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ILOG AMPL CPLEX System Version 11.0 User`s Guide

1. eee hh mnn 25 Customizing AMPLE 2 22 9 lac bee eee be weeds 27 Command Line Switches ce e RI m ER ane eee ates GRE 27 Persistent Option Settings 0 0 0 cece eee eee I nnn 28 Using CPLEX with AMPL oo 0oooocooo n 31 Problems Handled by CPLEX 0 ccc cece eee eee eee n n n nnn 31 Piecewise linear Programs 0 cect HH 32 Quadratic Programs 2 2 2 ett rn 32 Quadratic Constraints oss eeri eena e nna a e n E E a oa E e E a 33 Specifying CPLEX Directives leleseeeeseeeeeee n n nn nnn 34 Directives for Handling Infeasible Problems leeren 35 Directive for TUNINYQ ooooococconccnnnn e ehh hh em hart 36 Using CPLEX for Continuous Optimizati0N ooooocooroommooo 39 CPLEX Algorithms for Continuous Optimization o ooocoooooommmmmmoo 39 Directives for Problem and Algorithm Selection llle 40 Directives for Preprocessing lesser n n n nnn 43 Directives for Controlling the Simplex Algorithm cece eee eee eee 45 Directives for Controlling the Barrier Algorithm llle 49 Directives for Improving Stability o ooooocoocororncrncan ar 51 Directives for Starting and Stopping 0 0 e eee ee eee eee eee 52 Directives for Controlling Output lille RII III 54 Using CPLEX for Integer Programming lesen 57 CPLEX Mixed Integer Algorithm lese RII 57 Dire
2. ILOG AMPL CPLEX System Version 11 0 User s Guide Standard Command line Version Including CPLEX Directives January 2008 COPYRIGHT NOTICE Copyright 1987 2007 by ILOG S A and ILOG Inc All rights reserved General Use Restrictions 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 nondisclosure agreement and may be used or copied only within the terms of such license or nondisclosure 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 or ILOG Inc Trademarks ILOG the ILOG design CPLEX and all other logos and product and service names of ILOG are registered trademarks or trademarks of ILOG in France the U S and or other countries All other company and product names are trademarks or registered trademarks of their respective holders Java and all Java based marks are either trademarks or registered trademarks of Sun Microsystems Inc in the United States and other countries Microsoft Windows and Windows NT are either trademarks or registered trademarks of Microsoft Corporation in the United States and other countries document version 11 0 Chapter 1 Chapter 2 Chapter 3 Table of Contents Welcome to AMPL elc ARI rm e ee en n mm nn 9 Using this Guide 1 010 lif 9 IIo a et Rte EK P eR
3. which accomplishes the same thing as C gt ampl ampl include steel mod ampl include steel dat ampl include steel run ampl quit C gt 16 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE If you intend to load several files and solve a problem but you want to type a few interactive commands in the middle of the process type the character in place of a filename AMPL processes the files on the command line from left to right when it encounters the symbol it displays the amp1 prompt and accepts commands until you type end For example you could type C gt ampl steel mod steel dat steel run ampl let avail 50 ampl end This will solve the problem as before but with the parameter avail set to 50 instead of 40 the value specified in steel dat To start AMPL load a model and data file and wait for your interactive commands type C gt ampl steel mod steel dat ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 17 18 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE AMPL Solver Interaction Choosing a Solver AMPL s solver interface supports linear nonlinear and mixed integer models with no built in size limitations This interface is rich enough to support many of the features used by advanced solvers to improve performance and solution accuracy such as piecewise linear constructs representation of network problems and automatic differentiation of nonlinear functions To take advan
4. S GUIDE 67 Disk node files are created in the temporary directory specified by the value of the workfiledir directive If no value is specified the directory specified by the TMPDIR on Unix or TMP on Windows environment variable is used If TMPDIR or TMP are not set either the current working directory is used Node files are deleted automatically when CPLEX terminates normally ordertype i default 0 CPLEX can automatically generate certain priority orders which determine the choice of branching variable based on specific problem features Use ordertype to specify the type of priority order The default value 1 0 bypasses order generation Setting i 1 generates a priority order where variables with larger costs receive higher priority Setting 1 2 generates a priority order where variables with smaller bound ranges receive higher priority This setting tends to be useful for models with binary variables that represent a logical decision and associated general integer variables that represent resource levels enabled by the outcome of the decision Setting 1 3 tends to help set covering problems In such problems setting a binary variable to 1 covers a group of rows but incurs a cost Binary variables with smaller costs per row covered are good choices to set to 1 An i value of 3 gives higher priority to variables with smaller cost per coefficient count This tends to identify such binary variables quickly polishtime r default 0 0
5. S GUIDE 69 submipnodelim default 500 The submipnodelim directive restricts the number of nodes searched during application of the RINS heuristic and the processing of MIP start values varselect i default 0 Once a node has been selected for branching this directive determines how CPLEX chooses a fractional valued variable to branch on By default 1 0 the choice is made by an internal heuristic based on the problem and its progress The maximum infeasibility rule 1 1 chooses the variable with the largest fractional part This forces larger changes earlier in the tree but it tends to disregard the objective function in doing so The minimum infeasibility rule i 1 chooses the variable with the smallest fractional part This may lead more quickly to a first integer feasible solution but will usually be slower overall to reach the optimal integer solution A pseudocost rule 1 2 estimates the worsening of the objective that will result by forcing each fractional variable to an adjacent integer and uses these degradations in an internal heuristic for choosing a variable to branch on This setting tends to be most effective when the problem embodies complex tradeoffs and the dual variables have an economic interpretation Strong branching 1 3 considers several different branches by actually solving subproblems for different choices of branching variable The variable yielding the best results is then chosen Strong branching r
