPLEX More extensive coverage of the modeling classes can be found in the chapter about 11oCplex in the ILOG Concert Technology User s Manual and in the Concert Technology Reference Manual More information about the ILOG CPLEX 8 1 GETTING STARTED COMPILING AND LINKING CPLEX IN CONCERT TECHNOLOGY APPLICATIONS algorithm class 1 1 and its nested classes can be found in the ILOG CPLEX User s Manual and ILOG CPLEX Reference Manual Compiling and Linking CPLEX in Concert Technology Applications To exploit a C library like ILOG CPLEX in Concert Technology you need to tell your compiler where to find the ILOG CPLEX and Concert include files that is the header files and you also need to tell the linker where to find the ILOG CPLEX and Concert libraries The sample projects and makefiles illustrate how to carry out these crucial steps for the exampl
36. other CPLEX routines the errors will be seen if the CPX SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen Status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Status CPXsetintparam env CPX PARAM SIMDISPLAY 2 if status fprintf stderr Failed to turn up simplex display level n goto TERMINATE Create the problem lp CPXcreateprob env amp status chvatal if lp NULL fprintf stderr Failed to create subproblem n status 1 goto TERMINATE Copy network part of problem status CPXcopylp env lp COLSORIG ROWSSUB CPX MIN Hcost Hrhs Hsense Hmatbeg Hmatcnt Hmatind Hmatval Hlb Hub NULL if status 4 fprintf stderr CPXcopylp failed n goto TERMINATE Status CPXsetintparam env CPX PARAM LPMETHOD CPX ALG NET ILOG CPLEX 8 1 GETTING STARTED 135 D aqe ADDING ROWS A PROBLEM EXAMPLE 1 136 if status fprintf stderr Failed to set the optimization method error d n status goto TERMINATE status CPXlpopt env lp if status fprintf stder
37. so if you successfully compile link and execute them then you can be sure that your installation is correct ILOG CPLEX 8 1 GETTING STARTED 65 THE ANATOMY CONCERT TECHNOLOGY APPLICATION In Case of Problems If you encounter difficulty when you try this test then there is a problem in your installation and you need to correct it before you begin real work with ILOG CPLEX For example if you get a message from the compiler such as ilolpex3 cpp 1 Can t find include file ilcplex ilocplex h then you need to verify that your compiler knows where you have installed ILOG CPLEX and its include files that is its header files If you get a message from the linker such as ld lcplex No such file or directory then you need to verify that your linker knows where the ILOG CPLEX library is located on your system If you get a message such as ilm CPLEX no license found for this product or ilm CPLEX invalid encrypted key MNJVUXTDJV82 in usr ilog ilm access ilm run ilmcheck then there is a problem with your license to use ILOG CPLEX Review the LOG License Manager User s Guide and Reference to see whether you can correct the problem If not call the technical support hotline and repeat the error message there If you successfully compile link and execute one of the examples in the standard distribution then you can be sure that your installation is correct and you can begin to use ILOG C
38. the options display parts of the problem description while others display parts of the problem solution Options about the problem solution are not available until after the problem has been solved The list looks like this Display Options iis display infeasibility diagnostics IIS constraints problem display problem characteristics sensitivity display sensitivity analysis settings display parameter settings solution display existing solution Display what If you type problem in reply to that prompt that option will list a set of problem characteristics like this Display Problem Options all display entire problem binaries display binary variables bounds display a set of bounds constraints display a set of constraints or node supply demand values generals display general integer variables histogram display a histogram of row or column counts integers display integer variables names display names of variables or constraints qpvariables display quadratic variables semi continuous display semi continuous and semi integer variables sos display special ordered sets stats display problem statistics variable display a column of the constraint matrix Display which problem characteristic Enter the option 11 to display the entire problem Maximize objr xL X x2 3 x3 Subject To x1 a x2 x3 lt 20 a2 x3 lt 30 Bounds lt 1 lt 40 All other variables are gt 0 ILOG CPLEX 8 1
39. to use change coefficient You must now specify both the constraint row and the variable column identifying the coefficient you wish to change Enter both the constraint name or number and variable name or number on the same line separated by at least one space The constraint name is new3 and the variable is number 3 so in response to the following prompt type new3 and 3 like this to identify the one to change Change which coefficient constraint variable new3 3 Present coefficient of constraint new3 variable 3 is 3 000000 The final step is to enter the new value for the coefficient of x3 Change coefficient of constraint new3 variable 3 to what 30 Coefficient of constraint new3 variable 3 changed to 30 000000 Objective amp RHS Coefficients To change a coefficient in the objective function or in the right hand side use the corresponding change command option objective or rhs For example to specify the right hand side of constraint 1 to be 25 0 we could enter the following but for this tutorial do not enter this now FEAT ez e AEST change rhs 1 25 0 Deleting Another option to the change command is delete This option is used to remove an entire constraint or a variable from a problem Return the problem to its original form by removing the constraint you added earlier Type change delete ILOG CPLEX displays a list of delete options Delete Options
40. which in turn are used to define objects of class IloObjective and IloRange For example IloObjective obj IloMinimize env 1 2 x2 3 x3 ILOG CPLEX 8 1 GETTING STARTED THE ANATOMY A CONCERT TECHNOLOGY APPLICATION This creates the extractable obj of type 1100bjective which represents the objective function of the example presented in Introducing ILOG CPLEX Let us look in more detail what this line does The function IloMinimize takes the environment and an expression as arguments and constructs new IloOb jective object from it that describes the objective function to minimize the expression This new object is returned and assigned to the new handle obj After an objective extractable is created it must be added to the model As noted above this is done with the add method of 11oMode1 If this is all we need variable obj for we can instead write more compactly model add IloMinimize env 1 2 x2 3 x3 This way there is no need for the program variable obj and the program is shorter If in contrast the objective function is needed later for example to change it and reoptimize the model when doing scenario analysis the variable ob j must be created in order to refer to the objective function From the standpoint of algorithmic efficiency the two approaches are comparable Creating constraints and adding them to the model can be done just as easily with the following statement 1
41. with their lower and upper bound only No expression is given which is impossible since the variables are not yet created Similarly the objective function is created with only its intended optimization sense and without any expression Next the variables are created and installed in the already existing ranges and objective The description of how the newly created variables are to be installed in the ranges and objective is by means of column expressions which are represented by the class IloNumColumn Column expressions consist of objects of class IloAddNumVar linked together with operator These IloAddNumVar objects are created using operator of the classes I1o00bjective and IloRange They describe how to install a new variable to the invoking objective or range objects For example obj 1 0 creates IloAddNumVar ILOG CPLEX 8 1 GETTING STARTED 73 BUILDING AND SOLVING A SMALL LP MODEL IN 74 capable of adding a new modeling variable with a linear coefficient of 1 0 to the expression in obj Column expressions can be built in loops using operator Column expressions objects of class IloNumColumn are handle objects like most other Concert Technology objects The method end must therefore be called to delete the associated implementation object when it is no longer needed However for implicit column expressions where 11oNumColumn object is explicitly created such as the ones used in this example method
42. 1 2 uses command line arguments to determine the name of the input file and the optimizer to call Usage lpex2 filename optimizer Where filename is a file with extension MPS SAV or LP lower case is allowed and optimizer is one of the following letters default p primal simplex d dual simplex n network with dual simplex cleanup h barrier with crossover barrier without crossover 122 ILOG CPLEX 8 1 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C S sifting o concurrent For example this command lpex2 example mps d reads the file example mps and solves the problem with the dual simplex optimizer To illustrate the ease of reading a problem the example uses the routine CPXreadcopyprob This routine detects the type of the file reads the file and copies the data into the ILOG CPLEX problem object that is created with call to CPXcreateprob The user need not be concerned with the memory management of the data Memory management is handled transparently by CPXreadcopyprob After calling CPXopenCPLEX and turning on the screen indicator by setting the CPX PARAM SCRIND parameter to CPX ON the example creates an empty problem object with a call to CPXcreateprob This call returns a pointer 1p to the new problem object Then the data is read in by the routine CPXreadcopyprob After the data is copied the appropriate optimization routine is called based on the comman
43. 1oCplex not only implements these interfaces but also provides additional methods for solving a model and querying its results After a model has been created as described in the previous section the IloCplex object cplex is ready to solve the model which consists of all the modeling objects that have been added to it Invoking the optimizer is as simple as calling method solve Method solve returns a Boolean indicating whether the optimization succeeded in finding a solution If no solution was found false is returned If t rue is returned then CPLEX found a feasible solution though it is not necessarily an optimal solution More precise information about the outcome of the last call to method solve can be obtained by calling IloCplex getStatus The returned value tells you what CPLEX found out about the model whether it found the optimal solution or only a feasible solution whether it proved the model to be unbounded or ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING SMALL LP MODEL IN JAVA infeasible or whether nothing at all has been determined at this point Even more detailed information about the termination of the solver call is available through the method IloCplex getCplexStatus Query the Results If the solve method succeeded in finding a solution you will then want to access that solution The objective value of that solution can be queried using method double objval cplex getObjValue S
44. 2 3 0 0 0 matbeg 1 2 matbeg 2 4 0 0 matind 2 0 matind 4 0 0 1 0 matval 2 1 0 matval 4 1 0 1 1 matind 3 1 matind 5 1 1 1 0 matval 3 3 0 matval 5 1 0 0 0 0 lb 1 0 0 lb 2 0 0 0 40 0 ub 1 CPX INFBOUND ub 2 CPX INFBOUND 0 1 colname 1 x2 colname 2 x3 CPXaddcols env lp NUMCOLS NUMNZ obj matbeg matind matval lb ub colname GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN if status goto TERMINATE TERMINATE return status END populatebycolumn To populate by nonzero we first create the rows then create the columns and then change the nonzeros of the matrix 1 at a time static int populatebynonzero CPXENVptr env CPXLPptr lp int status 0 double ob j NUMCOLS double lb NUMCOLS double ub NUMCOLS char colname NUMCOLS double rhs NUMROWS char sense NUMROWS char rowname NUMROWS int rowlist NUMNZ int collist NUMNZ double vallist NUMNZ CPXchgobjsen env lp CPX MAX Problem is maximization Now create the new rows First populate the arrays rowname 0 cl sense 0 71 rhs 0 20 0 rowname 1 c2 sense 1 71 rhs 1 30 0 status CPXnewrows env lp NUMROWS rhs sense NULL rowname if status goto TERMINATE Now add the new columns First populate the arrays obj 0
45. 53 The BIN and TXT options create solution files The BIN option writes a binary format solution file while the TXT option writes an ASCII text file The DPE and PPE options are used for saving perturbed problems in SAV format DUA writes out the dual formulation of a problem in MPS format EMB writes a file for an embedded network in MPS format The IIS format is used for infeasibility diagnostics The LP format was discussed in Using the LP Format on page 35 Using this format is described in Writing LP Files on page 49 and Reading LP Files on page 51 The MIN format was developed by DIMACS to represent minimum cost network flow problems The MPS format is described in Reading MPS Files on page 52 The MST format allows an integer feasible solution to be saved ILOG CPLEX 8 1 GETTING STARTED WRITING PROBLEM AND SOLUTION FILES NET writes a file for an embedded network in ILOG CPLEX format The ORD format allows an integer priority order file to be written PRE writes out a presolved version of the problem in SAV format The QP format specifies the quadratic coefficient matrix elements The REW option creates an MPS format problem file with generic names 9 5 9 9 The SAV format is a special binary format which facilitates very fast problem reading and writing Because SAV format is binary rather than ASCII text it is not possible for you to view and edit SAV files using standard editors
46. 8 IloCplex add modeling object 94 class 89 IloCplex class 64 69 exportModel member function 79 getCplexStatus member function 70 GETTING STARTED 145 IN DEX getDuals member function 73 getObjValue member function 70 getReducedCosts member function 73 getSlacks member function 73 getStatus member function 70 73 getValue member function 70 getValues member function 73 importModel member function 79 81 setParam member 80 setRootAlgorithm member function 81 solve member function 70 73 81 85 IloCplex addLe 97 IloCplex addMinimize 97 IloCplex prod 97 IloCplex scalProd 97 IloCplex sum 97 IloCplex Algorithm enumeration 80 IloCplex BoolParam enumeration 86 IloCplex Exception class 71 IloCplex IntParam enumeration 86 IloCplex NumParam enumeration 86 IloCplex StringParam enumeration 86 IloEnv class 66 end member function 67 IloException class 71 IloExpr class 69 IloExtractable class 67 lloG ILOG technical support 23 Web sites 23 ILOG License Manager ILM PLEX and 28 ILOG LICENSE FILE environment variable 28 TloLinearNumExpr 93 146 ILOG CPLEX 8 1 IloMinimize function 69 IloModel class 64 68 add member function 68 69 IloNumArray class 73 IloNumColumn class 73 IloNumExpr 93 IloNumVar 93 IloNumVar class 68 74 79 lloO IloObjective 93 IloObjective class 68 73 79 setCoef member function 74
47. A returned pointer of NULL may mean that not enough memory was available or there was some other problem In the case of failure an error message will have been written to the error channel from inside CPLEX In this example the setting of the parameter CPX_PARAM_SCRIND causes the error message to appear on stdout if lp NULL fprintf stderr Failed to create LP n goto TERMINATE Now populate the problem with the data For building large problems consider setting the row column and nonzero growth le parameters before performing this task gt Q switch argv 1 1 oo case r status populatebyrow env 1 gt break D lt ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING SMALL LP MODEL IN case c status populatebycolumn env 1 break case n status populatebynonzero env 1 break if status fprintf stderr Failed to populate problem n goto TERMINATE Optimize the problem and obtain solution status CPXlpopt env lp if status 1 fprintf stderr Failed to optimize LP n goto TERMINATE The size of the problem should be obtained by asking CPLEX what the actual size is rather than using sizes from when the problem was built cur_numrows and cur_numcols store the current number of rows and columns respectively cur numrows CPXgetnumrows env 1p cur numcols CPXgetnumcols
48. ARTED INDEX 151 INDEX 152 ILOG CPLEX 8 1 GETTING STARTED
49. All these file formats are described in more detail in the ILOG CPLEX Reference Manual Reading LP Files At the CPLEX gt prompt type read The following message appears requesting a file name ILOG CPLEX 8 1 GETTING STARTED 51 READING PROBLEM FILES 52 Name of file to read Four files have been saved at this point in our tutorial example example2 example lp example bas Specify the file named example that you saved while practicing the write command You recall that the example problem was saved in LP format so in response to the file type prompt enter 1 ILOG CPLEX displays confirmation message like this Problem example read Read Time 0 03 sec The example problem is now in memory and you can manipulate it with ILOG CPLEX commands Tip The intermediate prompts for the read command can be avoided by entering the entire command on one line like this read example lp Using File Extensions If the file name has an extension that corresponds to one of the supported file formats ILOG CPLEX automatically reads it without your having to specify the format Thus the following command automatically reads the problem file example 1p in LP format read example lp Reading MPS Files ILOG CPLEX can also read industry standard MPS formatted files We use a problem called a iro mps provided in the ILOG CPLEX distribution as an example If you include the mps extension in the f
50. CPLEX It contains instructions for installing ILOG CPLEX Optimizer Options This manual explains how to use all the LP QP and MIP algorithms that are part of ILOG CPLEX Some users may not have access to all algorithms Such users should consult their ILOG account manager or the ILOG support web site to determine to which algorithms they have access ILOG CPLEX 8 1 GETTING STARTED 13 WHAT 14 Is ILOG CPLEX Default settings will result in a call to an optimizer that is appropriate to the class of problem you are solving However you may wish to choose a different optimizer for special purposes An LP or QP problem can be solved using any of the following CPLEX optimizers Dual Simplex Primal Simplex Barrier and perhaps also the Network Optimizer if the problem contains an extractable network substructure Pure network models are all solved by the Network Optimizer MIP models are all solved by the Mixed Integer Optimizer which in turn may invoke any of the LP or QP optimizers in the course of its computation Table 2 summarizes these possible choices Table 2 Optimizers LP Network QP MIP Dual Optimizer Primal Optimizer Barrier Optimizer Mixed Integer Optimizer Network Optimizer Note 1 Note 1 Note 1 The problem must contain an extractable network substructure The choice of optimizer or other parameter settings may have a very large effec
51. Constraints and Bounds Changing a Problem Executing Operating System Commands Quitting ILOG CPLEX 9999 99999 5 5 0 ILOG CPLEX 8 1 GETTING STARTED 31 STARTING ILOG CPLEX Starting ILOG CPLEX To start the ILOG CPLEX Interactive Optimizer at your operating system prompt type the command cplex A message similar to the following one appears on the screen Welcome to CPLEX Interactive Optimizer 8 1 0 with Simplex Mixed Integer amp Barrier Optimizers Copyright c ILOG 1997 2002 CPLEX is a registered trademark of ILOG Type help for a list of available commands Type help followed by a command name for more information on commands CPLEX gt The last line CPLEX gt is the prompt indicating that the product is running and is ready to accept one of the available ILOG CPLEX commands Use the help command to see a list of these commands Using Help 32 ILOG CPLEX accepts commands in several different formats You can type either the full command name or any shortened version that uniquely identifies that name For example enter help after the CPLEX gt prompt as shown CPLEX help You will see a list of the ILOG CPLEX commands on the screen Since all commands start with a unique letter you could also enter just the single letter h CPLEX gt ILOG CPLEX does not distinguish between upper and lower case letters so you could enter h H help or HELP All of these variations invoke
52. EX still interprets the multiple lines as a single constraint When you split a constraint in this way do not press return in the middle of a variable name or coefficient The following is acceptable time 1 x2 return x3 lt 20 return labor 1 3x2 x3 lt 30 return The entry below however is incorrect since the return key splits a variable name time 1 x2 x return 3 2 20 return labor xl 3x2 x3 lt 30 return If you type a line that ILOG CPLEX cannot interpret a message describing the problem will appear and the entire line will be ignored You must then re enter the line The final thing to remember when you are entering a problem is that once you have pressed return you can no longer directly edit the characters that precede the return As long as you have not pressed the return key you can use the backspace key to go back and change what you typed on that line Once return has been pressed the change command must be used to modify the problem The change command is described in Changing a Problem on page 56 ILOG CPLEX 8 1 GETTING STARTED 37 DISPLAYING A PROBLEM Displaying a Problem 38 Now that you have entered a problem using ILOG CPLEX you must verify that the problem was entered correctly To do so use the display command At the CPLEX gt prompt type display A list of the items that can be displayed then appears Some of
53. Exception Thus IloException should be caught in the catch statement In summary here is the structure of a Java application that calls CPLEX import ilog concert import ilog cplex static public class Application static public main String args try IloCplex cplex new IloCplex create model and solve it catch IloException e System err println Concert exception caught e 92 ILOG CPLEX 8 1 GETTING STARTED THE ANATOMY CONCERT TECHNOLOGY APPLICATION Create the Model The 11oCplex object provides the functionality to create an optimization model that can be solved with 11oCplex The interface functions for doing so are defined by the Concert Technology interface 11o0Modeler and its extension 110MPModeler These interfaces define the constructor functions for modeling objects of the following types which can be used with TloCplex IloNumVar modeling variables IloRange ranged constraints of the type lb lt expr lt ub IloObjective optimization objective IloNumExpr expression using variables Modeling variables are represented by objects implementing the 11oNumvVar interface defined by Concert Technology Here is how to create three continuous variables all with bounds 0 and 100 IloNumVar x cplex numVarArray 3 0 0 100 0 There is a wealth of other functions for creating arrays or individual modeling variables The documentation for 11oModeler and 11oMPModeler
54. G CPLEX 8 1 GETTING STARTED 89 COMPILING CPLEX APPLICATIONS IN CONCERT TECHNOLOGY 90 Concert Technology class library To do this you add the cplex jar file to your classpath This is most easily done by passing the command line option classpath path to cplex jar to the Java compiler javac If you need to include other Java class libraries you should add the corresponding jar files to the classpath as well Ordinarily you should also include the current directory to be part of the Java classpath At execution time the same classpath setting is needed Additionally since CPLEX is implemented via JNI you need to instruct the Java Virtual Machine JVM where to find the shared library or dynamic link library containing the native code to be called from Java This may be done with the command line option Djava library path path to shared library to the java command Note that unlike the cplex jar file the shared library is system dependent thus the exact pathname of the location for the library to be used differs depending on the platform you are using Pre configured compilation and runtime commands are provided in the standard distribution through the Unix makefiles and Windows javamake file for Nmake However these scripts presume a certain relative location for the files mentioned above and for application development most users will have their source files in some other location Below are suggest
55. IFYING AN OPTIMIZATION PROBLEM EXAMPLE 11 Starting from a Previous Basis Before solving the modified problem example ilolpex3 cpp sets the optimizer option to IloCplex Dual as this is the algorithm that can generally take best advantage of the optimal basis from the previous solve after the addition of constraints Complete Program The complete program follows You can also view it online in the file ilolpex3 cpp ff Se SSS ete pese Se SSS ee See ee eee SS uten ae eRe Ke pedo File examples src ilolpex3 cpp Version 8 1 Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products aS SSIS Se Se eee ees sae Se Lf ilolpex3 cpp example of adding constraints to solve a problem Modified example from Chvatal Linear Programming Chapter 26 minimize c x 8 subject to Hx 5 Ax b E 1 lt x lt u 35 o where S i 5 3 H 1 0101000 d 3 25 1 1 0 1 0 0 0 1 v0 4 Qs 9E i3 3 0 0 0 0 1 0 1 1 oy A 2 1 2 1 2 1 2 3 b X 3 2 ah 27 7 o 1 4 2 8 2 3812 l1 0 0 0 0 0 0 0 0 50 50 50 50 50 50 50 50 Z4 Treat the constraints with
56. LP MODEL IN As a debugging aid the application writes the problem to a ILOG CPLEX LP file named 1 1 1 by calling the routine CPXwriteprob This file can be examined to determine whether any errors occurred in the setproblemdata or CPXcopylp routines CPXwriteprob can be called at any time after CPXcreateprob has created the 1p pointer The label TERMINATE is used as a place for the program to exit if any type of failure occurs or if everything succeeds In either case the problem object represented by 1p is released by the call to CPX reeprob and any memory allocated for solution arrays is freed The application then calls CPXcloseCPLEX it tells ILOG CPLEX that all calls to the Callable Library are complete If an error occurs when this routine is called then a call to CPXgeterrorstring is needed to determine the error message since CPXcloseCPLEX causes no screen output Complete Program The complete program follows You can also view it online in the file 1pex1 c p re File examples src lpexl c Version 8 1 M REN Copyright 1997 2002 by 1106 All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ee EUR DIE lp
57. Licensing instructions are provided in the ZLOG License Manager User s Guide amp Reference which is included with the standard CPLEX product distribution The basic steps are 1 Install ILM Normally you obtain ILM distribution media from the same place that you obtain CPLEX 2 Run the ihostid program which is found in the directory where you install ILM 3 Communicate the output of step 2 to your local ILOG sales administration department They will send you a license key in return 4 Create a file on your system to hold this license key and set the environment variable ILOG LICENSE FILE so that CPLEX will know where to find the license key The environment variable need not be used if you install the license key in a platform dependent default file location Using the Component Libraries 28 After you have completed the installation and licensing steps you can verify that everything is working by running one or more of the examples that are provided with the standard distribution Verifying Installation on UNIX On a UNIX system go to the subdirectory examples machine libformat that matches your particular platform and in it you will find a file named makefile Execute one of the examples for instance 1pex1 c by doing make 1 1 1 1 r 5 example takes one argument either r c or n If your interest is in running one of the examples try make ilolpexl ilolpex1 r this is
58. ND populatebycolumn To populate by nonzero we first create the rows then create the columns and then change the nonzeros of the matrix 1 at a time static void populatebynonzero IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv IloObjective obj IloMaximize env c add IloRange env IloInfinity 20 0 c add IloRange env IloInfinity 30 0 x add IloNumVar env 0 0 40 0 x add IloNumVar env x add IloNumVar env obj setCoef 0 1 0 obj setCoef 1 2 0 obj setCoef 2 3 0 c 0 setCoef x 0 1 0 c 0 setCoef x 1 1 0 c 0 setCoef x 2 1 0 ILOG CPLEX 8 1 GETTING STARTED 77 penon i D 4 o Q 2 5 lt BUILDING AND SOLVING A SMALL LP MODEL IN c 1 setCoef x 0 1 0 c 1 setCoef x 1 3 0 c 1 setCoef x 2 1 0 model add obj model add c END populatebynonzero 78 ILOG CPLEX 8 1 GETTING STARTED WRITING AND READING MODELS AND FILES Writing and Reading Models and Files In example ilolpex1 cpp we left one line unexplained cplex exportModel 1 1 1 This statement causes cplex to write the model it has currently extracted to the file called lpex1 1p In this case the file will be written in LP format whose usage is described in detail in the CPLEX Reference Manual Other formats supported for writing problems to a file are M
59. NULL int status 0 int ds 35 int cur numrows cur numcols Check the command line arguments if argc 2 argv 1 0 E strchr rcn argv 1 1 NULL yd usage argv 0 goto TERMINATE Initialize the CPLEX environment env CPXopenCPLEX amp status reason for If an error occurs the status value indicates the failure call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will 114 ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN be seen if the CPX SCRIND indicator is set to CPX ON if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg goto TERMINATE Turn on output to the screen status CPXsetintparam env CPX PARAM SCRIND CPX ON if status fprintf stderr Failure to turn on screen indicator error d n status goto TERMINATE Turn on data checking Status CPXsetintparam env CPX PARAM DATACHECK CPX ON if status 1 fprintf stderr Failure to turn on data checking error d n status goto TERMINATE Create the problem lp CPXcreateprob env amp status lpex1
60. PLEX in Concert Technology seriously The Anatomy of a Concert Technology Application 66 Concert Technology is a C class library and therefore Concert Technology applications consist of interacting objects This section gives a short introduction to the most important classes that are usually found in a complete Concert Technology CPLEX application Constructing the Environment An IloEnv is typically the first object created in any Concert Technology application ILOG CPLEX 8 1 GETTING STARTED THE ANATOMY A CONCERT TECHNOLOGY APPLICATION You construct an 11oEnv object by declaring a variable of type 11oEnv For example to create an environment named env you do this IloEnv env Note The environment object created in a Concert Technology application is different from the environment created in the CPLEX C library by calling the routine CPXopenCPLEX The environment object is of central importance and needs to be available to the constructor of all other Concert Technology classes because among other things it provides optimized memory management for objects of Concert Technology classes This provides a boost in performance compared to using the system memory management system As is the case for most Concert Technology classes IloEnv is a handle class This means that the variable env is a pointer to an implementation object which is created at the same time as env in th
61. PS and SAV also described in the ILOG CPLEX Reference Manual 11oCplex decides which file format to write based on the extension of the file name IloCplex also supports reading of files through one of its importModel methods A call to cplex importModel model file lp causes CPLEX to read a problem from the file ile 1p and add all the data in it to model as new objects Again MPS and SAV format files are also supported In particular CPLEX creates an instance of signatures are provided IloObjective for the objective function found in 1 1 IloNumVar for each variable found in file 1p except IloSemiContVar foreach semi continuous or semi integer variable found in file 1p 9 IloRange for each row found in 11 1 5 1105051 for each SOS of type 1 found in file 1p and 8 s 1105052 for each SOS of type 2 found in 1 1 If you also need access to the modeling objects created by importModel two additional 3 S void IloCplex importModel IloModel amp m const char filename IloObjective amp obj IloNumVarArray vars IloRangeArray rngs const and void IloCplex importModel IloModel amp m const char filename IloObjective amp obj IloNumVarArray vars IloRangeArray rngs IloSOSlArray 5051 IloSOS2Array sos2 const They provide additional parameters so that the newly created modeling objects will be returned to the caller Example program ilolpex2 cpp gives an example of how to
62. SORIG 20 50 50 50 50 50 50 501 double Hcost COLSORIG 2 95 Ly 93 2 8 12 Hsense ROWSTOT int Hmatbeg COLSORIG 0 724705 67 85 TOS int Hmatcnt COLSORIG 2 2 int Hmat ind NZTOT 610 De OF Ber 0 4 2 3 2 4 3 4 double Hmatval NZTOT S107 2 0 1207 X20 1 0 1 0y 150 91 0544L 05 41 207 3570 35 Data for CPXaddrows call double Arhs ROWSCOMP a2 char Asense ROWSCOMP E Note use a trick for rmatbeg by putting the total nonzero count in the last element This is not required by the CPXaddrows call int Armatbeg ROWSCOMP 1 0 8 16 int Armat ind NZCOMP Lp La 2 3 4 5545 6 7 Oy X525 354 5500 T d double Armatval NZCOMP 2 0 PaO lt 20 20 Slay ES SS Sid DU Sl AO pm 2 007 double x COLSORIG CPXENVptr env NULL CPXLPptr lp NULL int d int status lpstat double objval 134 Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for ILOG CPLEX 8 1 GETTING STARTED ADDING ROWS TO A PROBLEM EXAMPLE LPEX8 C failure A call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For
63. The output operator lt lt is defined for type IloAlgorithm Status as returned by the call to cplex getStatus Itis also defined for 11oNumArray the Concert Technology class for an array of numerical values as returned by the calls to cplex getValues cplex getDuals cplex getSlacks cplex getReducedCosts In general the output operator is defined for any Concert Technology array of elements if the output operator is defined for the elements The functions named populateby are purely about modeling and are completely decoupled from the algorithm IloCplex In fact they don t use the cplex object which is created only after executing one of these functions Modeling by Rows The function populatebyrow creates the variables and adds them to the array x Then the objective function and the constraints are created using expressions on the variables stored in x The range constraints are also added to the array of constraints c The objective object and the constraints are added to the model Modeling by Columns penon Aq Function populatebycolumn can be viewed as the transpose of populatebyrow While for simple examples like this one population by rows may seem the most straightforward and natural approach there are some models where modeling by column is a more natural or more efficient approach 5 D 4 Q 5 o lt When modeling by columns range objects are created
64. Therefore you have the option of leaving out either the upper or lower name or index number on either side of the hyphen To see every possible item you would simply enter Displaying Variable or Constraint Names You can display a variable name by using the display command with the options problem names variables If you do not enter the word variables ILOG CPLEX prompts you to specify whether you wish to see a constraint or variable name Type display problem names variables In response ILOG CPLEX prompts you to specify a set of variable names to be displayed like this Display which variable name s Specify these variables by entering the names of the variables or the numbers corresponding to the columns of those variables A single number can be used or a range such as 1 2 All of the names can be displayed at once if you type a hyphen the character Try this by entering a hyphen at the prompt and pressing the lt return gt key Display which variable name s In the example there are three variables with default names CPLEX displays these three names xl x2 x3 If you want to see only the second and third names you could either enter the range as 2 3 or specify everything following the second variable with 2 Try this technique display problem names variables Display which variable name s 2 ILOG CPLEX 8 1 GETTING STARTED DISPLAYING A PROBLEM 2 3 If you enter number wi
65. UMROWS define NUMCOLS define NUMNZ 9 Usage s progname sets ptr to NULL where X is one of the following options Mn f generate problem by row n generate problem by column n i n generate problem by nonzero n all populate the problem with data RZ 037 KS for the following To populate by row we first create the columns and then add the rows ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN static int populatebyrow CPXENVptr env CPXLPptr 1 int status 0 double obj NUMCOLS double lb NUMCOLS double ub NUMCOLS char colname NUMCOLS int rmatbeg NUMROWS int rmatind NUMNZ double rmatval NUMNZ double rhs NUMROWS char sense NUMROWS char rowname NUMROWS CPXchgobjsen env lp CPX MAX Problem is maximization Now create the new columns First populate the arrays obj 0 1 0 obj 1 2 0 obj 2 3 0 lb 0 0 0 lb 1 0 0 lb 2 0 0 ub 0 40 0 ub 1 CPX INFBOUND ub 2 CPX INFBOUND colname 0 x1 colname 1 x2 colname 2 x3 status CPXnewcols env lp NUMCOLS obj lb ub NULL colname if status goto TERMINATE Now add the constraints rmatbeg 0 0 rowname 0 c1 rmatind 0 0 rmatind 1 1 rmatind 2 2 sense 0 L rmatval 0 1 0 rmatval 1 1 0 rmatval 2 1 0 rhs 0 20 0 rm
66. Var representing modeling variables IloRange describing constraints of the form lt expr lt where expr is some sort of linear expression and IloObjective representing an objective function You create objects of these classes for each variable constraint and objective function of your optimization problem Then you add the objects to the model by calling model add obj for each extractable ob j There is no need to explicitly add the variable objects to a model as they are implicitly considered when they are used in the range constraints instances of IloRange or the objective At most one objective can be used in a model with 11oCplex Modeling variables are constructed as objects of class 11o0NumVar by defining variables of type IloNumVar Concert Technology provides several constructors for doing this the most flexible version for example is IloNumVar xl env 0 0 40 0 ILOFLOAT This definition creates the modeling variable x1 with lower bound 0 0 upper bound 40 0 and type ILOFLOAT which indicates the variable is continuous Other possible variable types include ILOINT for integer variables and 110BOOL for boolean variables For each variable in the optimization model a corresponding object of class 11o0NumVar must be created Concert Technology provides a wealth of ways to help you construct all the IloNumVar objects Once all the modeling variables have been constructed they can be used to build expressions
67. a Version 8 1 Copyright C 2001 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products LPexl java Entering and optimizing an LP problem Demonstrates different methods for creating a problem The user has to choose the method on the command line java LPexl r generates the problem by adding constraints java LPexl c generates the problem by adding variables java LPexl n generates the problem by adding expressions import ilog concert ILOG CPLEX 8 1 GETTING STARTED COMPLETE CODE LPEX1 JAVA import ilog cplex public class LPexl static void usage System out println usage 1 lt option gt System out println options r build model row by row System out println options c build model column by column System out println options n build model nonzero by nonzero public static void main String args if args length 1 args O charAt 0 usage return try Create the modeler solver object IloCplex cplex new IloCplex IloNumVar var new IloNumVar 1 IloRange rng new IloRange 1 0 Evaluate command line option and call appropriate populate method The created ranges and variables are returned as element 0 of arrays var and rng switch args 0 charAt 1 case r populat
68. actable objects 68 extracting 67 optimization problem reading from file 80 representing 72 solving with IloCplex 69 optimize Interactive Optimizer command 42 re solving 44 syntax 43 optimizer choosing 44 80 81 110 options 13 parallel 14 106 ORD file format 49 ordering variables 41 OutputStream 96 parallel optimizers 14 106 parameter boolean 86 changing 54 86 displaying settings 55 integer 86 list of settable 54 numeric 86 resetting to defaults 54 GETTING STARTED string 86 parameter specification file 55 path names using 50 populateByColumn 96 populateByNonzero 96 populateByNonzero 98 populateByRow 96 PPE file format 48 PRE file format 49 primal simplex optimizer availability 44 selecting 80 primopt Interactive Optimizer command 44 problem change options 57 changing 56 creating binary representation 111 data entry options 14 display options 38 displaying 38 displaying a part 39 displaying statistics 39 entering from the keyboard 34 entering in LP format 35 naming 34 reading files 122 solving 42 112 verifying entry 38 57 problem file reading 51 writing 47 problem formulation 1 1 112 problem object creating 107 modifying 107 problem type solved by CPLEX 12 prod 97 Q description 12 ILOG CPLEX 8 1 INDEX solving pure 80 QP file format 49 QP model applicable solution algorithms 80 quit Interactive Optimizer command 61 quitting ILOG CPLEX 61 Inter
69. active Optimizer 61 R range constraint 73 ranged constraints add to a model 94 read Interactive Optimizer command 51 52 53 file type options 51 syntax 53 reading file format for 51 LP files 51 model from file 79 81 MPS files 52 problem files 51 122 reduced cost 95 reduced costs accessing 45 removing bounds 58 representing optimization problem 72 re solving 44 REW file format 49 right hand side RHS changing coefficient 59 sensitivity analysis 46 138 root LP solving 80 5 SAV file format 49 132 saving problem files 47 solution files 47 scalProd 97 sense GETTING STARTED 149 INDEX changing 57 sensitivity analysis performing 46 138 set Interactive Optimizer command 54 advance 44 available parameters 54 defaults 54 logfile 44 simplex 43 basisinterval 50 syntax 55 setExpr 98 setRootAlgorithm member function IloCplex class 81 setting parameters 54 86 parameters to default 54 sifting select algorithm 80 slack accessing values 45 slacks 95 solution accessing basic rows and columns 45 accessing values 45 displaying 45 displaying basic rows and columns 45 outputting 73 process 43 querying results 70 reporting optimal 43 restarting 44 sensitivity analysis 46 138 solution file writing 47 solve 94 solve member function IloCplex class 70 73 81 85 solving model 69 81 node LP 80 problem 42 112 root LP 80 with network optimizer 86 SOS 150 ILOG CPLEX 8 1 creating 79
70. ailed to optimize LP endl throw 1 IloNumArray vals env env out lt lt Solution status lt lt cplex getStatus lt lt endl env out lt lt Solution value lt lt cplex getObjValue lt lt endl cplex getValues vals x ILOG CPLEX 8 1 GETTING STARTED SOLVING AN LP WITH CPLEX TECHNOLOGY env out lt lt Values lt lt vals lt lt endl catch IloException amp cerr lt lt Concert exception caught lt lt lt lt endl catch cerr lt lt Unknown exception caught lt lt endl env end return 0 END main ILOG CPLEX 8 1 GETTING STARTED 17 SOLVING AN LP WITH CPLEX TECHNOLOGY Concert Technology for Java Users Here is a Java program using ILOG Concert Technology to solve the example model An expanded version of this example is discussed in detail in Chapter 4 Concert Technology for Java Users import ilog concert import ilog cplex public class Example public static void main String args try IloCplex cplex new IloCplex double lb 0 0 0 0 0 0 double ub 40 0 Double MAX VALUE Double MAX VALUE IloNumVar x cplex numVarArray 3 lb ub double objvals 1 0 2 0 3 0 cplex addMaximize cplex scalProd x objvals cplex addLe cplex sum cplex prod 1 0 x 0 cplex prod 1 0 x 1 cplex prod Og BEEZ II 22050 cplex addLe cplex sum cplex prod 1 0 x 0 cplex