6. primary names is recommended Table A 1 CPLEX Synonyms Synonym agglim dense display doperturb endbasis endvector growth heuristic iterations mipsolutions Primary Directive aggfill densecol Ipdisplay perturb writebasis writevector bargrowth rootheuristic Ipiterlim solutionlim ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 91 92 Synonym nodes nodesel presolvedual startalg startalgorithm startbasis startvector subalgorithm time treememory varsel writeprob ILOG AMPL CPLEX SYSTEM 11 0 Primary Directive nodelim nodeselect predual mipstartalg mipstartalg readbasis readvector mipalgorithm timelimit treememlim varselect file USER S GUIDE symbol notation for options 21 syntax set initial values 21 A absmipgap directive 70 advance directive 46 aggcutlim directive 59 aggfill directive 43 aggregate directive 43 algorithm directives for selection 40 mixed integer 57 algorithmic control directives 62 AMPL notation for options 21 and Paralle CPLEX installing 11 batch mode 16 command line switches 27 configuration table 10 end session 15 execute solver outside AMPL 24 installing 10 launching AMPL 15 learning the AMPL language 9 let command 90 licensing 11 requirements 10 solver interface 19 ampl prompt 15 append directives 35 ASCII format problem and solution files 23 autoopt directive 41 auxiliary files creating 23 backtrack direct
7. subsections If you consistently fail to receive any useful solution in response to the solve command after a reasonable amount of time and are in doubt as to how to proceed consult the troubleshooting tips at the end of this section Directives for Preprocessing All of the preprocessing directives described in Using CPLEX for Continuous Optimization are also applicable to problems that specify integer valued variables The following directives control additional preprocessing steps that are applicable to certain mixed integer programs only aggcutlim i default 3 This directive controls the number of constraints that can be aggregated for generating flow cover and mixed integer rounding cuts In most cases the default setting of 3 will be satisfactory Set it to 0 to prevent any aggregation boundstr i default 1 Bound strengthening tightens the bounds on variables in mixed integer programs This may enable CPLEX to fix the variable and remove it from consideration during the branch amp cut algorithm By default 12 1 CPLEX automatically decides whether to perform bound strengthening This reduction usually improves performance but occasionally takes a long time due to its iterative nature In cases where the time required for bound strengthening outweighs any subsequent reduction in run time disable this feature by setting 1 0 To turn on bound strengthening set 1 1 coeffreduce i default 2 Coefficient reduction during the pre
8. the values of the variables define the feasible point The direction of unboundedness is given by an additional value associated with each variable through the associated solver defined suffix unbdd An application of the direction of unboundedness can be found in our example of Benders decomposition applied to a transportation location problem One part of the decomposition scheme is a subproblem obtained by fixing the variables Build i which indicate the warehouses that are to be built to trial values build i When all values build i are set to zero no warehouses are built and the primal subproblem is infeasible As a result the dual formulation of the subproblem which always has a feasible solution is unbounded When this dual problem is solved from the AMPL command line CPLEX returns the direction of unboundedness in the expected way ampl model trnlocid mod ampl data trnlocl dat ampl problem Sub Supply Price Demand Price ampl Dual Ship Cost Dual Ship ampl let i in ORIG build i 0 ampl option solver cplexamp ampl option cplex options presolve 0 ampl solve CPLEX 11 0 0 presolve 0 CPLEX 11 0 0 unbounded problem 30 iterations 0 in phase I variable unbdd returned suffix unbdd OUT ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 83 The suffix message indicates that unbdd has been created automatically You can use this suffix to display the direction of unboundedness which is qui
9. to variables constraints and other model components Yet only the most standard kinds of results such as reduced costs given by X rc where x is a variable name and slacks given by C slack where C is a constraint name are covered by the built in suffixes To allow for solver specific optimization results AMPL permits solvers to define new suffixes and to associate solution result information with them Similarly users can also define suffixes to control the solver User defined suffixes understood by CPLEX and suffixes defined by CPLEX are described in this section Algorithmic Control For each integer variable in a problem CPLEX recognizes a preferred branching direction and a branching priority specified by the following two suffixes direction priority Branching direction preference can be specified for each variable by setting its direction suffix to a value between 1 and 1 Variables not assigned a suffix value get a default value of zero A negative value indicates a preference for branching down and a positive value indicates a preference for branching up ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 7T For variables with direction at zero the branching direction is determined by the branching related directives described in Directives for Algorithmic Control on page 62 Each time that CPLEX must choose a fractional valued integer variable on which to branch it gives preference to the fractional variables
10. 0 non not in the iis 1 low at lower bound 2 fix fixed 3 upp at upper bound 4 mem member 5 pmem possible member 6 plow possibly at lower bound 7 pupp possibly at upper bound 8 bug You can use display to look at the iis values that have been returned ampl display varname var iis conname _con iis E varname var iis conname _con iis 1 Buy BEEF upp diet A non 2 Buy CHK low diet B1 non 3 Buy FISH low diet B2 mem 4 Buy HAM upp diet C non 5 Buy MCH upp diet NA mem 6 Buy MTL upp diet CAL non 7 Buy SPG non s 8 Buy TUR low This information indicates that the IIS consists of four upper and three lower bounds on the variables plus the constraints on B2 and on NA in the diet Together these restrictions have no feasible solution but dropping any one of them will permit a solution to be found to the remaining ones Of course in our example we shouldn t actually drop the lower bounds on ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE the Buy variable we could end up with negative values However we could reduce certain lower bounds to zero Direction of Unboundedness For an unbounded linear program one that effectively has a minimum objective value of Infinity or a maximum of Infinity the solution is characterized by a feasible point together with a direction of unboundedness from that point On return from CPLEX