71. ailing list Access to these pages is restricted to owners of an ongoing maintenance contract The maintenance contract number and the name of the person this contract is sent to in your company will be needed for access as explained on the login page All three of the following sites contain the same information but access is localized so we recommend that you connect to the site corresponding to your location and select the support page from the home page The Americas http www ilog com Asia amp Pacific nations http www ilog com sg Europe Africa and Middle East http www ilog fr On those Web pages you will find additional information about ILOG CPLEX in technical papers that have also appeared at industrial and academic conferences ILOG CPLEX 8 1 GETTING STARTED Setting Up CPLEX You install ILOG CPLEX in two steps first transfer the files from the distribution medium a CD or an FTP site into a directory on your local file system then activate your license At that point all of the features of CPLEX become functional and are available to you The chapters that follow this one provide tutorials in the use of each of the Technologies that CPLEX provides the Concert Technology Tutorials for C and Java users and the Callable Library Tutorial for C and other languages This chapter provides guidelines for Installing CPLEX Setting Up Licensing Using the Component Libraries Import
72. also contains a table of parameters that can be modified by parameter routines a list of error messages and details about file formats The ILOG CPLEX Java Reference Manual supplies detailed definitions of the Concert Technology interfaces and CPLEX Java classes It is available only in online form as HTML and Microsoft compiled HTML help CHM form The ILOG Concert Technology Documentation Kit includes the Concert Technology Reference Manual which documents the classes methods and functions of the Concert Technology library the ILOG Concert Technology User s Manual which provides examples that show how to use Concert Technology to model problems the ILOG Hybrid Cooperating Optimizers User s Guide amp Reference which documents the class IloLinConstraint and shows how to use ILOG s main algorithm classes IloSolver and IloCplex in cooperation and ILOG Concert Technology Migration Guide which shows how to translate applications created in previous versions of ILOG products to Concert Technology ILOG CPLEX 8 1 GETTING STARTED FOR MORE INFORMATION As you work with ILOG CPLEX on a long term basis you should read the complete User s Manual to learn how to design models and implement solutions to your own problems Consult ILOG CPLEX Reference Manual for authoritative documentation of the Component Libraries and Interactive Optimizer For More Information ILOG offers technical support and comprehensive Web
73. ameters it creates empty arrays for storing the variables and range constraints of the optimization model Then depending on the command line parameter the example calls one of the functions populatebyrow populatebycolumn or populatebynonzero to fill the model object with a representation of the optimization problem These functions return the variable and range objects in the arrays var and con which are passed to them as parameters After the model has been populated the IloCplex algorithm object cplex is created and the model is extracted to it The following call of method solve invokes the optimizer If it fails to generate a solution an error message is issued to the error stream of the environment cplex error and the integer 1 thrown as exception IloCplex provides the output streams out for general logging warning for warning messages and error for error messages They are preconfigured to cout cerr and ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN cerr respectively Thus by default you will see logging output on the screen when invoking the method solve This can be turned off by calling cplex setOut env getNullStream that is by redirecting the out stream of the IloCplex object cplex to the null stream of the environment If a solution is found solution information is output through the channel env out which is initialized to cout by default
74. and Your session should look like this add Enter new constraints and bounds end terminates 1 2x2 3x3 gt 50 end Problem addition successful ILOG CPLEX 8 1 GETTING STARTED 55 CHANGING A PROBLEM When the problem is displayed again the new constraint appears like this display problem all Maximize Ohjr xl 272 x2 3 x3 Subject To els x2 x3 lt 20 xl 3x2 x3 lt 30 C3 xl 2 x2 3 x3 gt 50 Bounds 0 lt 1 lt 40 All other variables are gt 0 end Adding from a File Alternatively you may read in new constraints and bounds from a file If you enter a file name after the add command ILOG CPLEX will read a file matching that name The file contents must comply with standard ILOG CPLEX LP format ILOG CPLEX does not prompt for a file name if none is entered Without a file name interactive entry is assumed Summary The general syntax for the add command is add or add filename Changing a Problem 56 The enter and add commands allow you to build a problem from the keyboard but they do not allow you to change what you have built You make changes with the change command The change command can be used for Changing Constraint or Variable Names Changing Sense Changing Bounds and Removing Bounds Changing Coefficients 5 99 Deleting entire constraints or variables Start out by changing the name of the constraint that you added with the add command
75. ant Please read these instructions in their entirety before beginning the installation Remember that most CPLEX distributions will operate correctly only on the specific platform and operating system version for which they are designed If you upgrade your operating system you may need to obtain a new CPLEX distribution ILOG CPLEX 8 1 GETTING STARTED 25 o Q U r m gt lt INSTALLING CPLEX Installing CPLEX 26 The steps to perform CPLEX installation involve identifying the correct distribution file for your particular platform and then executing a command that uses that distribution file The identification step is described in the booklet that comes with the CD ROM or is provided with the FTP instructions for download Once the correct distribution file is at hand the installation proceeds as follows Installation on UNIX On UNIX systems CPLEX 8 1 is installed in a subdirectory named cplex81 under the current working directory where you perform the installation Use the cd command to move to the top level directory into which you wish to install the CPLEX subdirectory Then type this command gzip dc lt path cplex tgz tar xf where path is the full path name pointing to the location of the CPLEX distribution file either on the CD ROM or on a disk where you performed the FTP download On UNIX systems both CPLEX and Concert are installed when you execute the above command Installat
76. antiated created and initialized by ILOG CPLEX when you call the routine CPXcreateprob It is destroyed when you call CPX reeprob ILOG CPLEX allows you to create more than one problem object although typical applications will use only one Each problem object is referenced by a pointer returned by CPXcreateprob and represents one specific problem instance All Callable Library functions except parameter setting functions and message handling functions require a pointer to a problem object Populating the Problem Object The problem object instantiated by CPXcreateprob represents an empty problem that contains no data it has zero constraints zero variables and an empty constraint matrix This empty problem object must be populated with data This step can be carried out in several ways The problem object can be populated by assembling arrays of data and then calling CPXcopylp to copy the data into the problem object For example see Building and Solving a Small LP Model in C on page 111 Alternatively you can populate the problem object by sequences of calls to the routines CPXnewcols CPXnewrows CPXaddcols CPXaddrows and CPXchgcoeflist these routines may be called in any order that is convenient For example see Adding Rows to a Problem Example lpex3 c on page 131 Ifthe data already exist in a file using MPS format or LP format you can use CPXreadcopyprob to read the file and copy t
77. ar TloRange rng throws IloException double lb 0 0 0 0 0 0 double ub 40 0 Double MAX VALUE Double MAX VALUE IloNumVar x model numVarArray 3 lb ub var 0 x double objvals 1 0 2 0 3 0 model add model maximize model scalProd x objvals rng 0 new IloRange 2 rng 0 0 model addRange Double MAX VALUE 20 0 9 rng 0 1 model addRange Double MAX VALUE 30 0 o 8 lt rng 0 0 setExpr model sum model prod 1 0 x 0 S 2 lt o model prod 1 0 x 1 model prod 1 0 x 2 cg rng 0 1 setExpr model sum model prod 1 0 x 0 m 5 model prod 3 0 x 1 mi S model prod 1 0 x 2 lt ILOG CPLEX 8 1 GETTING STARTED 101 COMPLETE CODE LPEX1 JAVA 102 ILOG CPLEX 8 1 GETTING STARTED Callable Library Tutorial This tutorial shows how to write programs that use the CPLEX Callable Library In this chapter you will learn about The Design of the ILOG CPLEX Callable Library Compiling and Linking Callable Library Applications How ILOG CPLEX Works Creating a Successful Callable Library Application Building and Solving a Small LP Model in C Reading a Problem from a File Example Ipex2 c Adding Rows to a Problem Example Ipex3 c 9 9 9 9 9 Performing Sensitivity Analysis The Design of the ILOG CPLEX Callable Library Figure 5 1 shows a picture of the ILOG CPLEX world The ILOG CPLEX Callable Libra
78. ar to that with o or obj files Simply substitute the library file in the link procedure This procedure simplifies linking and ensures that the smallest possible executable is generated ILOG CPLEX 8 1 GETTING STARTED COMPILING AND LINKING CALLABLE LIBRARY APPLICATIONS The following compilation and linking instructions assume that the example source programs and CPLEX Callable Library files are in the directories associated with a default installation of the software If this is not true additional compile and link flags would be required to point to the locations of the include file cplex h and Callable Library files respectively Note The instructions below were current at the time of publication As compilers linkers and operating systems are released different instructions may apply Be sure to check the Release Notes that come with your CPLEX distribution for any changes Also check the CPLEX web page http www ilog com products cplex Building CPLEX Callable Library Applications on UNIX Platforms To compile and execute an example 1pex1 do the following cd examples machine libformat make 1 1 to compile and execute the first CPLEX example A list of all the examples that can be built this way is to be found in the makefile by looking for c Ex C examples or you can view the files listed in examples src The makefile contains recommended compiler flags and other settings for your particular co
79. are described briefly in this manual File formats are documented in an appendix of the CPLEX Reference Manual Concert Technology and Callable Library users may read problem data from the same kinds of files as in the Interactive Optimizer or they may want to pass data directly into CPLEX to gain efficiency These options are discussed in a series of examples that begin with Building and Solving a Small LP Model in C Building and Solving a Small LP Model in Java and Building and Solving a Small LP Model in C for the CPLEX Callable Library users Solving an LP with CPLEX Technology To help you learn which CPLEX technology best meets your needs we briefly demonstrate here how to create and solve an LP model using four different interfaces to CPLEX Full details of writing a practical program are in the chapters containing the tutorials The problem to be solved is Maximize subject to with these bounds X 2x 3x3 X X x lt 20 X 3x5 X3 lt 30 0 x 40 0 x3 lt Using the Interactive Optimizer The following is screen output from a CPLEX Interactive Optimizer session where the example model is entered and solved CPLEX gt indicates the CPLEX prompt and text following this is user input Welcome to CPLEX Interactive Optimizer 8 1 0 with Simplex Copyright Mixed Integer amp Barrier Optimizers c ILOG 1997 2002 CPLEX is a registered trademark of ILOG Type Type inform
80. atbeg 1 3 rowname 1 c2 rmatind 3 0 rmatind 4 1 rmatind 5 2 sense 1 L rmatval 3 1 0 rmatval 4 3 0 rmatval 5 1 0 rhs 1 30 0 status CPXaddrows env lp 0 NUMROWS NUMNZ rhs sense rmatbeg rmatind rmatval NULL rowname if status goto TERMINATE TERMINATE return status END populatebyrow D aqe ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVI To popu columns static int populateby int oub oub oub oub char char CPXchgo Now rowname sense 0 rhs 0 rowname 1 rhs 1 status if st Now obj matbeg matind matval matind matval lb ub colname status 120 ILOG CPLEX 8 1 NG A SMALL LP MODEL IN C late by column we first create the rows and then add the column CPXENVptr env CPXLPptr lp status 0 obj NUMCOLS lb NUMCOLS ub NUMCOLS colname NUMCOLS matbeg NUMCOLS matind NUMNZ matval NUMNZ rhs NUMROWS sense NUMROWS rowname NUMROWS bjsen env lp CPX MAX Problem is maximization create the new rows First populate the arrays 0 oTNS 1 2 r 20 0 1 oa 30 0 CPXnewrows env lp NUMROWS rhs sense NULL rowname atus goto TERMINATE add the new columns First populate the arrays 0 1 0 obj 1 2 0 obj
81. ation on commands CPLEX gt enter example Enter new problem end maximize xl 2 x2 3 x3 subject to 1 help for a list of available commands help followed by a command name for more on a separate line terminates x2 x3 lt 20 xl 3 x2 x3 lt 30 bounds ILOG CPLEX 8 1 GETTING STARTED 15 SOLVING AN LP WITH CPLEX TECHNOLOGY 0 lt 1 lt 40 0 lt x2 0 lt x3 end CPLEX gt optimize Tried aggregator 1 time No LP presolve or aggregator reductions Presolve time 0 00 sec Iteration log Iteration E Dual infeasibility 0 000000 Iteration 2 Dual objective 202 500000 Dual simplex Optimal Objective 2 0250000000e 002 Solution time 0 01 sec Iterations 2 1 CPLEX gt quit Concert Technology for C Users Here is a C program using CPLEX in Concert Technology to solve the example model An expanded version of this example is discussed in detail in Chapter 3 Concert Technology Tutorial for C Users finclude lt ilcplex ilocplex h gt ILOSTLBEGIN int main int argc char argv IloEnv env try IloModel model env IloNumVarArray x env x add IloNumVar env 0 0 40 0 x add IloNumVar env x add IloNumVar env model add IloMaximize env x 0 2 x 1 3 x 2 model add x 0 x 1 x 2 lt 20 model add x 0 3 x 1 x 2 lt 30 IloCplex cplex model if cplex solve env error F
82. b env lp lpex3 sav NULL if status fprintf stderr CPXwriteprob failed n goto TERMINATE TERMINATE Free up the problem as allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp 1 if status 1 fprintf stderr CPXfreeprob failed error code status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON it status char errmsg 1024 fprintf stderr Could not close CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr s errmsg return status END main D ILOG CPLEX 8 1 GETTING STARTED 137 PERFORMING SENSITIVITY ANALYSIS Performing Sensitivity Analysis 138 In Performing Sensitivity Analysis on page 46 there is a discussion of how to perform sensitivity analysis in the Interactive Optimizer As with most interactive features of ILOG CPLEX there is a direct approach to this task from the Callable Library Here we modify the example 1 1 on page 111 to show how to perform sensitivity analysis with routines from the Callable Library We suggest that you mak
83. ch argv 2 0 case o method CPX ALG AUTOMATIC break case p method CPX ALG PRIMAL break case d method CPX ALG DUAL break case n method CPX ALG NET break case h method CPX ALG BARRIER break case b method CPX ALG BARRIER Status CPXsetintparam env CPX PARAM BARCROSSALG CPX ALG NONE if status ILOG CPLEX 8 1 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C fprintf stderr Failed to set the crossover method error d n status goto TERMINATE break case s method break CPX ALG SIFTING case c method break default method break CPX ALG CONCURRENT CPX ALG NONE Status CPXsetintparam env CPX PARAM LPMETHOD method if status fprintf stderr Failed to set the optimization method error d n status goto TERMINATE status CPXlpopt env 1 if status d fprintf stderr Failed to optimize LP n goto TERMINATE Solnstat CPXgetstat env lp if solnstat CPX STAT UNBOUNDED printf Model is unbounded An goto TERMINATE else if solnstat CPX_STAT_INFEASIBLE printf Model is infeasible n goto TERMINATE else if solnstat CPX_STAT_INForUNBD printf Model is infeasible or unbounded Wn goto TERMINATE status CPXsolninfo env lp amp solnmethod amp solntype NULL NULL if status fprintf stderr Failed t
84. clarations for the string and character functions and malloc include lt ctype h gt include lt stdlib h gt include lt string h gt Include declarations for functions in this program static void free_and_null char ptr usage char progname ILOG CPLEX 8 1 GETTING STARTED 8 5 e READING A PROBLEM FROM FILE EXAMPLE LPEX2 int main int argc char argv Declare and allocate space for the variables and arrays where we will store the optimization results including the status objective value maximum bound violation variable values and basis int solnstat solnmethod solntype double objval maxviol double NULL int cstat NULL int rstat NULL CPXENVptr env NULL CPXLPptr lp NULL int status 0 int j int cur_numrows cur_numcols int method char basismsg Check the command line arguments if argo 3 strchr podhbnsc argv 2 0 NULL ME usage argv 0 goto TERMINATE Initialize the CPLEX environment env CPXopenCPLEX amp status If an error occurs the status value indicates the reason for failure call to CPXgeterrorstring will produce the text of the error message Note that CPXopenCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON
85. cplex jar in your java command 2 If you get a message like java lang UnsatisfiedLinkError you need to set up the path correctly so that the JVM can locate the CPLEX shared library Make sure you use Djava library path path to shared library in your java command 3 If you get a message like ilm CPLEX no license found for this product or ilm CPLEX invalid encrypted key MNJVUXTDJV82 in usr ilog ilm access ilm run ilmcheck then there is a problem with your license to use ILOG CPLEX Review the ILOG License Manager User s Guide and Reference to see whether you can correct the problem If you have verified your system and license setup but continue to experience problems contact ILOG Technical Support and report the error messages The Design of CPLEX in Concert Technology User Written Application Concert Technology 5 modeling interfaces lloCplex 8 e 5 2 5 28 5 3 Y lt CPLEX database Figure 4 1 View of CPLEX in Concert Technology Figure 4 1 illustrates the design of Concert Technology and how a user program uses it Concert Technology defines a set of interfaces for modelling objects Such interfaces do not ILOG CPLEX 8 1 GETTING STARTED 91 THE ANATOMY CONCERT TECHNOLOGY APPLICATION actually consume memory this is the reason the box in the figure has a dotted outline When creating a Concert Technology mod
86. d example bas The message of confirmation Basis example bas read indicates that the basis file was successfully read If the advanced basis indicator is on this basis will be used as a starting point for the next optimization and any new basis created during the session will be used for future optimizations If the basis changes during a session you can save it by using the write command Summary The general syntax for the read command is read filename file format read filename file_extension where ile extension corresponds to one of the allowed file formats ILOG CPLEX 8 1 GETTING STARTED 53 JOZIWNdO 1 SETTING ILOG CPLEX PARAMETERS Setting ILOG CPLEX Parameters ILOG CPLEX users can vary parameters by means of the set command This command is used to set ILOG CPLEX parameters to values different from their default values The procedure for setting a parameter is similar to that of other commands Commands can be carried out incrementally or all in one line from the ILOG CPLEX prompt Whenever a parameter is set to a new value ILOG CPLEX inserts a comment in the log file that indicates the new value Setting a Parameter To see the parameters that can be changed type set The parameters that can be changed are displayed with a prompt like this Available Parameters advance set indicator for advanced starting information barrier set parameters for barrier optimi
87. d line argument After optimization the status of the solution is determined by a call to CPXget stat The cases of infeasibility or unboundedness in the model are handled in a simple fashion here a more complex application program might treat these cases in more detail With these two cases out of the way the program then calls CPXsolninfo to determine the nature of the solution Once it has been determined that a solution in fact exists then a call to CPXgetobjval is made to obtain the objective function value for this solution and report it Next preparations are made to print the solution value and basis status of each individual variable by allocating arrays of appropriate size these sizes are determined by calls to the routines CPXgetnumcols and CPXgetnumrows Note that a basis is not guaranteed to exist depending on which optimizer was selected at run time so some of these steps including the call to CPXgetbase are dependent on the solution type returned by CPXsolninfo The primal solution values of the variables are obtained by a call to CPXgetx and then these values along with the basis statuses if available are printed in a loop for each variable After that a call to CPXgetdblquality provides a measure of the numerical roundoff error present in the solution by obtaining the maximum amount by which any variable s lower or upper bound is violated After the TERMINATE label the data for the
88. d write command if the disk drive on your system contains a root directory named problems write problems example lp Summary The general syntax for the write command is write filename file format or write filename file extension where ile extension indicates the format in which the file is to be saved 50 ILOG CPLEX 8 1 GETTING STARTED READING PROBLEM FILES Reading Problem Files When you are using ILOG CPLEX to solve linear optimization problems you may frequently enter problems by reading them from files instead of entering them from the keyboard Continuing the tutorial from Writing Problem and Solution Files on page 47 the topics are Selecting a Read File Format Reading LP Files Using File Extensions Reading MPS Files 0 Reading Basis Files LT Selecting a Read File Format FEAT eg e EST When you type the read command in the Interactive Optimizer ILOG CPLEX displays the following prompt about file formats on the screen File Type Options bas INSERT format basis file 1 format problem file min DIMACS min cost network flow format file mps MPS format problem file mst MIP start file net CPLEX Network flow format file ord Integer priority order file qp Quadratic coefficient matrix file Sav Binary matrix and basis file sos Special ordered sets file tre Branch and bound treesave file vec Vector solution format file File Type Options Reminder
89. de lt ilcplex ilocplex h gt ILOSTLBEGIN static void usage const char progname int main int argc char argv IloEnv env try IloModel model env 82 ILOG CPLEX 8 1 GETTING STARTED READING A PROBLEM FROM FILE EXAMPLE ILOLPEX2 CPP IloCplex cplex env if argc 3 strchr podhbnsc argv 2 0 NULL usage argv 0 throw 1 switch argv 2 0 case o cplex setParam IloCplex RootAlg IloCplex AutoAlg break p cplex setParam IloCplex RootAlg IloCplex Primal break case d cplex setParam IloCplex RootAlg IloCplex Dual break case b cplex setParam IloCplex RootAlg IloCplex Barrier loCplex NoAlg H cplex setParam IloCplex BarCrossAlg break case h cplex setParam IloCplex RootAlg IloCplex Barrier break cplex setParam IloCplex RootAlg IloCplex Network break Pts cplex setParam IloCplex RootAlg IloCplex Sifting break penon cplex setParam IloCplex RootAlg IloCplex Concurrent break default break i D 4 o Q 2 5 lt IloObjective obj IloNumVarArray var IloRangeArray rng env cplex importModel model argv 1 obj var rng cplex extract model if cplex solve env error lt lt Failed to optimize LP lt lt endl throw 1 IloNumArray vals env cp
90. e Library 13 and Concert Technology 13 compiling and linking Callable Library 104 compiling and linking Component Libraries 29 compiling and linking Concert Technology 65 development steps 108 error handling 71 110 B baropt Interactive Optimizer command 44 barrier optimizer availability 44 selecting 80 BAS file format 50 53 basis accessing information 81 basis information 95 periodically written 50 starting from previous 87 basis file reading 53 writing 50 BIN file format 48 boolean parameter 86 boolean variable representing in model 68 bound GETTING STARTED 141 INDEX adding 55 changing 58 default values 36 displaying 42 entering in LP format 36 removing 58 sensitivity analysis 47 139 box variable 39 branch amp bound 80 branch amp cut 80 C Callable Library 103 to 139 application development steps 108 compiling and linking applications 104 conceptual design 103 CPLEX operation 106 description 13 distribution file 104 error handling 110 example model 18 opening CPLEX 106 see also individual CPXxxx routines change Interactive Optimizer command 56 bounds 58 change options 56 coefficient 59 delete 59 delete options 59 objective 59 rhs 59 sense 57 syntax 60 changing bounds 58 coefficients 58 constraint names 57 parameters 54 86 problem 56 sense 57 variable names 57 choosing optimizer 44 80 110 class library 90 142 ILOG CPLEX 8 1 classpath 91 command line option 90 coe
91. e a copy of 1pex1 c and edit this new source file Among the declarations for example immediately after the declaration for dj insert these additional declarations double lowerc NULL upperc NULL double lowerr NULL upperr NULL At some point after the call to CPX1popt for example just before the call to CPXwriteprob perform sensitivity analysis on the objective function and on the right hand side coefficients by inserting this fragment of code upperc double malloc cur numcols sizeof double lowerc double malloc cur numcols sizeof double status CPXobjsa env lp 0 cur numcols 1 lowerc upperc if status fprintf stderr Failed to obtain objective sensitivity n goto TERMINATE printf nObjective coefficient sensitivity n for j 0 j lt cur numcols j printf Column d Lower 10g Upper 10g n 3 lowerc j upperc j1 upperr double malloc cur numrows sizeof double lowerr double malloc cur numrows sizeof double status CPXrhssa env lp 0 cur numrows 1 lowerr upperr if status 1 fprintf stderr Failed to obtain RHS sensitivity n goto TERMINATE printf nRight hand side coefficient sensitivity n for 0 i lt cur numrows i printf Row Sd Lower 10g Upper 10g n i lowerr i upperr i This sample is familiarly known as throw away code For product
92. e above declaration One advantage of using handles is that if you assign handle objects all that is assigned is a pointer So the statement IloEnv env2 env creates a second handle pointing to the implementation object that env already points to Hence there may be an arbitrary number of 11oEnv handle objects all pointing to the same implementation object When terminating the Concert Technology application the implementation object must be destroyed as well This must be done explicitly by the user by calling env end for just ONE of the IloEnv handles pointing to the implementation object to be destroyed The call to env end is generally the last Concert Technology operation in an application penon i o D 4 2 5 lt Creating Model lloModel After creating the environment we are ready to create one or more optimization models Doing so consists of creating a set of modeling objects to describe each optimization model Modeling objects like IloEnv objects are handles to implementation objects Though you will be dealing only with the handle objects it is the implementation objects that contain the data that specifies the optimization model If you need to remove an implementation object from memory you need to call the end method for one of its handle objects We also refer to modeling objects as extractables This is because it is the individual
93. e other solution values since they are not printed by this example At the end the problem is written as a SAV file by CPXwriteprob This file can then be read into the ILOG CPLEX Interactive Optimizer to analyze whether the problem was correctly generated Using a SAV file is recommended over MPS and LP files as SAV files preserve the full numeric precision of the problem After the TERMINATE label CPX reeprob releases the problem object and CPXcloseCPLEX releases the ILOG CPLEX environment Complete Program The complete program follows You can also view it online in the file 1pex3 c File examples src lpex3 c Version 8 1 JEL Fae at Ro Sh Se PSS UE ODOT M ee Copyright 1997 2002 by ILOG 11 Rights Reserved xf ILOG CPLEX 8 1 GETTING STARTED ADDING ROWS TO A PROBLEM EXAMPLE LPEX8 C Permission is expressly granted to use this example in the course of developing applications that use ILOG products lpex3 c example of using CPXaddrows to solve a problem Bring in the CPLEX function declarations and the C library header file stdio h with the following single include finclude ilcplex cplex h Br
94. e write command This command writes the problem statement or a solution report to a file We continue with the tutorial example in the topics Selecting a Write File Format Writing LP Files Writing Basis Files Using Path Names ILOG CPLEX 8 1 GETTING STARTED 47 WRITING PROBLEM AND SOLUTION FILES 48 Selecting a Write File Format When you type the write command in the Interactive Optimizer ILOG CPLEX displays a menu of options and prompts you for a file format like this File Type Options bas INSERT format basis file bin Binary solution file dpe Binary format for dual perturbed problem dua MPS format of explicit dual of problem emb MPS format of embedded network iis Irreducibly inconsistent set LP format 1 LP format problem file min DIMACS min cost network flow format of embedded network mps MPS format problem file mst MIP start file net CPLEX network format of embedded network ord Integer priority order file ppe Binary format for primal perturbed problem pre Binary format for presolved problem qp Quadratic coefficient matrix file rew MPS format problem with generic names Sav Binary matrix and basis file sos Special ordered sets file tre Branch and bound treesave file txt Text solution file vec Vector solution format file File type The BAS format is used for storing basis information and is described in Writing Basis Files on page 50 See also Reading Basis Files on page
95. eByRow cplex var rng break case c populateByColumn cplex var rng break case n populateByNonzero cplex var rng break default usage return 85 write model to file s cplex exportModel 1 1 1 5 solve the model and display the solution if was found Cc if cplex solve m 5 double x cplex getValues var 0 74 S double dj cplex getReducedCosts var 0 e double pi 7 cplex getDuals rng 0 lt double slack cplex getSlacks rng 0 cplex out println Solution status cplex getStatus cplex out println Solution value cplex getObjValue int ncols cplex getNcols for int j 0 j lt ncols 7 cplex out println Column j Value x j ILOG CPLEX 8 1 GETTING STARTED 99 COMPLETE CODE LPEX1 JAVA 100 Reduced cost dj j int nrows cplex getNrows for int i 0 i lt nrows i cplex out println Row se m sg zh Slack slack i Pi pili cplex end catch IloException e System err println Concert exception e caught The following methods all populate the problem with data for the following linear program Maximize xl 2 x2 3 x3 Subject To xl x2 x3 lt 20 xl 3 2 x3 lt 30 Bounds if 0 lt xl lt 40 End using the IloMPModeler API static void
96. eface for example CPXcopyobjnames or IloCplex Combinations of keys from the keyboard are hyphenated For example control c indicates that you should press the control key and the c key simultaneously The lt return gt indicates end of line or end of data entry On some keyboards the key is labeled enter or Enter Related Documentation 22 In addition to this introductory manual the standard distribution of ILOG CPLEX comes with the CPLEX User s Manual the CPLEX Reference Manual and the Concert Technology Documentation Kit All ILOG documentation is available in an online version in HTML hypertext mark up language It is delivered with the standard distribution of the product and accessible through conventional HTML browsers The ILOG CPLEX User s Manual explains the relationship between the Interactive Optimizer and the Component Libraries It enlarges on aspects of linear programming with ILOG CPLEX and shows you how to handle quadratic programming QP problems and mixed integer programming MIP problems It tells you how to control ILOG CPLEX parameters debug your applications and efficiently manage input and output It also explains how to use parallel CPLEX optimizers The ILOG CPLEX Reference Manual documents the Callable Library routines and their arguments the Concert Technology classes methods and functions and the commands and options of the Interactive Optimizer The reference manual
97. elling object using CPLEX an object is created in the CPLEX database that implements the interface defined by Concert Technology However a user application never accesses such objects directly but only communicates with them through the interfaces defined by Concert Technology The only Concert Technology objects directly created and accessed by a user are objects from class 11oCplex This class implements two interfaces IloModeler and IloMPModeler that allow you to create modelling objects The class IloCplex also provides methods to solve models and query solutions The Anatomy of a Concert Technology Application To use the CPLEX Java interfaces you need to import the appropriate packages into your application This is done with the lines import ilog concert import ilog cplex As for every Java application a CPLEX application is implemented as a method of a class In this discussion we will assume the method to be the static main method The first task is to create an I1oCplex object It is used to create all the modeling objects needed to represent the model For example an integer variable with bounds 0 and 10 is created by calling cplex intVar 0 10 where 1 is IloCplex object Since Java error handling in CPLEX is done using exceptions you should include the Concert Technology part of an application in a try catch statement All the exceptions thrown by any Concert Technology method are derived from Ilo
98. em together with the method IloColumn and For example the first variable in populateByColumn is created like this var 0 0 model numVar model column obj 1 0 model column r0 1 0 model column rl 0 0 40 0 The three methods model column create IloColumn objects for installing a new variable in the objective obj and in the constraints x0 and r1 with linear coefficients 1 0 1 0 and 1 0 respectively They are all linked to an aggregate column object using the method and This aggregate column object is passed as the first argument to the method numVar along with the bounds 0 0 and 40 0 as the other two arguments The method numVar now creates a new variable and immediately installs it in the modeling objects obj and r1 as described by the aggregate column object Once installed the new variable is returned and stored in var 0 0 Modeling by Nonzeros The last of the three functions for building the model is populateByNonzero In this function we create the variables with only their bounds and the empty constraints that is ranged constraints only with lower and upper bound but with no expression Only after that do we construct the expressions in a manner similar to the ones already described using these existing variables and install them in the existing constraints with the method IloRange setExpr Complete Code of LPex1 java 98 File examples src LPexl jav
99. end should not be called The column expression is passed as a parameter to the constructor of class IloNumVar For example the constructor I1oNumVar 0obj 1 0 c 0 1 0 1 1 0 0 0 40 0 creates a new modeling variable with lower bound 0 0 upper bound 40 0 and by default type ILOFLOAT and adds it to the objective obj with a linear coefficient of 1 0 to the range c 0 with a linear coefficient of 1 0 and to c 1 with a linear coefficient of 1 0 Column expressions can be used directly to construct numerical variables with default bounds 0 IloInfinity and type ILOFLOAT as in the following statement x add obj 2 0 c 0 1 0 1 3 0 where 11oNumVar does not need to be explicitly written Here the C compiler recognizes that an 11oNumVar object needs to be passed to the add method and therefore automatically calls the constructor IloNumVar IloNumColumn in order to create the variable from the column expression Modeling by Nonzero Elements The last of the three functions that can be used to build the model is populatebynonzero It creates objects for the objective and the ranges without expressions and variables without columns Then methods 11o0bjective setCoef and IloRange setCoef are used to set individual nonzero values in the expression of the objective and the range constraints As usual the objective and ranges must be added to the model Complete Program The complete prog
100. es in the data are omitted in the example program CPLEX makes extensive use of sparse matrix methods and although CPLEX correctly handles any explicit zero coefficients given to it most programs solving models of more than modest size benefit in terms of both storage space and speed if the natural sparsity of the model is exploited from the very start Before the model is solved the network optimizer is selected by setting the RootAlg parameter to the value IloCplex Network as shown in example ilolpex2 cpp The simplex display parameter IloCplex 1101 1 is set so that the simplex algorithm issues logging information as it executes Setting CPLEX Parameters IloCplex provides a variety of parameters that allow you to control the solution process They can be categorized into boolean integer numerical and string parameters and are represented by the enumeration types IloCplex BoolParam IloCplex IntParam IloCplex NumParam and IloCplex StringParam respectively Modifying an Optimization Problem After the simple model is solved and the resulting objective value is passed to the output channel cplex out the remaining constraints are created and added to the model At this time the model has already been extracted to cplex As a consequence whenever the model is modified by adding a constraint this addition is immediately reflected in the cplex object via notification ILOG CPLEX 8 1 GETTING STARTED MOD
101. es in the standard distribution They use relative path names to indicate to the compiler where the header files are and to the linker where the libraries are Testing Your Installation on UNIX To run the test follow these steps 1 First check the readme html file in the standard distribution to locate the right subdirec tory containing a makefile appropriate for your platform 2 Go to that subdirectory 3 Then use the sample makefile located there to compile and link the examples that came in the standard distribution 4 Execute one of the compiled examples penon 5 D 4 o Q 2 5 o e lt Testing Your Installation on Windows To run the test on a Windows platform first consult the readme html file in the standard distribution That file will tell you where to find another text file that contains information about your particular platform That second file will have an abbreviated name that corresponds to a particular combination of machine architecture and compiler For example if you are working on a personal computer with Windows NT and Microsoft Visual C compiler version 6 then the readme htm1 file will direct you to the msvc html file where you will find detailed instructions about how to create a project to compile link and execute the examples in the standard distribution The examples have been tested repeatedly on all the platforms compatible with ILOG CPLEX
102. exl c Entering and optimizing a problem Demonstrates different methods for creating a problem The user has to choose the method on the command line lpexl r generates the problem by adding rows lpexl generates the problem by adding columns lpexl n generates the problem by adding a list of coefficients Bring in the CPLEX function declarations and the library header file stdio h with the following single include include lt ilcplex cplex h gt include lt stdlib h gt include assert h include lt math h gt fendif Bring in the declarations for the string functions include lt string h gt ILOG CPLEX 8 1 GETTING STARTED D BUILDING AND SOLVING A SMALL LP MODEL IN Include declaration for functions at end of program static int populatebyrow CPXENVptr env CPXLPptr lp populatebycolumn CPXENVptr env CPXLPptr lp populatebynonzero CPXENVptr env CPXLPptr 1p static void free and null char ptr usage char progname int main int argc char argv Declare and allocate space for the variables and arrays where we will store the optimization results including the status value variable values dual values row slacks and variable reduced costs int solstat double objval double x NULL double pi NULL double slack NULL double dj NULL CPXENVptr env NULL CPXLPptr lp
103. explain those steps Opening the ILOG CPLEX Environment ILOG CPLEX requires a number of internal data structures in order to execute properly These data structures must be initialized before any call to the ILOG CPLEX Callable Library The first call to the ILOG CPLEX Callable Library is always to the function CPXopenCPLEX This routine checks for a valid ILOG CPLEX license and returns a pointer to the ILOG CPLEX environment This pointer is then passed to every ILOG CPLEX Callable Library routine except CPXmsg The application developer must make an independent decision as to whether the variable containing the environment pointer is a global or local variable Multiple environments are allowed but extensive opening and closing of environments may create significant overhead on the licensor and degrade performance typical applications make use of only one ILOG CPLEX 8 1 GETTING STARTED How ILOG CPLEX WORKS environment for the entire execution since a single environment may hold as many problem objects as the user wishes After all calls to the Callable Library are complete the environment is released by the routine CPXcloseCPLEX This routine indicates to CPLEX that all calls to the Callable Library are complete any memory allocated by ILOG CPLEX is returned to the operating system and the use of the ILOG CPLEX license is ended for this run Instantiating the Problem Object A problem object is inst
104. f an application in the ILOG CPLEX Interactive Optimizer with a small prototype of the model Doing so will help identify the Callable Library routines required The test may also uncover any flaws in procedure logic before you invest significant development effort Trying the ILOG CPLEX Interactive Optimizer is an easy way to determine the best optimization procedure and parameter settings Assemble the Data You must decide which approach to populating the problem object is best for your application Reading an MPS or LP file may reduce the coding effort but can increase the run time and disk space requirements of the program Building the problem in memory and then calling CPXcopylp avoids time consuming disk file reading Using the routines CPXnewcols CPXnewrows CPXaddcols CPXaddrows and CPXchgcoeflist can lead to modular code that may be more easily maintained than if you assemble all model data in one step Another consideration is that if the Callable Library application reads an MPS or LP formatted file usually another application is required to generate that file Particularly in the case of MPS files the data structures used to generate the file could almost certainly be used to build the problem defining arrays for 1 directly The result would be less coding and a faster more efficient application These observations suggest that formatted files may be useful when prototyping your application
105. f the file cplex exe on Windows platforms or cplex on UNIX platforms Concert Technology is a set of and Java class libraries offering an API that includes modeling facilities to allow the programmer to embed CPLEX optimizers in C or Java applications The library is provided in the files in the table below Table 1 Concert Technologies Class Libraries MS Windows Unix ilocplex lib libilocplex a concert lib libconcert a Java cplex jar cplex jar The Concert Technology libraries make use of the Callable Library described next The CPLEX Callable Library is a C library that allows the programmer to embed CPLEX optimizers in applications written in C Visual Basic FORTRAN or any other language that can call C functions The library is provided in files cplex81 11ib and cplex81 d11 Windows platforms and in 1ibcplex a libcplex81 so and or libcplex81 s1 on UNIX platforms In this manual the phrase CPLEX Component Libraries is used when referring equally to any of these libraries While all of the libraries are callable the term CPLEX Callable Library as used here refers specifically to the C library Compatible Platforms ILOG CPLEX is available on Windows and UNIX platforms The programming interface works the same way and provides the same facilities on all platforms Installation Requirements If you have not yet installed ILOG CPLEX on your platform please consult Chapter 1 Setting Up