11. 37 8071 40 47 8571 3 25 32 45 4 30 40 62 5 Diagnosing Infeasibilities For a linear program that has no feasible solution you can ask CPLEX to find an irreducible infeasible subset or IIS of the constraints and variable bounds By definition members of an IIS have no feasible solution but dropping any one of them permits a solution to be found to the remaining ones Clearly knowing the composition of an IIS can help localize the source of the infeasibility The associated suffix is lis You turn on the IIS finder using the iisfind option described in Directives for Handling Infeasible Problems on page 35 An associated option iis table set up and displayed automatically by CPLEX shows the strings that may be associated with iis and gives brief descriptions of what they mean ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 81 The following example shows how IIS finding might be applied to the infeasible diet problem from chapter 2 of the AMPL book After solve detects that there is no feasible solution it is repeated with the iisfind directive ampl model diet mod ampl data diet2 dat ampl option solver cplexamp ampl solve CPLEX 11 0 0 infeasible problem 7 iterations 7 in phase I ampl option cplex options iisfind 1 ampl solve CPLEX 11 0 0 iisfind 1 CPLEX 11 0 0 infeasible problem 0 iterations Returning iis of 7 variables and 2 constraints suffix iis symbolic OUT option iis table
12. NR RES 9 Installing AMPL 2 ei x a ee a ads MOOR DE RR S RR REL RR Cn 10 Requirements x execs eee tha See e WIR OR IH Ga ee ee eee I 10 Unix Installation ot a rccte RR Wed ei bee RH RE nba aed EL ERN 10 Windows Installation ca snina ena ee RII II 11 AMPL and Parallel CPLEX coo eu do eh Rehan e bes hieu EUIS eds 11 Licensing ara peer Aa a e mI vie ee RP eae Gees REX Reid egi 11 Usage Notes ui ai EU REX XAR a Denes a eee bk beep GREEN 12 Installed Files 229r fare UAE A QC DRESGDUS EID OPERI RED ENG ERN 13 USING AMPL clle IR Rime ae ae ea ee e virus 15 Running AMPL atada ia ia Regu KORR AL Te R7 L ince EUR RI R R B a 15 Using a Text Editor eiii sr rag eee s RR te RIA we ee ROSEO CR eee 15 Running AMPL in Batch Mode 00 e seen eee n hh n nmn n 16 AMPL Solver Interaction ooococcoocnccn nn 19 Choosing a Solver ners terium ualet nga pn eee E rr BERE E ER Rm 19 Specifying Solver Options 0 0 c eee eee eee n nnn 20 Initial Variable Values and Solvers 0000 e eee eee eee eee eee eee 21 Problem and Solution FileS 0 cece eee eee eee eee eee 21 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Saving temporary files 2 0 00 ccc eet teens 22 Creating Auxiliary Files s tata a estes 23 Running Solvers Outside AMPL 0000 c eee eee eee eee 24 Using MPS File Format 2 ee er Rh hm hh mh 24 Temporary Files Directory
13. The default of 0 corresponds to a balance between searching for feasible solutions and proving optimality and works well for most users purposes A setting of 1 shifts the emphasis strongly toward finding new feasible solutions and may be an appropriate setting with difficult models for which a proof of optimality is unlikely to be reached anyway A setting of 2 shifts the emphasis slightly more toward the proof of optimality and away from finding new feasibles A setting of 3 shifts the emphasis very aggressively toward the optimality proof by concentrating on moving the best bound value and may be an appropriate setting for models resistant to other solution techniques or when feasible solutions without a proof of optimality are of no value None of these emphasis settings changes the fundamental nature of the CPLEX branch amp cut algorithm which is to deliver proved optimal solutions if given enough time the setting merely changes some internal strategies and tactics along the way and represents a way for the user to express his or her aims in a way that is separate from the model formulation A setting of 4 indicates emphasis on hidden feasibles With this setting the MIP optimizer works hard to find high quality feasible solutions that are otherwise very difficult to find Use this setting when you more are interested in a good feasible solution than a provably optimal solution and when feasibility emphasis has difficulty finding solut
14. a quadratic program is given as T T minimize ix Ox cx subject to Ax b lt x lt u where represents 2 or operators E v In the above formula Q represents a matrix of quadratic objective function coefficients Its diagonal elements Q are the coefficients of the quadratic terms x The nondiagonal elements Q and Qj are added together to be the coefficient of the term x x ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE The CPLEX linear programming algorithms incorporate an extension for quadratic programming For a problem to be solvable using this option the following conditions must hold 1 All constraints must be linear 2 The objective must be a sum of terms each of which is either a linear expression or a product of two linear expressions 3 Forany values of the variables whether or not they satisfy the constraints the quadratic part of the objective must have a nonnegative value if a minimization or a nonpositive value if a maximization The last condition is known as positive semi definiteness for minimization or negative semi definiteness for maximization CPLEX automatically recognizes nonlinear problems that satisfy these conditions and invokes the barrier algorithm to solve them Nonlinear problems of any other kind are rejected with an appropriate message Most CPLEX features applying to continuous LP models apply also to continuous QP models likewise most features applying to li
15. absmipgap 70 advance 46 aggcutlim 59 aggfill 43 aggregate 43 autoopt 41 backtrack 64 baralg 49 barcorr 49 bardisplay 54 bargrowth 49 94 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE bariterlim 52 barobjrange 50 baropt 41 barstart 50 bbinterval 64 boundstr 59 branch 65 cliquecuts 66 clocktype 52 72 coeffreduce 59 comptol 50 concurrentopt 41 conflictdisplay 35 covercuts 66 crash 46 crossover 50 cutpass 60 cutsfactor 60 densecol 50 dependency 44 dgradient 47 disjcuts 66 doperturb 51 dual 40 dualopt 41 dualthresh 40 eachcutlim 60 feasibility 52 feasopt 35 feasoptobj 35 file 54 flowcuts 66 flowpathcuts 66 fpheur 65 fraccand 60 fraccuts 66 fracpass 60 gubcuts 66 heuristicfreq 65 iisfind 35 impliedcuts 66 integrality 71 lazy 65 78 logfile 54 lowercutoff 71 lowerobj 53 lpdisplay 54 lpiterlim 53 markowitz 52 maximize 43 memoryemphasis 41 minimize 43 mipalgorithm 65 mipcrossover 65 mipcuts 66 mipdisplay 74 mipemphasis 63 mipgap 70 mipinterval 74 mipsearch 67 mipstartstatus 60 mipstartvalue 60 miqcpstrat 67 mircuts 66 netfind 49 netopt 42 nodefile 67 nodelim 72 nodeselect 64 objdifference 71 optimality 52 ordering 50 ordertype 68 parallelmode 42 paramfile 36 paramfileprm 36 perturbation 51 perturblimit 51 pgradient 46 polishtime 68 poolagap 73 poolcapacity 73 poolintensity 73 poolreplace 73 poolstub 73 populate 73 populatelim 73 predual 44 prereduce 44 prerelax 61
16. accounts that will use AMPL CD ROM The ILOG CD contains the AMPL CPLEX system for several different platforms First read the file INFO UNX TXT The section titled AMPL CPLEX System contains information to help you locate the distribution for your platform Note that the files listed in this section contain the entire AMPL CPLEX System not just the AMPL language processor After you have located the files read the CD booklet for instructions on extracting the distribution 10 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE FTP Execute gzip dc path ampl tgz tar xf where path is the full path name into which amp1 tgz was downloaded Windows Installation On Windows systems AMPL is installed into a directory which you can specify during the installation the default location is C AMPL CD ROM The ILOG CD contains the AMPL CPLEX system for several different platforms Follow the instructions in the CD booklet and in the setup program menus to set up the distribution FTP After downloading the files execute the downloaded EXE file from the Run dialog or in an MS DOS window Follow the instructions presented by the setup program To access the Run dialog box on Windows click on the Start button and select Run AMPL and Parallel CPLEX If you have purchased AMPL and Parallel CPLEX follow the above instructions for the appropriate media You will use the same programs to run in serial or para