106. fficient changing 58 column expressions 73 command executing from operating system 60 input formats 32 Interactive Optimizer list 33 compiler DNDEBUG option 71 error messages 66 Microsoft Visual Command Line 105 using with CPLEX 65 compiling applications 29 Callable Library applications 104 Concert Technology applications 65 Component Libraries defined 13 running examples 28 verifying installation 28 Concert Technology Library 63 to 88 C classes 66 C objects 64 compiling and linking applications 65 CPLEX design in 64 description 13 error handling 71 example model 16 running examples 65 see also individual routines constraint adding 55 86 changing names 57 changing sense 57 creating 73 default names 36 deleting 59 displaying 41 displaying names 40 displaying nonzero coefficients 39 displaying number of 39 displaying type 39 GETTING STARTED entering in LP format 36 name limitations 36 naming 36 range 73 representing in model 68 constraints adding to a model 94 continuous variable representing 68 cost reduced 95 CPLEX compatible platforms 13 Component Libraries 13 description 12 directory structure 27 installing 26 licensing 28 problem types 12 quitting 61 setting up 25 starting 32 technologies 13 Web site 23 cplex solve the model 94 cplex command 32 cplex jar location 89 lex log file 44 lex numVarArray 97 lex out 96 lex setOut 96 lex setWarning 96 lex solve 96
107. he bounds can be changed on this or other variables with the bounds option Again start by selecting the command and option change bounds Select the variable by name or number and then select which bound you would like to change For the example change the upper bound of variable x from 50 Change bounds on which variable x2 Present bounds on variable x2 The indicated variable is gt 0 Change lower or upper bound or both 1 u or b Change upper bound to what inf for no upper bound 50 New bounds on variable x2 0 lt x2 lt 50 Removing Bounds To remove a bound set it to es Interactively use the identifiers inf and inf instead of the symbols To change the upper bound on x2 back to use the one line command change bounds x2 u inf You receive the message New bounds on variable x2 The indicated variable is gt 0 The bound is now the same as it was when the problem was originally entered Changing Coefficients Up to this point all of the changes that have been made could be referenced by specifying a single constraint or variable In changing a coefficient however a constraint and a variable ILOG CPLEX 8 1 GETTING STARTED CHANGING A PROBLEM must be specified in order to identify the correct coefficient As an example let s change the coefficient of x3 in the new3 constraint from 3 to 30 As usual you must first specify which change command option
108. he data into the problem object For example see Reading a Problem from a File Example lpex2 c on page 122 Changing the Problem Object A major consideration in the design of ILOG CPLEX is the need to efficiently re optimize modified linear programs In order to accomplish that ILOG CPLEX must be aware of changes that have been made to a linear program since it was last optimized Problem modification routines are available in the Callable Library ILOG CPLEX 8 1 GETTING STARTED 107 D CREATING SUCCESSFUL CALLABLE LIBRARY APPLICATION Do not change the problem by changing the original problem data arrays and then making a call to CPXcopylp Instead change the problem using the problem modification routines allowing ILOG CPLEX to make use of as much solution information as possible from the solution of the problem before the modifications took place For example suppose that a problem has been solved and that the user has changed the upper bound on a variable through an appropriate call to the ILOG CPLEX Callable Library A re optimization would then begin from the previous optimal basis and if that old basis were still optimal then that information would be returned without even the need to refactor the old basis Creating a Successful Callable Library Application 108 Callable Library applications are created to solve a wide variety of problems Each application sha
109. he objective to IloCplex via cplex add obj Every modeling object that is to be used in model must be added to the 1 1 object The variables need not be explicitly added as they are treated implicitly when used in the expression of the objective More generally every modeling object that is referenced by another modeling object which itself has been added to 11oCp1ex is implicitly added to TloCplex as well There is a shortcut notation for creating and adding the objective to 11oCplex cplex addMinimize expr Since we don t need to access the objective otherwise we can avoid storing it in variable obj Adding constraints to the model is just as easy For example the constraint x 0 x 1 x 2 lt 20 0 can be added by calling cplex addLe cplex sum cplex negative x 0 x 1 x 2 20 Again many methods are provided for adding other constraint types including equality constraints greater than or equal to constraints and ranged constraints Internally they are all represented as IloRange objects with appropriate choices of bounds which is why all these methods return 11oRange objects Also note that the expressions above could have been created in many different ways including the use of IloLinearNumExpr Solve the Model So far we have discussed some methods of 1 1 for creating models such methods are defined in the interfaces 110Modeler and its extension I loMPModeler However 1
110. ifting n 3 fprintf stderr concurrent n fprintf stderr Exiting n END usage Adding Rows to a Problem Example 1pex3 c This example illustrates how to develop your own solution algorithms with routines from the Callable Library It also shows you how to add rows to a problem object Here is the problem example 1pex3 solves Minimize ctx subject to 1 lt where 10 1 01 00 0 3 1 1 0 1 0 0 0 0 at 0 1 1 0 0 1 1 0 4 0 0 0 1 0 1 0 1 C x13 0 0 0 0 1 0 1 1 5 A 2 1 2 1 2 1 2 3 b 4 1 3 2 3 12 1 1 2 c 9 1 4 2 8 2 812 l 0 0 0 0 0 0 0 0 u 50 50 50 50 50 50 50 50 The constraints Hx d represent a pure network flow The example solves this problem in two steps 1 The ILOG CPLEX Network Optimizer is used to solve E 2 Minimize gt subject to Hx d 2L 2 5 l amp u 5 lt ILOG CPLEX 8 1 GETTING STARTED 131 ADDING ROWS TO A PROBLEM EXAMPLE LPEXS C 132 2 The constraints Ax b are added to the problem and the dual simplex optimizer is used to solve the new problem starting at the optimal basis of the simpler network problem The data for this problem consists of the network portion using variable names beginning with the letter H and the complicating constraints using variable names beginning with the letter A The example first calls to create the environ
111. ile name ILOG CPLEX will recognize the file as being in MPS format If you omit the extension you must specify that the file is of the type MPS read afiro mps ILOG CPLEX 8 1 GETTING STARTED READING PROBLEM FILES Once the file has been read the following message appears Selected objective sense MINIMIZE Selected objective name obj Selected RHS name rhs Problem afiro read Read time 0 01 sec ILOG CPLEX reports additional information when it reads MPS formatted files Since these files can contain multiple objective function right hand side bound and other information ILOG CPLEX displays which of these is being used for the current problem See the ILOG CPLEX User s Manual to learn more about special considerations for using MPS formatted files Reading Basis Files In addition to other file formats the read command is also used to read basis files These files contain information for ILOG CPLEX that tells the simplex method where to begin the next optimization Basis files usually correspond to the result of some previous optimization and help to speed re optimization They are particularly helpful when you are dealing with very large problems if small changes are made to the problem data Writing Basis Files on page 50 showed you how to save a basis file for the example after it was optimized For this tutorial first read the example 1p file Then read this basis file by typing the following command rea
112. imilarly solution values for all the variables in the array x can be queried by calling double xval cplex getValues x More solution information can be queried from 1 1 including slacks and depending on the algorithm that was applied for solving the model duals reduced cost information and basis information Building and Solving a Small LP Model in Java The example LPex1 java which is distributed with the installation files for CPLEX is a program that builds a specific small LP model and then solves it This example follows the general structure found in many CPLEX Concert Technology applications and demonstrates three main ways to construct a model e modeling by rows e modeling by columns and e modeling by nonzero elements 9 Example LPex1 java is an extension of the example presented on page 34 8 c Maximize X 2x 3x3 subject to X X x lt 20 5 X lt 30 with these bounds 0 lt x lt 40 c 0 lt 2 lt 0 lt lt After an initial check that a valid option string was provided calling argument the program begins by enclosing all executable statements that follow in a try catch pair of statements In case of an error CPLEX Concert Technology will throw an exception of type IloException which the catch statement then processes In this simple example an ILOG CPLEX 8 1 GETTING STARTED 95 BUILDING AND SOLVING SMALL
113. ing CPLEX in Concert Technology Applications i D 4 o 2 2 5 lt The Anatomy of a Concert Technology Application Building and Solving a Small LP Model in C Writing and Reading Models and Files Selecting an Optimizer Reading a Problem from a File Example ilolpex2 cpp Modifying and Reoptimizing 9 9 9 9 9 Modifying an Optimization Problem Example ilolpex3 cpp ILOG CPLEX 8 1 GETTING STARTED 63 THE DESIGN CPLEX IN CONCERT TECHNOLOGY The Design of CPLEX in Concert Technology 64 A clear understanding of C objects is fundamental to using Concert Technology with CPLEX to build and solve optimization models These objects can be divided into two categories 1 Modeling objects are used to define the optimization problem Generally an application creates multiple modeling objects to specify one optimization problem Those objects are grouped into an I1oModel object representing the complete optimization problem 2 IloCplex objects are used to solve the problems that have been created with the modeling objects An 11oCplex object reads a model and extracts its data to the appropriate representation for the CPLEX optimizer Then the IloCplex objectis ready to solve the model it extracted and be queried for solution information Thus the modeling and optimization parts of a user written application program are represented by a group of interacting objects created and
114. ing in the declarations for the string functions include lt stdio h gt include lt stdlib h gt include assert h include lt math h gt Treat the constraints with A as the complicating constraints and the constraints with H as the simple problem The idea is to solve the simple problem first and then add the fendif Modified example from Chvatal Linear Programming Chapter 26 minimize c x subject to Hx b 1 lt x lt u where H 1 0 1 0100 0 3 1 1 01 00 00 5 1 0 1 1 0 0 1 1 0 4 0 0 0 1 0 1 0 1 3 h 0 0 0 10 0 0 1 35 3 R 2 1 2 1 2 1 2 3 b 4 1 3 2 3 12 1 1 2 c 9 1 4 2 8 2 812 1 0 0 29 Qd 9 50 50 50 50 50 50 50 50 constraints for the complicating constraints and solve with dual le 5 SOS define COLSORIG 8 2s define ROWSSUB 5 5 lt ILOG CPLEX 8 1 GETTING STARTED 133 ADDING ROWS TO A PROBLEM EXAMPLE LPEX3 C define NZSUB 2 COLSORIG define ROWSCOMP 2 define NZCOMP ROWSCOMP COLSORIG define ROWSTOT ROWSSUB ROWSCOMP define NZTOT NZCOMP NZ SUB int main Data for original problem Arrays have to be big enough to hold problem plus additional constraints double Hrhs ROWSTOT 237 lt 1 5 double Hlb COLSORIG Oy D Oy De Dy 07 double Hub COL
115. ion on Windows Before you install CPLEX you need to identify the correct distribution file for your platform There are instructions on how to identify your distribution in the booklet that comes with the CD ROM or with the FTP instructions for download This booklet also describes how to start the CPLEX installation on your platform ILOG CPLEX 8 1 GETTING STARTED INSTALLING CPLEX Directory Structure After completing the installation you will have a directory structure like the following concert12 9 include 7 L ilconcert 9 L lib m m platform e L lt lib format gt lt CONCERT LIBRARY gt cplex81 bin E tomas L EXECUTABLE FILES Interactive Optimizer dll and so files examples L data src platform ka lt lib format gt L makefile or MSVC project files include L ilcplex lib platform lt lib format gt lt LIBRARY gt Figure 1 0 Installation Directory Structures Be sure to read the readme htm1 carefully for the latest information on the version of CPLEX you have installed ILOG CPLEX 8 1 GETTING STARTED 27 SETTING UP LICENSING Setting Up Licensing CPLEX 8 1 runs under the control of the ILOG License Manager ILM Before you can run CPLEX or any application that calls it you must have established a valid license that ILM can read
116. ion purposes you probably want to observe good programming practices such as freeing these allocated arrays at the TERMINATE label in the application A bound value of Je CPX_INFBOUND is treated as infinity within ILOG CPLEX so this is the value printed by our sample code in cases where the upper or lower sensitivity range ILOG CPLEX 8 1 GETTING STARTED PERFORMING SENSITIVITY ANALYSIS on a row or column is infinite a more sophisticated program might print a string such as inf or inf when negative or positive CPX_INFBOUND is encountered as a value Similar code could be added to perform sensitivity analysis with respect to bounds via CPXboundsa D aqe ILOG CPLEX 8 1 GETTING STARTED 139 PERFORMING SENSITIVITY ANALYSIS 140 ILOG CPLEX 8 1 GETTING STARTED accessing basic rows and columns of solution 45 basis information 81 dual values 45 objective function value 45 reduced costs 45 slack values 45 solution values 45 70 add Interactive Optimizer command 55 syntax 56 add obj 94 adding bounds 55 constraint to model 86 constraints 55 from a file 56 interactively 55 objective function to model 69 rows to a problem 131 addLe 97 addMinimize 97 addMinimize expr 94 advanced basis advanced start indicator 44 using 50 algorithm automatic Aut oA1g 80 creating object 69 72 ILOG CPLEX 8 1 Index and 98 application and Callabl
117. ions for establishing build procedures for your application 1 First check the readme htm1 file in the standard distribution under the Supported Platforms heading to locate the machine and lt libformat gt entry for your Unix platform or the compiler and library format combination for Windows 2 Goto the subdirectory under the examples directory where CPLEX is installed on your machine On Unix this will be machine libformat and on Windows it will be compiler N libformat This subdirectory will contain a makefile javamake appropriate for your platform 3 Then use these files to compile the examples that came in the standard distribution by calling make execute java Unix or nmake f javamake execute Windows 4 Carefully note the locations of the needed files both during compilation and at run time and convert the relative path names to absolute path names for use in your own working environment In Case Problems Arise If a problem occurs in the compilation phase make sure your java compiler is correctly set up and that your classpath includes the cplex jar file If compilation is successful and the problem occurs when executing your application there are three likely causes ILOG CPLEX 8 1 GETTING STARTED THE DESIGN CPLEX IN CONCERT TECHNOLOGY 1 If you get a message like java lang NoClassDefFoundError your classpath is not correctly set up Make sure you use classpath path to
118. isplaying the Objective 41 Displaying Bounds AUN AE Ee AERE E 42 Solving a Problem et ee wees cepere Nae paie wie iai ere e 42 Solving the Example Problem 42 Sol tion Optiohs clie eedem Pe nk Pe 44 Displaying Post Solution 45 Performing Sensitivity Analysis 46 Writing Problem and Solution 47 Selecting a Write File 48 Writing EP Files ioo go oreet olet accent Vee Put RO Pu E Ro E a DR B URN e 49 Writing Basis Elles RR RR RENE E eb RR SER ERRARE RUE 50 Using Path Names 2 er Y le ee YR ERR PS 50 Reading Problem Files 00 0 c cece eee eee eee eee eee n I hh hh 51 Selecting a Read File nauau nanea 51 Reading UP Files os exe ERE RERO acq m cer um E Pe ed 51 Using File Extensions cte RP be eid Gd a y 52 Readirig MPS Files itinere icit pct pepe e oa an ed drca E ADLER ag A 52 ILOG CPLEX 8 1 GETTING STARTED Chapter 3 TABLE OF CONTENTS Reading Basis Files nee eI eats gels ee tie eid ee eS 53 Setting ILOG CPLEX lt
119. ive Function When you want to display only the objective function you must enter its name obj by default or an index number of 0 display problem constraints Display which constraint name s 0 ILOG CPLEX 8 1 GETTING STARTED 41 SOLVING A PROBLEM Maximize obj x1 2 x2 3 x3 Displaying Bounds To see only the bounds for the problem type the following command don t forget the hyphen character display problem bounds The result is 0 lt 1 lt 40 All other variables are gt 0 Summary The general syntax of the display command is display option option2 identifier identifier2 Solving a Problem 42 The problem is now correctly entered and ILOG CPLEX can be used to solve it We continue our example with the following topics Solving the Example Problem Solution Options Displaying Post Solution Information Solving the Example Problem The optimize command tells ILOG CPLEX to solve the LP problem CPLEX uses the dual simplex optimizer unless another method has been specified by setting the LPMETHOD parameter Entering the Optimize Command At the ILOG CPLEX prompt type the command optimize Preprocessing First ILOG CPLEX tries to simplify or reduce the problem using its presolver and aggregator If any reductions are made a message will appear However in our small example no reductions are possible ILOG CPLEX 8 1 GETTING STARTED SOLVING A PROBLEM
120. ke the program easier to understand and modify A list of good programming practices is provided in the ILOG CPLEX User s Manual Debug Your Program Your program may not run properly the first time you build it Learn to use a symbolic debugger and other widely available tools that support the creation of error free code Use the list of debugging tips provided in ILOG CPLEX User s Manual to find and correct problems in your Callable Library application ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN Test Your Application Once an application works correctly it still may have errors or features that inhibit execution speed To get the most out of your application be sure to test its performance as well as its correctness Again the ILOG CPLEX Interactive Optimizer can help Since the Interactive Optimizer uses the same routines as the Callable Library it should take the same amount of time to solve a problem as a Callable Library application Use the CPXwriteprob routine with the SAV format to create a binary representation of the problem object then read it in and solve it with the Interactive Optimizer If the application sets optimization parameters use the same settings with the Interactive Optimizer If your application takes significantly longer than the Interactive Optimizer performance within your application can probably be improved In such a case possible performance inhibitor
121. lacks in the range 1 2 are 0 To view the dual values sometimes called shadow prices for each constraint enter the command display solution dual ILOG CPLEX 8 1 GETTING STARTED 45 PERFORMING SENSITIVITY ANALYSIS The list of constraint names with the solution value for each constraint appears like this Constraint Name Dual Price cl 2 750000 c2 0 250000 Summary Display solution characteristics by entering a command with the syntax display solution identifier Performing Sensitivity Analysis 46 Sensitivity analysis of the objective function and right hand side provides meaningful insight about ways in which the optimal solution of a problem changes in response to small changes in these parts of the problem data Sensitivity analysis can be performed on the following objective function right hand side values bounds To view the sensitivity analysis of the objective function enter the command display sensitivity obj For our example ILOG CPLEX displays the following ranges for sensitivity analysis of the objective function OBJ Sensitivity Ranges Variable Name Reduced Cost Down Current Up 1 3 5000 2 5000 1 0000 tinfinity x2 zero 5 0000 2 0000 3 0000 x3 zero 2 0000 3 0000 tinfinity ILOG CPLEX displays each variable its reduced cost and the range over which its objective function coefficient can vary without forcing a change in the optimal basis The current value of each objective c
122. lex getValues vals var env out lt lt Solution status lt lt cplex getStatus lt lt endl ILOG CPLEX 8 1 GETTING STARTED 83 MODIFYING AND REOPTIMIZING env out lt lt Solution value lt lt cplex getObjValue lt lt endl env out lt lt Solution vector lt lt vals lt lt endl try basis may not exist TloCplex BasisStatusArray cstat env cplex getBasisStatuses cstat var env out lt lt Basis statuses lt lt cstat lt lt endl catch env out lt lt Maximum bound violation lt lt cplex getQuality IloCplex MaxPrimalInfeas lt lt endl catch IloException amp e cerr lt lt Concert exception caught lt lt e lt lt endl catch cerr lt lt Unknown exception caught lt lt endl env end return 0 END main static void usage const char progname cerr lt lt Usage lt lt progname lt lt filename algorithm lt lt endl cerr lt lt where filename is a file with extension lt lt endl cerr lt lt MPS SAV or LP lower case is allowed lt lt endl cerr and algorithm is one of the letters endl cerr default lt lt endl cerr lt lt primal simplex lt lt endl cerr lt lt d dual simplex lt lt endl cerr lt lt b barrier lt lt endl cerr lt lt h barrier with crossover lt lt endl cerr lt lt n netwo
123. lex warning 96 CPX CPXaddcols routine 107 109 112 CPXaddrows routine 107 109 112 132 CPXboundsa routine 139 CPXchgcoeflist routine 107 109 112 CPXcloseCPLEX routine 107 113 123 132 CPXcopylp routine 107 108 109 113 132 O O O Q00000 O ILOG CPLEX 8 1 INDEX CPXcreateprob routine 107 123 132 CPXfreeprob routine 107 113 123 132 CPXgeterrorstring routine 112 113 CPXgetob jval routine 132 CPXlpopt routine 112 132 138 CPXmsg routine 106 CPXnewcols routine 107 109 112 CPXnewrows routine 107 109 112 CPXopenCPLEX routine 106 112 123 132 CPXreadcopyprob routine 107 123 CPXsetintparam routine 112 CPXsolution routine 112 132 CPXwriteprob routine 111 113 132 138 C continued create model 93 creating algorithm object 69 72 automatic log file 44 binary problem representation 111 constraint 73 environment 132 environment object 66 72 model I1oModel 67 model object 72 objective function 73 79 optimization model 67 68 problem files 47 problem object 107 132 solution files 48 SOS 79 variable 79 D data entering 37 entry options 14 deleting constraints 59 problem options 59 variables 59 directory GETTING STARTED 143 INDEX installation structure 27 display Interactive Optimizer command 38 57 display options 38 problem 38 bounds 42 constraints 41 display problem options 38 names 40 41 stats 39 syntax 39 sensitivity 46
124. ment and then turns on the ILOG CPLEX screen indicator CPX_PARAM_SCRIND Next it sets the simplex display level CPX_PARAM_SIMDISPLAY to 2 to indicate iteration by iteration output so that the progress of each iteration of the hybrid optimizer can be observed Setting this parameter to 2 is not generally recommended the example does so only for illustrative purposes The example creates a problem object by a call to CPXcreateprob Then the network data is copied via a call to CPXcopylp After the network data is copied the parameter CPX PARAM LPMETHOD is set to CPX NET and the routine CPX1popt is called to solve the network part of the optimization problem using the network optimizer The objective value of this problem is retrieved by CPXgetobjval Then the extra rows are added by calling CPXaddrows For convenience the total number of nonzeros in the rows being added is stored in an extra element of the array rmatbeg and this element is passed for the parameter nzcnt The name arguments to CPXaddrows are NULL since no variable or constraint names were defined for this problem After the CPXaddrows call parameter PARAM LPMETHOD is set to _ DUAL and the routine CPX1popt is called to re optimize the problem using the dual simplex optimizer After re optimization CPXsolution is called to determine the solution status the objective value and the primal solution NULL is passed for th
125. modeling objects that are extracted one by one when you extract an optimization model to IloCplex So extractables are characterized by the possibility of being extracted to algorithms such as 11oCplex In fact they all are inherited from the class IloExtractable In other words I1oExtractable is the base class of all classes of extractables or modeling objects ILOG CPLEX 8 1 GETTING STARTED 67 THE ANATOMY CONCERT TECHNOLOGY APPLICATION 68 The most fundamental extractable class is 110Mode1 Objects of this class are used to describe a complete optimization model that can later be extracted to an IloCplex object You create a model by constructing a variable of type 11o0Mode1 For example to construct a modeling object named model within an existing environment named env you would do the following IloModel model env At this point we would like to point out that the environment is passed as a parameter to the constructor There is also a constructor that does not use the environment parameter but this constructor creates an empty handle the handle corresponding to a NULL pointer Empty handles cannot be used for anything but for assigning other handles to them We mention this because it is a common mistake to try to use empty handles for other things Once an 11oModel object has been constructed it is populated with the extractables that define the optimization model The most important classes here are IloNum
126. mputer which you can find by searching in it for Compiler options and use in your applications that call CPLEX Building CPLEX Callable Library Applications on Win32 Platforms Building a CPLEX application using MS Visual C Integrated Development Environment or the MS Visual C command line compiler are explained here Microsoft Visual C IDE To make a CPLEX Callable Library application using Visual first create or open a project in the Visual C Integrated Development Environment IDE Project files are provided for each of the examples found in the directory examples msvc6 lt libformat gt and examples msvc6 lt libformat gt For details on the build process refer to the information file msvc htm1 which is found in the top of the installed CPLEX directory structure Note The distributed application must be able to locate cp1ex81 d11 at run time Microsoft Visual Command Line Compiler If the Visual command line compiler is used outside of the IDE the command should resemble the following example The example command assumes that the file cplex81 1ib is in the current directory with the source file 1pex1 c and that the line in ILOG CPLEX 8 1 GETTING STARTED 105 ILOG CPLEX WORKS the source file include lt ilcplex cplex h gt correctly points to the location of the include file or else has been modified to do so or that the directo
127. n the part of the above example denoted by we catch all other exceptions with the statement catch Doing so is good practice as it assures that no exception is unhandled ILOG CPLEX 8 1 GETTING STARTED 71 BUILDING AND SOLVING SMALL LP MODEL IN Building and Solving a Small LP Model in C 72 A complete example of building and solving a small LP model can now be presented This example demonstrates General Structure of a CPLEX Concert Technology Application Modeling by Rows Modeling by Columns Modeling by Nonzero Elements Example ilolpex1 cpp which is one of the example programs in the standard CPLEX distribution is an extension of the example presented in Introducing ILOG CPLEX It shows three different ways of creating a Concert Technology LP model how to solve it using IloCplex and how to access the solution Here is the problem that the example optimizes Maximize X 2x subject to X x lt 20 X 3X5 X3 lt 30 with these bounds 0 lt x 40 0 Ex lt 0 lt lt General Structure of a CPLEX Concert Technology Application The first operation is to create the environment object env and the last operation is to destroy it by calling env end The rest of the code is enclosed in a try catch clause to gracefully handle any errors that may occur First the example creates the model object and after checking the correctness of command line par
128. nd by writing an LP format problem file ILOG CPLEX 8 1 GETTING STARTED 49 2 FEAT eg e EST WRITING PROBLEM AND SOLUTION FILES write example lp mps Writing Basis Files Another optional file format is BAS Unlike the LP and MPS formats this format is not used to store a description of the problem statement Rather it is used to store information about the solution to a problem information known as a basis Even after changes are made to the problem using a prior basis to jump start the optimization can speed solution time considerably A basis can be written only after a problem has been solved Try this now with the following command write example bas In response ILOG CPLEX displays a confirmation message like this Basis written to file example bas When a very large problem is being solved by the primal or dual simplex optimizer a file with the format extension xxx is automatically written after every 50 000 iterations a frequency that can be adjusted by the set simplex basisinterval command This periodically written basis can be useful as insurance against the possibility that a long optimization may be unexpectedly interrupted due to power failure or other causes because the optimization can then be restarted using this advanced basis Using Path Names A full path name may also be included to indicate on which drive and directory any file should be saved The following might be a vali
129. nd can be edited with any text editor Re Solving You may re solve the problem by reissuing the opt imize command ILOG CPLEX restarts the solution process from the previous optimal basis and thus requires zero iterations If you do not wish to restart the problem from an advanced basis use the set advance command to turn off the advanced start indicator Remember that a problem must be present in memory entered via the enter command or read from a file before you issue the optimize command Using Alternative Optimizers In addition to the optimize command ILOG CPLEX can use the primal simplex optimizer primopt command the dual simplex optimizer t ranopt command the barrier optimizer baropt command and the network optimizer netopt command Many problems can be solved faster using these alternative optimizers which are described in more detail in the CPLEX User s Manual If you want to solve a mixed integer programming problem the optimize command is equivalent to the mipopt command Interrupting the Optimization Process Our short example was solved very quickly However larger problems particularly mixed integer problems can take much longer Occasionally it may be useful to interrupt the optimization process ILOG CPLEX allows such interruptions if you use cont rol c The control and c keys must be pressed simultaneously Optimization is interrupted and ILOG CPLEX 8 1 GETTING STARTED SOLVING A PROBLEM
130. ng at all has been determined at this point Even more detailed information about the termination of the solve call is available through method IloCplex getCplexStatus Querying Results After successfully solving the optimization problem you probably are interested in accessing the solution The following methods can be used to query the solution value for a variable or a set of variables IloNum IloCplex getValue IloNumVar var const void IloCplex getValues IloNumArray val const IloNumVarArray var const For example IloNum vall cplex getValue x1 stores the solution value for the modeling variable x1 in variable 11 Other methods are available for querying other solution information For example the objective function value of the solution can be accessed using IloNum objval cplex getObjValue ILOG CPLEX 8 1 GETTING STARTED THE ANATOMY A CONCERT TECHNOLOGY APPLICATION Handling Errors Concert Technology provides two lines of defense for dealing with error conditions suited for addressing two kind of errors The first kind covers simple programming errors Examples of this kind are trying to use empty handle objects or passing arrays of incompatible lengths to functions This kind of error is usually an oversight and should not occur in a correct program In order not to pay any runtime cost for correct programs asserting such conditions the conditions are checked using assert statement
131. ng the contents of a directory or printing the contents of a file or as complex as starting a text editor to modify a file Anything that can be entered on one line after the operating system prompt can also be executed from within ILOG CPLEX However this command differs from other ILOG CPLEX commands in that it must be entered on a single line No prompt will be issued In addition the operating system may fail to carry out the 10 10 14 11 ld 11 11 34 32 LI 32 32 232 32 afiro mps cplex cplex log example example bas example lp example2 FEAT eg e AEST command if insufficient memory is available In that case no message is issued by the operating system and the result is a return to the CPLEX gt prompt Summary The general syntax for the xecute command is xecute command line Quitting ILOG CPLEX When you are finished using ILOG CPLEX and want to leave it type quit If a problem has been modified be sure to save the file before issuing a quit command ILOG CPLEX will not prompt you to save your problem ILOG CPLEX 8 1 GETTING STARTED 61 QUITTING ILOG CPLEX 62 ILOG CPLEX 8 1 GETTING STARTED Concert Technology Tutorial for C Users This tutorial shows you how to write C programs using CPLEX with Concert Technology In this chapter you will learn about The Design of CPLEX in Concert Technology penon Compiling and Link
132. nts However before you start entering the constraints you must indicate that the subsequent lines are constraints by typing subject to or st These terms can be placed alone on a line or on the same line as the first constraint if separated by at least one space Now you can type in the constraints in the following way st x2 x3 lt 20 1 3x2 x3 lt 30 Constraint Names In this simple example it is easy to keep track of the small number of constraints but for many problems it may be advantageous to name constraints so that they are easier to identify You can do so in ILOG CPLEX by typing a constraint name and a colon before the actual constraint If you do not give the constraints explicit names ILOG CPLEX will give them the default names c1 c2 cn Inthe example if we want to call the constraints time and labor for example we enter the constraints like this st time x1 x2 x3 lt 20 labor xl 3x2 x3 lt 30 Constraint names are subject to the same guidelines as variable names They must have no more than 16 characters consist of only allowed characters and not begin with a number a period or the letter e followed by a positive or negative number or another e Objective Function Names The objective function can be named in the same manner as constraints The default name for the objective function is ob j ILOG CPLEX assigns this name if no other is entered Bounds Finally
133. o obtain solution info n goto TERMINATE printf Solution status d solution method d n solnstat solnmethod D ILOG CPLEX 8 1 GETTING STARTED 127 READING A PROBLEM FROM FILE EXAMPLE LPEX2 C 128 if solntype CPX_NO_SOLN fprintf stderr Solution not available n goto TERMINATE status CPXgetobjval env lp amp objval if status 4 fprintf stderr Failed to obtain objective value n goto TERMINATE printf Objective value 10g n objval The size of the problem should be obtained by asking CPLEX what the actual size is cur_numrows and cur_numcols store the current number of rows and columns respectively cur_numcols CPXgetnumcols env 1 cur_numrows CPXgetnumrows env 1 Retrieve basis if one is available if solntype CPX_BASIC_SOLN cstat int malloc cur_numcols sizeof int rstat int malloc cur_numrows sizeof int if cstat NULL rstat NULL fprintf stderr No memory for basis statuses n goto TERMINATE status CPXgetbase env lp cstat rstat if status fprintf stderr Failed to get basis error d n status goto TERMINATE else printf No basis available n Retrieve solution vector x double malloc cur_numcols sizeof double if x NULL fprintf stderr No memory for solution Wn
134. oblem This is done by creating a variable of type IloCplex For example to create an object named 1 do the following ILOG CPLEX 8 1 GETTING STARTED 69 i o D E Q 2 5 e lt THE ANATOMY CONCERT TECHNOLOGY APPLICATION 70 IloCplex cplex env again using the environment env as parameter The CPLEX object can then be used to extract the model to be solved This can be done by calling cplex extract model However we recommend a shortcut that performs the construction of the cplex object and the extraction of the model in one line IloCplex cplex model This works because the modeling object model contains within it the reference to the environment named env After this line object 1 is ready to solve the optimization problem described by model Solving the model is done by calling cplex solve This method returns an 1 1 value where IloTrue indicates that cplex successfully found a feasible yet not necessarily optimal solution and 1 1 indicates that no solution was found More precise information about the outcome of the last call to method solve can be obtained by calling cplex getStatus The returned value tells you what CPLEX found out about the model whether it found the optimal solution or only a feasible solution whether it proved the model to be unbounded or infeasible or whether nothi
135. oefficient is also displayed for reference Objective function sensitivity analysis is useful to determine how sensitive the optimal solution is to the cost or profit associated with each variable Similarly to view sensitivity analysis of the right hand side type the command display sensitivity rhs ILOG CPLEX 8 1 GETTING STARTED WRITING PROBLEM AND SOLUTION FILES For our example ILOG CPLEX displays the following ranges for sensitivity analysis of the right hand side RHS RHS Sensitivity Ranges Constraint Name Dual Price Down Current Up cl 2 7500 36 6667 20 0000 tinfinity c2 0 2500 140 0000 30 0000 100 0000 ILOG CPLEX displays each constraint its dual price and a range over which its right hand side coefficient can vary without changing the optimal basis The current value of each RHS coefficient is also displayed for reference Right hand side sensitivity information is useful for determining how sensitive the optimal solution and resource values are to the availability of those resources ILOG CPLEX can also display lower bound sensitivity ranges with the command display sensitivity lb and upper bound sensitivity with the command display sensitivity ub FEAT ez e AEST Summary Display sensitivity analysis characteristics by entering a command with the syntax display sensitivity identifier Writing Problem and Solution Files The problem or its solution can be saved by using th
136. ollowing message appears to tell you more about the use and syntax of the primopt command The PRIMOPT command solves the current problem using a primal simplex method or crosses over to a basic solution if a barrier solution exists Syntax A problem must exist in memory from using either the ENTER or READ command in order to use the PRIMOPT command Sensitivity information dual price and reduced cost information as well as other detailed information about the solution can be viewed using the DISPLAY command after a solution is generated Summary The syntax for the help command is help command name ILOG CPLEX 8 1 GETTING STARTED 33 1do 1 AOZIWI ENTERING PROBLEM Entering a Problem 34 Most users with larger problems enter problems by reading data from formatted files That practice is described in Reading Problem Files on page 51 For now let s enter a smaller problem from the keyboard by using the enter command The process is described step by step in the topics Entering the Example Problem Using the LP Format Entering Data Entering the Example Problem As an example we will use the following problem Maximize X 2x 3x subject to X X x lt 20 X 3x x3 lt 30 with these bounds 0 x 40 0 lt x lt 00 0 lt lt This problem has three variables x and and two less
137. om gt to lt using the sense option of the change command At the CPLEX gt prompt type change sense ILOG CPLEX prompts you to specify a constraint There are two ways of specifying this constraint if you know the name for example new3 you can enter the name if you do not know the name you can specify the number of the constraint In this example the number is 3 for the new3 constraint Try the first method and type Change sense of which constraint new3 Sense of constraint new3 is gt ILOG CPLEX 8 1 GETTING STARTED 57 CHANGING A PROBLEM 58 ILOG CPLEX tells you the current sense of the selected constraint All that is left now is to enter the new sense which can be entered as lt gt or You can also type simply lt interpreted as 3X or gt interpreted as 2 The letters 1 g and e are also interpreted as lt gt and respectively New sense lt or gt or z lt Sense of constraint new3 changed to The sense of the constraint has been changed The sense of the objective function may be changed by specifying the objective function name its default is obj or the number 0 when ILOG CPLEX prompts you for the constraint You are then prompted for a new sense The sense of an objective function can take the value maximum or minimum or the abbreviation max or min Changing Bounds When the example was entered bounds were set specifically only for the variable x1 T
138. plex ttt eee 69 Querying Results a toe Ett tu b ette eid pe i 70 Handling Errors A e qa 71 Building and Solving a Small LP Model in 72 General Structure of a CPLEX Concert Technology 72 Modeling by ROWS cos rm Vd vu es pepe genis e grep ics 73 Modelinig by Gol mh s rocket ccc eoe s tre deed S etx io E RITE hes deci P 73 Modeling by Nonzero Elements 74 Gomplete Progtam 2 REE Abd ele ood 74 Writing and Reading Models and Files 79 ILOG CPLEX 8 1 GETTING STARTED 7 TABLE OF CONTENTS Chapter 4 Chapter 5 Selecting an Optimizer 80 Reading a Problem from a File Example 1 2 80 Reading the Model froma 81 Selecting the eects 81 Accessing Basis Information 81 Querying Quality 0000 cette eee 82 Complete Program ue ae fig Wve aoe RR he ence Dds Wa eee a 82 Modifying and 1 2 84 Modifying an Optimization Problem Example
139. populateByRow IloMPModeler model TloNumVar var IloRange rng throws IloException double lb 0 0 0 0 0 0 double ub 40 0 Double MAX_VALUE Double MAX_VALUE IloNumVar x model numVarArray 3 lb ub var 0 x double objvals 1 0 2 0 3 0 model addMaximize model scalProd x objvals rng 0 new IloRange 2 rng 0 0 model addLe model sum model prod model prod model prod rng 0 1 model addLe model sum model prod model prod model prod static void populateByColumn IloMPModeler model TloNumVar var IloRange rng throws IloException ILOG CPLEX 8 1 GETTING STARTED COMPLETE CODE LPEX1 JAVA IloObjective obj model addMaximize rng 0 new IloRange 2 rng 0 0 model addRange Double MAX VALUE 20 0 rng 0 1 model addRange Double MAX VALUE 30 0 IloRange r0 rng 0 0 IloRange r1 rng 0 1 var 0 new IloNumVar 3 var 0 0 model numVar model column obj 0 and model column r0 1 0 and model column r1 0 0 0 40 0 0 1 model numVar model column obj 2 0 model column r0 0 and model column rl 3 0 0 0 Double MAX VALUE var 0 2 model numVar model column obj 3 0 model column r0 0 and model column rl 0 0 0 Double MAX VALUE static void populateByNonzero IloMPModeler model IloNumVar v
140. prod 3 0 x 1 cplex prod 0 x 2 30 0 if cplex solve cplex out println Solution status cplex getStatus cplex out println Solution value cplex getObjValue double val cplex getValues x int ncols cplex getNcols for int J 0 j lt ncols 3 cplex out println Column j Value val j 1 catch IloException System err println Concert exception caught Using the Callable Library Here is a C program using the CPLEX Callable Library to solve the example model An expanded version of this example is discussed in detail in Chapter 5 Callable Library Tutorial include lt ilcplex cplex h gt include lt stdlib h gt 18 ILOG CPLEX 8 1 GETTING STARTED SOLVING AN LP WITH CPLEX TECHNOLOGY include lt string h gt define NUMROWS 2 define NUMCOLS 3 define NUMNZ 6 int main int argc char argv int status 0 CPXENVptr env NULL CPXLPptr 1 NULL double obj NUMCOLS double lb NUMCOLS double ub NUMCOLS double x NUMCOLS int rmatbeg NUMROWS int rmatind NUMNZ double rmatval NUMNZ double rhs NUMROWS char sense NUMROWS int solstat double objval env CPXopenCPLEX amp status if env NULL char errmsg 1024 fprintf stderr Could not open CPLEX environment Mn CPXgeterrorstring env status errmsg fprintf stderr s errmsg