17. equivalent formulation using multiple binary variables sos2 i default 1 An optimization problem containing piecewise linear terms may have to be converted to an equivalent mixed integer program as explained in Piecewise linear Programs on page 32 When i is at its default value of 1 this conversion results in only one extra variable per piecewise linear breakpoint All of the extra variables associated with a particular piecewise linear term are marked as belonging together so that CPLEX s branch amp cut procedure knows to treat them specially Variables so marked have come to be known as a special ordered set of type 2 whence the name sos2 for this directive When i is changed to 0 from its default of 1 the conversion creates a larger number of variables but does not employ the special ordered set feature This alternative has no known advantages and is supplied for completeness only symmetry i default 1 This directive controls the amount of symmetry breaking CPLEX should use The default of 1 tells CPLEX to choose Set i 0 to turn off symmetry breaking and i 1 2 3 for increasing amounts of symmetry breaking effort Directives for Algorithmic Control CPLEX has default values for the algorithmic control directives that often work well for solving a wide range of mixed integer programs However it is sometimes necessary to specify alternative values for one or more of the following directives to improve solution times You
18. file by specifying solve filename mipdisplay i1 default 0 mipinterval i2 default 1 The default of 11 0 produces a minimal few lines of output from CPLEX summarizing the results of the run When i1 1 a single log line is displayed for every integer solution found The information includes the number of nodes processed and the objective values of the best integer solution found so far and of the best unprocessed node subproblem The optimal value lies between these two When i1 2 a more detailed log line is displayed once every 12 nodes as well as for each node where an integer solution is found A indicates lines of the latter type The default of i2 1 gives a complete picture of the branch amp cut process which may be instructive for small examples With a larger choice of 12 this setting can be very useful for evaluating the progress of long runs the log line includes a count of the number of active nodes which gives an indication of the rate at which the search tree is growing or shrinking in memory When i1 3 CPLEX also prints information on node cut and node presolve The LP iteration log for the root node 11 4 and for all subproblems 11 5 can also be displayed timing i default 0 This directive can be used to display a summary of processing times It works the same for integer programming as for linear programming as described in Using CPLEX for Continuous Optimization on page 39 Common Difficulties The
19. files that can be created and the letter you use to request them via the AMPL option auxfiles Table 3 1 Auxiliary Files Letter Extension Description a adj adjustment to objective for example to compensate for fixed variables eliminated by presolve c col AMPL names of the variables columns sent to the solver f fix names of variables fixed by presolve and the values to which they are fixed r row AMPL names of the constraints rows sent to the solver S slc names of slack constraints eliminated by presolve because they can never be binding u unv names of variables dropped by presolve because they are never used in the problem instance ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 23 Running Solvers Outside AMPL With the write and solution commands you can arrange to execute your solver outside the AMPL session You might want to do this if you receive an out of memory message from your solver not from AMPL itself When the solver is invoked from within AMPL a fair amount of memory is already used for the AMPL Modeling System program code and for data structures created by AMPL for its own use in memory If you execute the solver alone it can use all available memory To run your solver separately first use AMPL to create a problem file C X gt ampl ampl model steel mod data steel dat ampl write bsteel ampl quit Then run your solver with a command like the one below for CPLEX
20. following discussion addresses the difficulties most often encountered in solving integer programs with CPLEX Running Out of Memory The most common difficulty when solving MIP problems is running out of memory This problem arises when the branch amp cut tree becomes so large that insufficient memory is available to solve an LP subproblem As memory gets tight you may observe warning messages while CPLEX attempts to navigate through various operations within limited 74 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE memory If a solution is not found shortly the solutions process will be terminated with an error termination message The tree information saved in memory can be substantial CPLEX saves a basis for every unexplored node When utilizing the best bound or best estimate method of node selection the list of unexplored nodes can become very long for large or difficult problems How large the unexplored node list can become is entirely dependent on the actual amount of physical memory available the size of the problem and the solution algorithm selected Certainly increasing the amount of memory available extends the problem solving capability Unfortunately once a problem has failed because of insufficient memory you cannot project how much further the process needed to go or how much memory would be required to ultimately solve it Some parts of the branch amp cut tree can be stored in compressed files either on disk or
21. integer variables It thus provides a feasible solution to the original integer program If this solution yields a better objective value than any other feasible solution found so far it becomes the incumbent and is saved for future comparison The node s subproblem has no feasible solution or has an optimum that is worse than a certain cutoff value Since any subproblems under this node would be more restricted they would also either be infeasible or have an optimum value worse than the cutoff Thus none of these subproblems need be considered In these cases the node is said to be fathomed Because subproblems become more restricted with each branching the likelihood of fathoming a node becomes greater as the algorithm gets deeper into the tree So long as nodes are not created by branching much faster than they are inactivated by fathoming the tree can be kept to a reasonable size When no active nodes are left CPLEX is finished and it reports the final incumbent solution back to AMPL If the cutoff value has been set throughout the algorithm to the objective value of the current incumbent CPLEX s default strategy then the reported solution is declared optimal Other cutoff options described below cannot provide a provably optimal solution but may allow the algorithm to finish much faster CPLEX s memory requirement for solving linear subproblems is about the same as its requirement for linear programs discussed in the previous
22. matrix in order to reduce fill in the Cholesky factor There is a trade off between ordering speed and sparsity of the Cholesky factor The automatic default setting usually chooses the best ordering for the problem The approximate minimum degree AMD algorithm 1 1 balances speed and fill The approximate minimum fill AMF algorithm 1 2 usually generates slightly better orderings than AMD at the cost of more ordering run time The nested dissection ND algorithm triggered by using 1 3 sometimes reduces Barrier run time dramatically ten fold reductions have been observed for some problems This option sometimes produces worse orderings though and it requires much more ordering run time qcpconvergetol default 1e 7 This directive sets the tolerance on complementarity for convergence in quadratically constrained problems QCP The barrier algorithm terminates with an optimal solution if the relative complementarity is smaller than this value ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Changing this tolerance to a smaller value may result in greater numerical precision of the solution but also increases the chance of a convergence failure in the algorithm and consequently may result in no solution at all Therefore caution is advised in deviating from the default setting For LPs and QPs that is when all the constraints are linear see the comptol directive Directives for Improving Stability CPLEX is highly robust a
23. means the current incumbent You can arrange to save the entire search tree when CPLEX halts so that the search may be resumed from where it left off Directives for this purpose are also listed below clocktype i default 1 The default setting of clocktype 1 means that CPLEX will measure time in terms of CPU seconds A setting of 2 means that CPLEX will measure time in terms of elapsed wall clock seconds nodelim i default 2 1e9 The search is terminated after i linear programming subproblems have been solved The default value can vary depending on the hardware solutionlim i default 2 1e9 The search is terminated after i feasible solutions satisfying the integrality requirements have been found timelimit r default 1 0e75 The search is terminated after x seconds of computing time treememlim r default 1 0e75 The total size of the branch amp cut tree is limited to x megabytes Directives to Manage the Solution Pool 72 CPLEX can store multiple solutions for integer programs in a solution pool The poolstub directive must be specified in order to display and query the solution pool its value is used to recover the solutions For example to display all the solutions in the pool use these commands in AMPL option cplex_options poolstub somename solve New problem suffix npool should be returned If it s positive we can examine the solutions for i in 1 Current npool solution somename amp i am
24. previous optimization Information on interpreting and setting variable statuses is provided in Chapter 9 CPLEX Status Codes in AMPL Problem and Solution Files When you type solve AMPL processes your model and data to create a temporary problem file such as steel n1 which will be read by the solver It then loads and executes the solver program which is responsible for creating a solution file such as steel so1 AMPL reads the solution file and makes the solution values available through the variable constraint and objective names you have declared in your AMPL model Unless you specify otherwise AMPL then deletes the temporary problem and solution files ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 21 You can display the solution information for example the values of the decision variables and constraints in your AMPL session with commands such as display For example if you have just solved a problem created from steel mod and steel dat you could type ampl display Make Time To save this output in a file you can use redirection ampl display Make Time mysol txt Note that when you simply mention the name of a constraint in a display statement AMPL will display the dual value shadow price of that constraint not its left hand side value You can use the AMPL suffix notation to display the left hand side value as described in the book AMPL A Modeling Language for Mathematical Programming 2nd edition Savi
25. proven in commercial applications and is successfully used in demanding model applications around the world AMPL helps you create models with maximum productivity By using AMPL s natural algebraic notation even a very large complex model can often be stated in a concise often less than one page understandable form As its models are easy to understand debug and modify AMPL also makes maintaining models easy Using this Guide This brief guide describes starting up AMPL reading a model and supplying data and solving optimizing the model using CPLEX Chapters 2 4 cover issues such as using command line options and environment variables and using AMPL on different operating systems Later chapters provide a detailed description of CPLEX directives This Guide does not teach you the AMPL language To learn and effectively use the features of the AMPL language you should have a copy of the book AMPL A Modeling Language for Mathematical Programming 2nd edition by Robert Fourer David M Gay and Brian W Kernighan copyright 2003 publisher Thomson Brooks Cole ISBN number 0 534 38809 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 9 4 This book includes a tutorial on AMPL and optimization modeling models for many classical problems such as production transportation blending and scheduling discussions of modeling concepts such as linear nonlinear and piecewise linear models integer linear models and columnwise formulati
26. that have the highest priority value A judicious choice of priorities any number between 0 and 9999 is valid can guide the search in a way that reduces the number of nodes generated For example let us consider a model drawn from pages 446 447 of the AMPL book ampl model models multmip3 mod ampl data models multmip3 dat ampl solve CPLEX 11 0 0 optimal integer solution objective 235625 601 simplex iterations 91 branch and bound nodes Note that CPLEX takes 91 nodes and 601 simplex iterations to find the optimal integer solution Now let us provide CPLEX with branching priorities for all variables as well as a preferred branching direction for a single variable Note that before we re run CPLEX we set mipstartvalue to discard the existing solution ampl option cplex options mipstartvalue 0 ampl suffix priority IN integer gt 0 lt 9999 ampl suffix direction IN integer gt 1 lt 1 ampl let i in ORIG j in DEST ampl Use i jl priority ampl sum p in PROD demand j p ampl let Use GARY FRE direction 1 ampl solve CPLEX 11 0 0 optimal integer solution objective 235625 446 simplex iterations 64 branch and bound nodes Indeed CPLEX now requires fewer nodes 64 and fewer simplex iterations 446 to reach optimality While this is not a dramatic improvement larger cases where directing branch and bound in this manner makes the difference between unsolvability and finding the soluti