141. r Failed to optimize LP n goto TERMINATE status CPXgetobjval env lp amp objval if status fprintf stderr CPXgetobjval failed n goto TERMINATE printf After network optimization objective is 10g n objval Now add the extra rows to the problem status CPXaddrows env lp 0 ROWSCOMP Armatbeg ROWSCOMP Arhs Asense Armatbeg Armatind Armatval NULL NULL if status fprintf stderr CPXaddrows failed n goto TERMINATE Because the problem is dual feasible with the rows added using the dual simplex method is indicated Status CPXsetintparam env CPX PARAM LPMETHOD CPX ALG DUAL if status fprintf stderr Failed to set the optimization method error d n status goto TERMINATE status CPXlpopt env lp if status fprintf stderr Failed to optimize LP n goto TERMINATE Status CPXsolution env lp amp lpstat amp objval x NULL NULL NULL if sLatus fprintf stderr CPXsolution failed n goto TERMINATE printf Solution status dMn lpstat ILOG CPLEX 8 1 GETTING STARTED ADDING ROWS TO A PROBLEM EXAMPLE LPEX8 C printf Objective value g n objval printf Solution is n for j 0 j lt COLSORIG j printf x d gWn j3 xl31 Put the problem and basis into a SAV file to use it in the Interactive Optimizer and see if problem is correct status CPXwritepro
142. r how to start it how to enter problems and data how to read and save files how to modify objective functions and constraints and how to display solutions and analytical information Chapter 3 Concert Technology Tutorial for C Users describes the same activities using the classes in the C version of the CPLEX Concert Technology Library Chapter 4 Concert Technology for Java Users describes the same activities using the classes in the Java version of the CPLEX Concert Technology Library Chapter 5 Callable Library Tutorial describes the same activities using the routines in the ILOG CPLEX Callable Library All tutorials use examples that are delivered with the standard distribution Notation in this Manual To make this manual easier to use we ve followed a few conventions in notation and names Important ideas are italicized the first time they appear Text that is entered at the keyboard or displayed on the screen and commands and their options available through the Interactive Optimizer appear in this typeface for example set preprocessing aggregator n Entries that you must fill in appear in this typeface for example write filename ILOG CPLEX 8 1 GETTING STARTED 21 RELATED DOCUMENTATION The names of C routines and parameters in the ILOG CPLEX Callable Library begin with the names of and Java classes in the CPLEX Concert Technology Library begin with 110 and both appearin this typ
143. r generate problem by row lt lt endl cerr lt lt generate problem by column endl cerr n generate problem by nonzero lt lt 1 cerr Exiting endl END usage To populate by row we first create the variables and then use them to create the range constraints and objective static void populatebyrow IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv x add IloNumVar env 0 0 40 0 x add IloNumVar env x add IloNumVar env model add IloMaximize env x 0 2 1 3 x 2 c add x 0 x 1 x 2 lt 20 76 ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN c add x 0 3 x 1 x 2 lt 30 model add c END populatebyrow To populate by column we first create the range constraints and the objective and then create the variables and add them to the ranges and objective using column expressions static void populatebycolumn IloModel model IloNumVarArray x IloRangeArray c IloEnv env model getEnv IloObjective obj IloMaximize env c add IloRange env IloInfinity 20 0 c add IloRange env IloInfinity 30 0 x add IloNumVar obj 1 0 0 71 0 c 11 1 0 0 0 40 0 x add IloNumVar obj 2 0 c 0 1 0 c 11 3 0 x add IloNumVar obj 3 0 c 0 1 0 c 1 1 0 model add obj model add c E
144. r settings for compilation and linking Compiling and Linking Your Own Applications The source files for the examples and the makefiles provide guidance for how your own application can call CPLEX The following chapters give more specific information on the necessary header files for compilation and how to link CPLEX and Concert Technology library files into your application Chapter 3 Concert Technology Tutorial for C Users contains information and platform specific instructions for compiling and linking the Concert Technology Library for C users Chapter 4 Concert Technology for Java Users contains information and platform specific instructions for compiling and linking the Concert Technology Library for Java users Chapter 5 Callable Library Tutorial contains information and platform specific instructions for compiling and linking the Callable Library ILOG CPLEX 8 1 GETTING STARTED 29 USING THE COMPONENT LIBRARIES 30 ILOG CPLEX 8 1 GETTING STARTED Interactive Optimizer Tutorial 1 This step by step tutorial introduces the major features of the ILOG CPLEX Interactive Optimizer In this chapter you will learn about Starting ILOG CPLEX Using Help Entering a Problem Displaying a Problem Solving a Problem Performing Sensitivity Analysis Writing Problem and Solution Files Reading Problem Files Setting ILOG CPLEX Parameters Adding
145. ram follows You can also view it online in the file ilolpex1 cpp E nunc D P Ede ed p Ses File examples src ilolpexl cpp Version 8 1 Rl eS E Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products Ma Mrz a ee ee c MD PME RE ilolpexl cpp Entering and optimizing a problem Demonstrates different ILOG CPLEX 8 1 GETTING STARTED BUILDING AND SOLVING A SMALL LP MODEL IN methods for creating a problem The user has to choose the method on the command line 7 ilolpexl r generates the problem by adding rows ilolpexl c generates the problem by adding columns ilolpexl n generates the problem by adding a list of coefficients include lt ilcplex ilocplex h gt ILOSTLBEGIN static void usage const char progname populatebyrow IloModel model IloNumVarArray var IloRangeArray con populatebycolumn IloModel model IloNumVarArray var IloRangeArray con populatebynonzero IloModel model IloNumVarArray var IloRangeArray con int main int argc char argv IloEnv env try IloModel model env if arge 2 argv 1 0 strchr rcn argv 1 1 NULL usage argv 0 throw 1 penon IloNumVarArray var IloRangeArray con env i D 4 o Q 2 5
146. res certain common characteristics regardless of its apparent uniqueness The following steps can help you minimize development time and get maximum performance from your programs 1 Prototype the Model Identify the Routines to be Called Test Procedures in the Application Assemble the Data Choose an Optimizer Observe Good Programming Practices Debug Your Program Test Your Application Use the Examples Prototype the Model Create a small version of the model to be solved An algebraic modeling language is sometimes helpful during this step Identify the Routines to be Called By separating the application into smaller parts you can easily identify the tools needed to complete the application Part of this process consists of identifying the Callable Library routines that will be called ILOG CPLEX 8 1 GETTING STARTED CREATING SUCCESSFUL CALLABLE LIBRARY APPLICATION In some applications the Callable Library is a small part of a larger program In that case the only ILOG CPLEX routines needed may be for problem creation optimizing obtaining results In other cases the Callable Library is used extensively in the application If so Callable Library routines may also be needed to modify the problem set parameters determine input and output messages and files query problem data Test Procedures in the Application Itis often possible to test the procedures o
147. ries containing these files have been added to the environment variables LIB and INCLUDE respectively cl lpexl c cplex81 1lib This command will create the executable file 1pex1 exe Using Dynamic Loading Some projects require more precise control over the loading and unloading of DLLs For information on loading and unloading DLLs without using static linking please refer to the compiler documentation or to a book such as Advanced Windows by Jeffrey Richter from Microsoft Press If this is not a requirement the static link implementations mentioned above are easier to use Building Applications that Use the CPLEX Parallel Optimizers When compiling and linking programs that use the CPLEX Parallel Optimizers it is especially important to review the relevant flags for the compiler and linker These are found in the makefile provided with UNIX distributions or in the sample project files provided with Windows distributions We recommend you also review the section on Using Parallel Optimizers in the ILOG CPLEX User s Manual for important details pertaining to each specific parallel optimizer How ILOG CPLEX Works 106 When your application uses routines of the ILOG CPLEX Callable Library it must first open the ILOG CPLEX environment then create and populate a problem object before it solves a problem Before it exits the application must also free the problem object and release the ILOG CPLEX environment The following sections
148. rk simplex lt lt endl cerr lt lt 5 sifting lt lt endl cerr lt lt c concurrent endl cerr Exiting endl END usage Modifying and Reoptimizing In many situations the solution to a model is only the first step One of the important features of Concert Technology is the ability to modify and then re solve the model even after it has been extracted and solved one or more times 84 ILOG CPLEX 8 1 GETTING STARTED MODIFYING AN OPTIMIZATION PROBLEM EXAMPLE 11 A look back to examples ilolpex1 cpp and ilolpex2 cpp reveals that we have been performing modification operations on models all along Each time we add an extractable to a model we are changing the model However those examples made all such changes before the model was extracted to cplex Concert Technology maintains a link between the model and all 1 1 objects that may have extracted it This link is known as notification Each time a modification of the model or one of its extractables occurs the change is notified to the IloCplex objects that extracted the model They then track the modification in their internal representations Moreover 11oCplex tries to maintain as much information from a previous solution as is possible and reasonable when the model is modified in order to have a better start when solving the modified model In particular when solving LPs or QPs with a simplex method IloCple
149. ry together with the ILOG CPLEX database make up the ILOG CPLEX core The core becomes associated with your application through Callable Library routines The ILOG D ILOG CPLEX 8 1 GETTING STARTED 103 COMPILING AND LINKING CALLABLE LIBRARY APPLICATIONS CPLEX environment and all problem defining data are established inside the ILOG CPLEX core User Written Application CPLEX Callable Library CPLEX database Figure 5 1 View of the CPLEX Callable Library The ILOG CPLEX Callable Library includes several categories of routines optimization and result routines for defining a problem optimizing it and getting the results utility routines for addressing application programming matters problem modification routines to change a problem once it has been created within the ILOG CPLEX database problem query routines to access information about a problem once it has been created file reading and writing routines to move information from the file system into your application or out of your application to the file system parameter setting and query routines to access and modify the values of control parameters maintained by ILOG CPLEX Compiling and Linking Callable Library Applications 104 Each Callable Library is distributed as a single library file Libcplex a or cplex81 1ib Use of the library file is simil
150. s The checking is disabled for production runs if compiled with the DNDEBUG compiler option The second kind of error is more complex and cannot generally be avoided by correct programming An example is memory exhaustion The data may simply require too much memory even when the program is correct This kind of error is always checked at runtime In cases where such an error occurs Concert Technology throws a C exception In fact Concert Technology provides a hierarchy of exception classes that all derive from the common base class IloExcept ion Exceptions derived from this class are the only kind of exceptions that are thrown by Concert Technology The exceptions thrown by IloCplex objects all derive from class IloAlgorithm Exception or IloCplex Exception e To gracefully handle exceptions in a Concert Technology application we advise including all Miss 5 of the code in a try catch clause 5 8 4 loEnv env lt o try go 5 catch IloException amp D cerr lt lt Concert Exception lt lt lt lt endl um catch 4 dn cerr Other Exception endl env end Note The construction of the environment comes before the t xy catch clause In case of an exception env end must still be called To protect against failure during the construction of the environment another t xy catch clause may be added If code other than Concert Technology code is used i
151. s allocated by CPXcreateprob if necessary if lp NULL status CPXfreeprob env amp lp it status 4 IN fprintf stderr CPXfreeprob failed error code status Free up the CPLEX environment if necessary if env NULL status CPXcloseCPLEX amp env Note that CPXcloseCPLEX produces no output so the only way to see the cause of the error is to use CPXgeterrorstring For other CPLEX routines the errors will be seen if the CPX PARAM SCRIND indicator is set to CPX ON if status P 4 char errmsg 1024 fprintf stderr Could not close CPLEX environment n CPXgeterrorstring env status errmsg fprintf stderr Ss errmsg ILOG CPLEX 8 1 GETTING STARTED D BUILDING AND SOLVING A SMALL LP MODEL IN 118 return status END main This simple routine frees up the pointer ptr and static void free and null char ptr if ptr NULL free ptr ptr NULL END free and null static void usage char progname fprintf fprintf fprintf fprintf fprintf fprintf stderr stderr stderr stderr stderr stderr END usage These functions linear program Maximize obj 1 2 Subject xl x2 x3 lt 20 xl 3 x2 x3 lt 30 Bounds 0 lt 1 lt 40 cis c2 End define N
152. s are created and installed in the existing ranges and objective These newly created variables are introduced into the ranges and the objective by means of column objects which are implemented in the class IloColumn Objects of this class are created with the methods IloCplex column and can be linked together with the method IloColumn and to form aggregate IloColumn objects An IloColumn object created with the method IloCplex column contains information about how to use this column to introduce a new variable into an existing modeling object For example if obj is an I100bjective object cplex column obj 2 0 creates an IloColumn object containing the information to install a new variable in the expression of the 1100bjective object obj with a linear coefficient of 2 0 Similarly for an IloRange constraint rng the method call cplex column rng 1 0 creates an I1oColumn object containing the information to install a new variable into the expression of rng as a linear term with coefficient 1 0 When using a modeling by column approach new columns are created and installed as variables in all existing modeling objects where they are needed To do this with Concert Technology you create 11oColumn object for every modeling object in which you want ILOG CPLEX 8 1 GETTING STARTED 97 2 o t lt 5 lt COMPLETE CODE LPEX1 JAVA to install a new variable and link th
153. s include fragmentation of memory unnecessary compiler and linker options and coding approaches that slow the program without causing it to give incorrect results Use the Examples The ILOG CPLEX Callable Library is distributed with a variety of examples that illustrate the flexibility of the Callable Library The C source of all examples is provided in the standard distribution For explanations about the examples of quadratic programming problems QPs mixed integer programming problems MIPs and network flows see the ILOG CPLEX User s Manual Explanations of the following examples of LPs appear in this manual 1 1 illustrates various ways of generating a problem object lpex2 c demonstrates how to read a problem from a file optimize it via a choice of several means and obtain the solution lpex3 c demonstrates how to add rows to a problem object and reoptimize We strongly encourage you to compile link and run all of the examples provided in the standard distribution Building and Solving a Small LP Model in C The example 1pex1 c shows you how to use problem modification routines from the ILOG CPLEX Callable Library in three different ways to build a model The application in the example takes a single command line argument that indicates whether to build the constraint D ILOG CPLEX 8 1 GETTING STARTED 111 BUILDING AND SOLVING A SMALL LP MODEL IN 112 matri
154. s with settings that differ from the default values can be displayed with the command display settings changed For a description of all parameters and their default values see the Parameter Table in the ILOG CPLEX Reference Manual For examples of how to set parameters see the ILOG CPLEX User s Manual ILOG CPLEX also accepts customized system parameter settings via a parameter specification file See LOG CPLEX User s Manual for a description of the parameter specification file and its use FEAT eg e EST Adding Constraints and Bounds If you wish to add either new constraints or bounds to your problem use the add command This command is similar to the enter command in the way it is used but it has one important difference the enter command is used to start a brand new problem whereas the add command only adds new information to the current problem Suppose that in the example you need to add a third constraint X 2 2 3x3 2 50 You may do either interactively or from a file Adding Interactively Type the command then enter the new constraint on the blank line After validating the constraint the cursor moves to the next line You are in an environment identical to that of the enter command after having issued subject to At this point you may continue to add constraints or you may type bounds and enter new bounds for the problem For the present example type end to exit the add comm
155. se LP format throughout this tutorial 5 The problem should be entered in the following order o 1 Objective Function 3 0 2 Constraints 2 5 3 3 Bounds Objective Function Before entering the objective function you must state whether the problem is a minimization or maximization For this example you type maximize xl 2x2 3x3 You may type minimize or maximize on the same line as the objective function but you must separate them by at least one space Variable Names In the example the variables are named simply x1 x2 x3 but you can give your variables more meaningful names such as cars or gallons The only limitations on variable names in LP format are that the names must be no more than 255 characters long and use only the alphanumeric characters a z A Z 0 9 and certain symbols amp 9 Any line with more than 510 characters is truncated A variable name cannot begin with a number or a period and there is one character combination that cannot be used the letter e or E alone or followed by a number or another e since this notation is reserved for exponents Thus a variable cannot be named e24 nor e9cats nor eels nor any other name with this pattern This restriction applies only to problems entered in LP format ILOG CPLEX 8 1 GETTING STARTED 35 ENTERING PROBLEM 36 Constraints Once you have entered the objective function you can move on to the constrai
156. sites for its products Customer Support For technical support of ILOG CPLEX you should contact your local distributor or if you are a direct ILOG customer contact the nearest regional office Region E mail Telephone Fax France cplexsupportGilog r 0800092771 33 0 1 49083510 num ro vert 33 0 1 49 08 35 62 Germany cplex support ilog de 49 6172 40 6033 49 6172 40 60 10 Spain cplex support ilog es 34 91 710 2480 34 91 372 9976 United Kingdom cplex support ilog co uk 44 0 1344 661600 44 0 1344 661601 Other European cplex support ilog fr 33 0 1 49 08 35 62 33 0 1 49 08 35 10 countries Japan cplex support ilog co jp 81 3 5211 5770 81 3 5211 5771 Singapore cplex support ilog com sg 65 6773 06 26 65 6773 04 39 USA cplex support ilog com 1 877 ILOG TECH 1 650 567 8001 1 877 456 4832 toll free or 1 650 567 8080 We encourage you to use e mail for faster better service Web Site The CPLEX Web site at http www ilog com products cplex offers product descriptions press releases and contact information It lists services such as training maintenance technical support and outlines special programs In addition it links you to an ftp site where you can pick up examples ILOG CPLEX 8 1 GETTING STARTED 23 FOR MORE 24 INFORMATION The technical support pages contain FAQ Frequently Asked Answered Questions and the latest patches for some of our products Changes are posted in the product m
157. solution x cstat and rstat are freed Then the problem object is freed by CPX reeprob After the problem is freed the ILOG CPLEX environment is freed by CPXcloseCPLEX ILOG CPLEX 8 1 GETTING STARTED 123 D READING A PROBLEM FROM A FILE EXAMPLE LPEX2 C Complete Program The complete program follows You can also view it online in the file 1pex2 c File examples src lpex2 c Version 8 1 Copyright 1997 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products 1 2 Reading in and optimizing a problem To run this example command line arguments are required 1 2 filename method where filename is the name of the file with mps lp or sav extension method is the optimization method default primal simplex dual simplex network with dual simplex cleanup barrier with crossover barrier without crossover sifting concurrent Example lpex2 example mps Bring the CPLEX function declarations and the library header file stdio h with the following single include include lt ilcplex cplex h gt Bring in the de