27. the relaxation of the integer program the LP that results when all integrality restrictions are dropped If this relaxation happened to have an integer solution then it would provide an optimal solution to the integer program Normally however the optimum for the relaxation has some fractional valued integer variables Additional constraints called cutting planes are added to the subproblem These cutting planes tighten the feasible region Also heuristic algorithms for finding integer solutions are applied using the information from the solution of the subproblem A fractional variable is then chosen for branching and two new subproblems are generated each with more restrictive bounds for the branching variable For example if the branching variable is binary or 0 1 one subproblem will have the variable fixed at zero the other node will have it fixed at one In the search tree the two new subproblems are represented by two new nodes connected to the root Most likely each of these subproblems also has fractional valued integer variables in which case the branching process must be repeated successive branchings produce the tree structure shown above If there are more than a few integer variables the branching process has the potential to create more nodes than any computer can hold There are two key circumstances however in which branching from a particular node can be discontinued The node s subproblem has no fractional valued
28. to turn off the aggregation routine and save memory and processing time ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 43 To request a report of the number of aggregations see the prestats directive later in this section dependency i default 1 By default 12 1 CPLEX chooses automatically when to use dependency checking This parameter offers several settings that make it possible for a user to control dependency checking more precisely Table 6 1 shows you the possible settings of the parameter that controls dependency checking and indicates their effects Table 6 1 Settings for the dependency Directive Setting Effect 1 default automatic let CPLEX choose when to use dependency checking 0 turn off dependency checking 1 turn on only at the beginning of preprocessing 2 turn on only at the end of preprocessing 3 turn on at the beginning and at the end of preprocessing predual i default 0 By default after presolving the problem CPLEX decides whether to solve the primal or dual problem based on which problem it determines it can solve faster Setting i 1 explicitly instructs CPLEX to solve the dual problem while setting it to 1 explicitly instructs CPLEX to solve the primal problem Regardless of the problem CPLEX solves internally it still reports primal solution values This is often a useful technique for problems with more constraints than variables prereduce i default 3 This dire
29. C gt cplexamp steel AMPL solver options In this example the first argument steel matches the filename after the initial letter b in the AMPL write command The AMPL argument tells the solver that it is receiving a problem from AMPL This may optionally be followed by any solver options you need for the problem using the same syntax used with the option solver options command but omitting the outer quotes for example crash 1 relax Assuming that the solver runs successfully to completion it will write a solution file stee1 so1 in this case You can then restart AMPL and read in the results with the solution command as outlined earlier C X gt ampl ampl model steel mod data steel dat ampl solution steel sol Using MPS File Format MPS file format originally developed decades ago for IBM s Mathematical Programming System is a widely recognized format for linear and integer programming problems Although it is a standard supported by many solvers and modeling systems including AMPL MPS file format is neither compact nor easy to read and understand AMPL s binary file format is a much more efficient way for modeling systems and solvers to communicate Also MPS file format cannot be used for nonlinear problems and not all MPS compatible solvers support exactly the same format particularly for mixed integer problems 24 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE AMPL does have the ability to translate a model into MPS fil
30. EO ODE MR EIU ROBUR aces Meta a 23 AMPL Option Names for Command Line Switches 0 0 cece eee eee eee nn 27 Settings for the dependency Directive 0 cece eee eee eee n m nnn 44 Settings for the advance Directive 2 0 cece eee eee I nn 46 Settings for the pgradient Directive llle n nn 47 Dual Pricing Indicator dgradient ooooococcnccncan RR I III hn 48 Values of the AMPL Option send_statuSeS 2 0 60 cece eee eee 61 Settings for the mipemphasis Directive 1 0 06 cece eee RI 63 Settings for the mipcrossover Directive 2 ec eee hn I nnn 65 Settings for the round Directive 2 0 6 cece eee he hh n hh hh rn 69 Settings for the startalgorithm Directive 0 cee II n 69 Settings for the lazy Directive lceseeleeeeeeeeeer hl n hh hh hh hm rn 79 Interpretation of Numeric Result Codes eseeeeeeeeee e n n n n nnn 86 Solve Codes and Termination Messages lesse nn nnn 86 CPLEX Synonyms iei xxx km ha mde e mesi sm bass y IY AS CL eee ened RETIRER RES eee ZA 91 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 7 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Welcome to AMPL Welcome to the AMPL Modeling System a comprehensive powerful algebraic modeling language for problems in linear nonlinear and integer programming AMPL is based upon modern modeling principles and utilizes an advanced architecture providing flexibility most other modeling systems lack AMPL has been
31. ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 95 presolve 44 presolvenode 61 prestats 45 pretunefile 36 pretunefileprm 36 pricing 48 primal 40 primalopt 41 priorities 68 probe 61 probetime 61 qcpconvergetol 50 readbasis 53 readvector 53 refactor 48 relax 43 relobjdiff 71 repairtries 68 repeatpresolve 61 rinsheur 68 round 69 scale 45 sensitivity 54 siftopt 41 singular 53 solutionlim 72 sos1 61 sos2 62 startalgorithm 69 strongcand 69 strongit 69 submipnodelim 70 threads 42 timelimit 53 72 timing 55 74 treememlim 72 tunedisplay 36 tunefile 36 tunefileprm 36 tunefix 36 tunefixfile 36 tunerepeat 37 tunetime 37 uppercutoff 71 upperobj 53 varselect 70 version 55 workfiledir 41 67 workfilelim 41 67 writebasis 53 writevector 53 directives algorithmic control 62 append additional CPLEX directives 35 control barrier algorithm 49 control output 54 72 74 control simplex algorithm 45 CPLEX directives 34 CPLEX directives for linear programs 40 halt and resume search 72 improving stability 51 infeasible problems 43 preprocessing 43 preprocessing integer programs only 59 relax optimality 70 select algorithm 40 starting and stopping 52 store multiple 34 disjcuts directive 66 display command 22 doperturb directive 51 down suffix 80 dual directive 40 dual pricing indicator 48 dual simplex algorithm 39 dualopt directive 41 dualthresh directive 40 E eachcutlim directive 60 editing us
32. MPL s notation for options the symbol option name is replaced by the current value of option name To add an optimality tolerance to the CPLEX options in the above example you would write ampl option cplex options cplex options ampl optimality 1 0e 8 Initial Variable Values and Solvers Some optimizers including most nonlinear solvers but excluding simplex based linear solvers make use of initial values for the decision variables as a starting point in their search for an optimal solution A good choice of initial values can greatly speed up the solution process in some cases Moreover in nonlinear models with multiple local optima the optimal solution reported by the solver may depend on the initial values for the variables AMPL passes initial values for decision variables and dual values if available to the solver You can set initial values using the syntax in the var declaration of your AMPL model When you solve a problem two times in a row the final values from the first solver invocation become the initial values for the second solver invocation unless you override this behavior with statements in your AMPL model In nonlinear models with multiple local optima this can cause some solvers to report a different solution on the second invocation Simplex based solvers typically discard initial values However they can use basis status information if available Basis statuses can be set either within AMPL or by a
33. R S GUIDE 33 Specifying CPLEX Directives In many instances you can successfully apply CPLEX by simply specifying a model and data setting the solver option to cplex and typing solve For larger linear programs and especially the more difficult integer programs however you may need to pass specific options also referred to as directives to CPLEX to obtain the desired results To give directives to CPLEX you must first assign an appropriate character string to the AMPL option called cplex options When CPLEX is invoked by solve it breaks this string into a series of individual directives Here is an example ampl model diet mod ampl data diet dat ampl option solver cplexamp ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 ampl solve CPLEX 11 0 0 crash 0 dual feasibility 1e 08 scale 1 lpiterlim 100 CPLEX 11 0 0 optimal solution objective 88 2 1 iterations 0 in phase I CPLEX confirms each directive it will display an error message if it encounters one that it does not recognize CPLEX directives consist of an identifier alone or an identifier followed by an sign and a value a space may be used as a separator in place of the You may store any number of concatenated directives in cplex options The example above shows how to type all the directives in one long string using the character to indicate that the string continues on the next line A
34. This directive lets you indicate to CPLEX how much time in seconds to spend after branch amp cut in polishing a solution The default results in no polishing time priorities i default 0 Set i 1 to consider the MIP priorities during variable selection Set i 0 to ignore the priorities repairtries i default 0 This directive lets you indicate to CPLEX whether and how many times it should try to repair an infeasible MIP start that you supplied The directive has no effect if the MIP start you supplied is feasible It has no effect if no MIP start was supplied Set 1 1 to prevent repair Set i to any positive integer to limit the number of attempts rinsheur default 0 The rinsheur directive determines how often to apply the relaxation induced neighborhood search heuristic RINS heuristic Setting the value to 1 turns off the RINS heuristic Setting the value to 0 the default applies the RINS heuristic at an interval chosen automatically by CPLEX Setting the value to a positive integer applies the RINS heuristic at the requested node interval For example setting RINSHeur to 20 dictates that the RINS heuristic be called at node 0 20 40 60 etc ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE round default 1 This directive specifies whether to round integer variables to integral values before returning the solution and whether to report that CPLEX returned noninteger values for integer values Table 7 4 Settings for the
35. X Multiple runs of the same problem with the same settings will get identical solution paths with deterministic mode but not with opportunistic mode Opportunistic mode can be faster than deterministic mode due to less synchronization among the threads The default automatic setting allows CPLEX to ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE choose between deterministic and opportunistic mode depending on the threads parameter If the threads directive is set to its automatic setting the default CPLEX chooses deterministic mode If the threads directive is set to one CPLEX runs sequentially in deterministic mode in a single thread Otherwise if the threads directive is set to a value greater than one CPLEX chooses opportunistic mode The value i 1 is used to set deterministic mode and the value i 1 is used to set opportunistic mode relax This directive instructs CPLEX to ignore any integrality restrictions on the variables The resulting linear program is solved by whatever algorithm the above directives specify maximize minimize While AMPL completely specifies the problem and its objective sense it is possible to change the objective sense after specifying the model The two directives instruct CPLEX to set the objective sense to be minimize or maximize respectively Directives for Preprocessing Prior to applying any simplex algorithm CPLEX modifies the linear program and initial basis in ways that tend to reduce the numb
36. a rule of thumb if the number of iterations to solve your linear program exceeds three times the number of constraints you should consider experimenting with alternative pricing procedures ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 47 The dual pricing indicator allows you to indicate devex pricing Table 6 4 lists the valid settings for this directive Table 6 4 Dual Pricing Indicator dgradient Setting Effect 0 Let CPLEX determine automatically 1 Standard dual pricing 2 Steepest edge pricing 3 Steepest edge pricing in slack space 4 Steepest edge pricing unit initial norms 5 Devex pricing These settings can be further described as follows The default value 1 0 lets CPLEX choose a dual pricing procedure through an internal heuristic based on problem characteristics Standard dual pricing 1 1 described in many textbooks selects as leaving variable one that is farthest outside its bounds The three steepest edge alternatives employ more elaborate computations which can better predict the improvement to the objective offered by each candidate for leaving variable Steepest edge pricing involves an extra initialization cost but its extra cost per iteration is much less in the dual simplex algorithm than in the primal Thus if you find that your problems solve faster using the dual simplex you should consider experimenting with the steepest edge procedures e The standard p