158. syntax 47 settings 55 solution 45 syntax 46 specifying item ranges 40 syntax 42 displaying basic rows and columns 45 bounds 42 constraint names 40 constraints 41 nonzero constraint coefficients 39 number of constraints 39 objective function 41 optimal solution 43 parameter settings 55 post solution information 45 problem 38 problem options 38 problem part 39 problem statistics 39 sensitivity analysis 46 138 type of constraint 39 variable names 40 variables 39 DPE file format 48 DUA file format 48 dual simplex optimizer as default 42 availability 44 finding a solution 112 selecting 80 dual values accessing 45 144 ILOG CPLEX 8 1 duals 95 E EMB file format 48 enter Interactive Optimizer command 34 bounds 36 maximize 35 minimize 35 subject to 36 55 syntax 35 entering bounds 36 constraint names 36 constraints 36 example problem 34 item ranges 40 keyboard data 37 objective function 35 36 objective function names 36 problem 34 35 problem name 34 variable bounds 36 variable names 35 Environment construct 66 environment object creating 66 72 destroying 67 memory management and 67 equality constraints add to a model 94 Error NoClassDefFoundError 91 error invalid encrypted key 91 no license found 91 UnsatisfiedLinkError 91 error handling programming errors 71 runtime errors 71 testing installation 29 66 error message compiler 66 license manager 66 GETTING STARTED linker 66 example
159. t and terminates with destroying it by calling the end method The code in between is enclosed in try catch statements for error handling Reading the Model from a File The model is created by reading it from the file specified as the first command line argument argv 1 This is done using the method importModel of an IloCplex object Here the IloCplex object is used a model reader rather than an optimizer Calling importModel does not extract the model to the invoking cplex object This must be done later by calling cplex extract model We pass objects obj var and rng to importModel to be able to access the variables later on when querying results penon 5 D 4 o Q 2 5 o e lt Selecting the Optimizer The selection of the optimizer option is done in the switch statement controlled by the second command line parameter A call to setParam IloCplex RootAlg alg selects the desired 11o0Cplex Algorithm option Accessing Basis Information After solving the model by calling method solve the results are accessed in the same way as in 11 1 1 With the exception of basis information for the variables It is important to understand that not all optimizer options compute basis information and thus it cannot be queried in all cases In particular basis information is not available when the model is solved using the barrier optimizer IloCplex Barrier wi
160. t on the solution speed of your particular class of problem The ILOG CPLEX User s Manual describes the optimizers provides suggestions for maximizing performance and notes the features and algorithmic parameters unique to each optimizer Using the Parallel Optimizers On a computer with multiple CPUs the Barrier Optimizer and the MIP Optimizer are each capable of running in parallel that is they can apply these additional CPUs to the task of optimizing the model The number of CPUs used by an optimizer is controlled by the user under default settings these optimizers run in serial single CPU mode When solving small models such as those described in this document the effect of parallelism will generally be negligible On larger models the effect is ordinarily beneficial to solution speed See the section Using Parallel Optimizers in the ILOG CPLEX User s Manual for information on using CPLEX on a parallel computer Data Entry Options CPLEX provides several options for entering your problem data When using the Interactive Optimizer most users will enter problem data from formatted files CPLEX supports the industry standard MPS Mathematical Programming System file format as well as CPLEX LP format a row oriented format many users may find more natural Interactive entry using CPLEX LP format is also a possibility for small problems ILOG CPLEX 8 1 GETTING STARTED SOLVING AN LP WITH CPLEX TECHNOLOGY Data entry options
161. than or equal to constraints The enter command is used to enter a new problem from the keyboard The procedure is almost as simple as typing the problem on a page At the CPLEX gt prompt type enter A prompt appears on the screen asking you to give a name to the problem that you are about to enter Naming a Problem The problem name may be anything that is allowed as a file name in your operating system If you decide that you do not want to enter a new problem just press the lt return gt key without typing anything The CPLEX prompt will reappear without causing any action The same can be done at any CPLEX gt prompt If you do not want to complete the command simply press the return key For now type in the name example at the prompt Enter name for problem example The following message appears Enter new problem end on a separate line terminates and the cursor is positioned on a blank line below it where you can enter the new problem ILOG CPLEX 8 1 GETTING STARTED ENTERING PROBLEM You can also type the problem name directly after the enter command and avoid the intermediate prompt Summary The syntax for entering a problem is enter problem name Using the LP Format Entering a new problem is basically like typing it on a page but there are a few rules to remember These rules conform to the ILOG CPLEX LP file format and are documented in the CPLEX Reference Manual We u
162. the help command The same rules apply to all ILOG CPLEX commands You need only type enough letters of the command to distinguish it from all other commands and it does not matter whether you type upper and lower case letters Throughout this manual we use lower case letters ILOG CPLEX 8 1 GETTING STARTED USING HELP After you type the help command a list of available commands with their descriptions appears on the screen like this add add constraints to problem baropt solve using barrier algorithm change change the problem display display problem solution or parameter settings enter enter a new problem help provide information on CPLEX commands mipopt solve a mixed integer program netopt solve the problem using network method optimize solve the problem primopt solve using the primal method quit leave CPLEX read read problem or basis information from a file set set parameters tranopt solve using the dual method write write problem or solution info to a file xecute execute a command from the operating system Enter enough characters to uniquely identify commands amp options Commands can be entered partially CPLEX will prompt you for further information or as a whole To find out more about a specific command type help followed by the name of that command For example to learn more about the primopt command type help primopt Typing the full name is unnecessary Alternatively you can try hp The f
163. the primal simplex algorithm IloCplex Barrier use the barrier algorithm IloCplex Network use the network simplex algorithm for the embedded network IloCplex Sifting use the sifting algorithm IloCplex Concurrent allow CPLEX to use multiple algorithms on multiple computer processors For models only the AutoAlg Dual Primal Barrier and Network algorithms are applicable The optimizer option used for solving pure LPs and QPs is controlled by setting the root algorithm parameter This is demonstrated next in example ilolpex2 cpp Reading a Problem from a File Example ilolpex2 cpp This example shows how to read an optimization problem from a file and solve it with a specified optimizer option It prints solution information including a Simplex basis if available Finally it prints the maximum infeasibility of any variable of the solution 80 ILOG CPLEX 8 1 GETTING STARTED READING A PROBLEM FROM A FILE EXAMPLE ILOLPEX2 CPP The file to read and the optimizer choice are passed to the program via command line parameters For example this command ilolpex2 example mps d reads the file example mps and solves the problem with the dual simplex optimizer Example ilolpex2 demonstrates Reading the Model from a File Selecting the Optimizer Accessing Basis Information Querying Quality Measures The general structure of this example is the same as for example ilolpex1 cpp It starts by creating the environmen
164. the same as 1pex1 and takes the same arguments If your interest is in running one of the Java examples try make LPexl class java Djava library path bin lt platform gt classpath lib cplex jar LPexl r ILOG CPLEX 8 1 GETTING STARTED USING THE COMPONENT LIBRARIES Any of these examples should return an optimal objective function value of 202 5 Verifying Installation on Windows On a Windows machine you can follow a similar process using the facilities of your compiler interface to compile and then run any of the examples A project file for each example is provided in a format for Microsoft Visual C 6 and Visual C NET In Case of Errors If an error occurs during the make or compile step then check that you are able to access the compiler and the necessary linker loader files and system libraries If an error occurs on the next step when executing the program created by make then the nature of the error message will guide your actions If the problem is in licensing consult the ILOG License Manager User s Guide and Reference for further guidance For Windows users if the program has trouble locating cplex81 d11 make sure the DLL is stored either in the current directory or in a directory listed in your PATH environment variable o e c v r gt lt The UNIX makefile or Windows project file contains useful information regarding recommended compiler flags and othe
165. thout hyphen you will see a single variable name display problem names variables Display which variable name s 2 2 Summary You can display variable names by entering the command display problem names variables You can display constraint names by entering the command display problem names constraints Ordering Variables In the example problem there is a direct correlation between the variable names and their numbers x1 is variable 1 x2 is variable 2 etc that is not always the case The internal ordering of the variables is based on their order of occurrence when the problem is entered For example if x2 had not appeared in the objective function then the order of the variables would be x1 x3 x2 JOZIWNdO You can see the internal ordering by using the hyphen when you specify the range for the variables option The variables are displayed in the order corresponding to their internal ordering All of the options of the display command can be entered directly after the word display to eliminate intermediate steps The following command is correct for example display problem names variables 2 3 Displaying Constraints To view a single constraint within the matrix use the command and the constraint number For example type the following display problem constraints 2 The second constraint appears C2 xl 3 x2 x3 lt 30 Displaying the Object
166. thout crossover parameter IloCplex BarCrossAlg set to IloCplex NoAlg ILOG CPLEX 8 1 GETTING STARTED 81 READING PROBLEM FROM FILE EXAMPLE ILOLPEX2 CPP Querying Quality Measures Finally the program prints the maximum primal infeasibility or bound violation of the solution To cope with the finite precision of the numerical computations done on the computer IloCplex allows some tolerances by which for instance optimality conditions may be violated A long list of other quality measures is available Complete Program The complete program follows You can also view it online in the file ilolpex2 cpp I cs Se es Ac Che es File examples src ilolpex2 cpp Version 8 1 fat a Ac Cz M DM E M a eae Copyright C 1999 2002 by ILOG All Rights Reserved Permission is expressly granted to use this example in the course of developing applications that use ILOG products ilolpex2 cpp Reading in and optimizing problem To run this example command line arguments are required i e ilolpex2 filename method where filename is the name of the file with mps lp or sav extension method is the optimization method default primal simplex d dual simplex h barrier with crossover b barrier without crossover n network with dual simplex cleanup 5 sifting concurrent Example ilolpex2 example mps o inclu
167. use method importModel ILOG CPLEX 8 1 GETTING STARTED 79 SELECTING OPTIMIZER Selecting an Optimizer IloCplex treats all problems it solves as Mixed Integer Programming MIP problems The algorithm used by 11oCplex for solving MIP is known as branch amp cut referred to in some contexts as branch amp bound and is described in more detail in the ILOG CPLEX User s Manual For this tutorial it is sufficient to know that this consists of solving a sequence of LPs or QPs that are generated in the course of the algorithm The first LP or QP to be solved is known as the root while all the others are referred to as nodes and are derived from the root or from other nodes If the model extracted to the cplex object is a pure LP or QP no integer variables then it will be fully solved at the root As mentioned in Optimizer Options on page 13 various optimizer options are provided for solving LPs and QPs While the default optimizer works well for a wide variety of models IloCplex allows you to control which option to use for solving the root and for solving the nodes respectively by the following lines void IloCplex setParam IloCplex RootAlg alg void IloCplex setParam IloCplex NodeAlg alg where IloCplex Algorithm is an enumeration type It defines the following symbols with their meaning IloCplex AutoAlg allow CPLEX to choose the algorithm IloCplex Dual use the dual simplex algorithm IloCplex Primal use
168. variable from the deleted constraint appears in the objective function it may still influence the solution process If that is not what you want these variables can be explicitly removed using the delete option Summary The general syntax for the change command is change option identifier identifier2 new value Executing Operating System Commands The execute command xecute is simple but useful It is used to execute operating system commands outside of the ILOG CPLEX environment By using xecute you avoid having to save a problem and quit ILOG CPLEX in order to carry out a system function such as viewing a directory for example 60 ILOG CPLEX 8 1 GETTING STARTED QUITTINGILOG CPLEX As an example if you wanted to check whether all of the files saved in the last session are really in the current working directory the following ILOG CPLEX command shows the contents of the current directory in a UNIX operating system using the UNIX command 1s xecute ls 1 total 7448 ApIcr sr I 3258 Jul 14 r WXr Xr x 1 3783416 Apr 22 rw r r 1 3225 Jul 14 rw r r 1 145 Jul 14 rw r r 1 112 Jul 14 1 148 Jul 14 rw r r 1 146 Jul 14 After the command is executed the CPLEX gt prompt returns indicating that you are still in ILOG CPLEX Most commands that can normally be entered from the prompt for your operating system can also be entered with the xecute command The command may be as simple as listi
169. will give you the complete list Modeling variables are typically used to build expressions of type IloNumExpr for use in constraints or the objective function of an optimization model For example the expression x 0 2 x 1 3 x 2 can be created like this IloNumExpr expr cplex sum x 0 cplex prod 2 0 x 1 cplex prod 3 0 x 2 Another way of creating an object representing the same expression is to use an IloLinearNumExpr expression Here is how IloLinearNumExpr expr cplex linearNumExpr expr addTerm 1 0 x 0 expr addTerm 2 0 x 1 2 o t lt 5 lt expr addTerm 3 0 x 2 The advantage of using IloLinearNumExpr over the first way is that you can more easily build up your linear expression in a loop which is what is typically needed in more complex applications Interface IloLinearNumExpr is an extension of 11oNumExpr and thus can be used anywhere an expression can be used As mentioned before expressions can be used to create constraints or an objective function for a model Here is how to create a minimization objective for the above expression IloObjective obj cplex minimize ILOG CPLEX 8 1 GETTING STARTED 93 THE ANATOMY CONCERT TECHNOLOGY APPLICATION 94 In addition to creating an objective IloCplex must be instructed to use it in the model it solves This is done by adding t
170. x attempts to maintain a basis which will be used the next time method solve is invoked with the aim of making subsequent solves go faster Modifying an Optimization Problem Example ilolpex3 cpp This example demonstrates Setting CPLEX Parameters Modifying an Optimization Problem Starting from a Previous Basis Here is the problem example ilolpex3 solves penon Minimize i D 4 o 2 2 5 lt subject to Hx d Ax b 15 lt where H 10 1 0 1 0 0 0 d 3 1 1 0 1 0 0 0 0 e d 0 1 1 0 0 1 1 0 4 0 0 0 1 0 1 0 1 3 0 0 0 0 1 0 1 1 5 A 2 1 2 1 2 1 2 3 b 64 1 3 2 3 1 2 1 1 2 ILOG CPLEX 8 1 GETTING STARTED 85 MODIFYING AN OPTIMIZATION PROBLEM EXAMPLE ILOLPEX3 CPP 86 c 9 1 4 2 8 2 812 l 0 000000 0 u 50 50 50 50 50 50 50 50 The constraints Hx d represent a pure network flow The example solves this problem in two steps 1 The CPLEX Network Optimizer is used to solve Minimize c x subject to Hx d 1 lt lt 2 The constraints Ax b added to the problem and the dual simplex optimizer is used to solve the full problem starting from the optimal basis of the network problem The dual simplex method is highly effective in such a case because this basis remains dual feasible after the slacks artificial variables of the added constraints are initialized as basic Notice that the 0 valu
171. x by rows columns or nonzeros After building the problem the application optimizes it and displays the solution Here is the problem that the example optimizes Maximize X 2x 3x3 subject to X X x lt 20 X 3x5 lt 30 with these bounds 0 x 40 0 Ex lt 0 lt lt Before any ILOG CPLEX Callable Library routine can be called your application must call the routine CPXopenCPLEX to get a pointer called env to the ILOG CPLEX environment Your application will then pass this pointer to every Callable Library routine If this routine fails it returns an error code This error code can be translated to a string by the routine CPXgeterrorstring After the ILOG CPLEX environment is initialized the ILOG CPLEX screen indicator parameter CPX PARAM SCRIND is turned on by the routine CPXsetintparam This causes all default ILOG CPLEX output to appear on the screen If this parameter is not set then ILOG CPLEX will generate no viewable output on the screen or in a file At this point the routine setproblemdata is called to create an empty problem object Based on the problem building method selected by the command line argument the application then calls a routine to build the matrix by rows by columns or by nonzeros The routine populatebyrow first calls CPXnewcols to specify the column based problem data such as the objective bounds and variables names The routine CPXaddrows
172. x out lt lt Solution is lt lt vals lt lt endl cplex exportModel lpex3 sav catch IloException amp cerr lt lt Concert exception caught lt lt lt lt endl catch cerr lt lt Unknown exception caught lt lt endl env end return 0 END main 88 ILOG CPLEX 8 1 GETTING STARTED Concert Technology for Java Users This chapter is an introduction to using ILOG CPLEX through Concert Technology in the Java programming language It gives you an overview of a typical application program and describes procedures for Creating a model Solving that model Querying results after solving Handling error conditions ILOG Concert Technology allows your application to call CPLEX directly through the JNI Java Native Interface This Java interface supplies a rich functionality allowing you to use Java objects to build your optimization model The 11oCplex class implements the Concert Technology interface for creating variables and constraints It also provides functionality for solving Mathematical Programing MP problems and accessing solution information 2 x C o lt 5 lt Compiling CPLEX Applications Concert Technology When compiling a Java program that uses ILOG CPLEX Concert Technology you need to inform the Java compiler where to find the file cplex jar containing the CPLEX ILO
173. you must enter the lower and upper bounds on the variables If no bounds are specified ILOG CPLEX will automatically set the lower bound to 0 and the upper bound to You must explicitly enter bounds only when the bounds differ from the default values In our example the lower bound on x1 is 0 which is the same as the default The upper bound 40 however is not the default so you must enter it explicitly You must type bounds on a separate line before you enter the bound information bounds 1 lt 40 ILOG CPLEX 8 1 GETTING STARTED ENTERING PROBLEM Since the bounds on x2 and x3 are the same as the default bounds there is no need to enter them You have finished entering the problem so to indicate that the problem is complete type end on the last line The CPLEX gt prompt returns indicating that you can again enter a ILOG CPLEX command Summary Entering a problem in ILOG CPLEX is straightforward provided that you observe a few simple rules The terms maximize or minimize must precede the objective function the term subject to must precede the constraints section both must be separated from the beginning of each section by at least one space The word bounds must be alone a line preceding the bounds section On the final line of the problem end must appear FEAT eg e AEST Entering Data You can use the return key to split long constraints and ILOG CPL
174. zation clocktype set type of clock used to measure time defaults set all parameter values to defaults logfile set file to which results are printed lpmethod set method for linear optimization mip set parameters for mixed integer optimization network set parameters for network optimizations output set extent and destinations of outputs preprocessing set parameters for preprocessing qpmethod set method for quadratic optimization read set problem read parameters sifting set parameters for sifting optimization simplex set parameters for primal and dual simplex optimizations threads set default parallel thread count timelimit set time limit in seconds workdir set directory for working files workmem set memory available for working storage in megabytes Parameter to set If you press the return key without entering a parameter name the following message is displayed No parameters changed Resetting Defaults After making parameter changes it is possible to reset all parameters to default values by issuing one command set defaults This resets all parameters to their default values except for the name of the log file 54 ILOG CPLEX 8 1 GETTING STARTED ADDING CONSTRAINTS AND BOUNDS Summary The general syntax for the set command is set parameter option new_value Displaying Parameter Settings The current values of the parameters can be displayed with the command display settings all A list of parameter

ILOG CPLEX 8.1 Getting Started

Contents

Download Pdf Manuals

Related Search

Related Contents