37. and to switch among them by simply choosing the appropriate solver with the option solver command For example ampl option cplex options relax scale 1 Solver options consist of an identifier alone or an identifier followed by an sign and a value Some solvers treat uppercase and lowercase versions of an option identifier as equivalent while others are sensitive to case so that RELAX is not the same as relax for example Solver option settings can easily become long enough to stretch over more than one line In such cases you can either continue a single quoted string by placing a character at the end of each line as in ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 Or you can write a series of individually quoted strings which will be concatenated automatically by AMPL as in ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 If you use the latter approach be sure to include spaces at the beginning or end of the individual strings so that the identifiers will be separated by spaces when all of the strings are concatenated 20 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Often you will want to add solver options to the set you are currently using If you simply type a command such as option solver options new options however you will overwrite the existing option settings To avoid this problem you can use A
38. asibilities ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Table 9 2 Solve Codes and Termination Messages Continued Number Message at termination 200 infeasible problem 201 infeasible with phase ll singularities 202 infeasible with phase singularities 204 converged dual feasible primal infeasible 205 converged primal and dual infeasible 206 best solution found primal infeasible 207 best solution found primal dual infeasible 208 infeasible or unbounded in presolve 209 integer infeasible or unbounded in presolve 210 infeasible problem found by dualopt dunbdd returned 220 integer infeasible 300 unbounded problem 301 converged primal feasible dual infeasible 302 best solution found dual infeasible 310 unbounded problem found by primalopt unbdd returned 320 integer unbounded ray 400 phase II objective limit exceeded 401 phase ll iteration limit 402 phase iteration limit 403 phase ll time limit 404 phase time limit 405 primal objective limit reached 406 dual objective limit reached 410 node limit with no integer solution 411 time limit with no integer solution ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 87 88 Table 9 2 Solve Codes and Termination Messages Continued Number 412 413 420 421 422 423 424 500 501 502 503 504 505 506 507 508 509 510 511 512 520 521 523 530 531 ILOG AMPL Message at termination treememory limit with no integer solution node file limit with no integer sol
39. at the optimal basic solution For example consider the following ampl model oil mod ampl data oil dat ampl option solver cplex ampl solve CPLEX 11 0 0 optimal solution objective 12 20834324 37 iterations 0 in phase I ampl option sstatus table option sstatus table equ nonbasic at equal lower and upper bounds btw nonbasic between bounds 0 none no status assigned 1 bas basic 2 sup superbasic 3 low nonbasic lt normally lower bound 4 upp nonbasic gt normally upper bound 5 6 ampl display InCr sstatus InCr sstatus MID C bas W TEX low 7 A table of the recognized CPLEX status values is stored in the AMPL option sstatus_table displayed above Numbers and short strings representing status values are given in the first two columns The numbers are mainly for communication between AMPL and CPLEX though you can access them by using the suffix sstatus num in place of Sstatus The entries in the third column are comments The output of the display command shows that variable InCr MID_C is in the basis and InCr W_TEX at its lower bound at optimality You can change a variable s basis status using AMPL s let command This may be useful in instances where you want to provide an initial basis to jump start CPLEX ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE CPLEX Synonyms The following list contains alternative names for certain CPLEX directives The use of
40. ause it avoids some overhead processing If you anticipate that the simplex optimizer will require many iterations even with the advanced basis or if the model is large and preprocessing typically removes much from the model then setting 2 may yield a faster solution by giving you the advantages of preprocessing However in such cases you might also consider not using the advanced basis by setting this parameter to 0 instead on the grounds that the basis may not be giving you a helpful starting point after all Setting 2 may also be effective for MIPs in which the percentage of integer constraints is low It may also reduce the solution time of fixed MIPs crash i default 1 This directive governs CPLEX s procedure for choosing an initial basis except when the basis is read from a file as specified by the directive readbasis described below A value of i 0 causes the objective to be ignored in choosing the basis whereas values of 1 and 1 select two different heuristics for taking the objective into account The best setting for your purposes will depend on the specific characteristics of the linear programs you are solving and must be determined through experimentation pgradient i default 0 This directive governs the primal simplex algorithm s choice of a pricing procedure that determines which variable is selected to enter the basis at each iteration Your choice is likely to make a substantial difference to the tradeoff between c
41. barrier method iterations and returns its current solution whether or not it has determined that the solution is optimal clocktype i default 1 The default setting of clocktype 1 means that CPLEX will measure time in terms of CPU seconds A setting of 2 means that CPLEX will measure time in terms of elapsed wall clock seconds 52 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE lpiterlim i default 2 1e 9 or larger CPLEX stops after i simplex method iterations and returns its current solution whether or not it has determined that the solution is optimal lowerobj r1 default 1 0e 75 upperobj r2 default 1 0e 75 CPLEX stops at the first iteration where the solution is feasible in the constraints and the objective value is below r1 or above r2 At their default values these directives have no practical effect Setting x1 for a minimization or r2 for a maximization to a good value for the objective will cause CPLEX to stop as soon as it achieves this value readbasis f1 writebasis f2 Current versions do not require you to explicitly save the basis to hot start CPLEX variable status is automatically stored and used between CPLEX invocations The readbasis and writebasis directives are included for backward compatibility with previous versions of CPLEX for AMPL which did not use variable status information If the readbasis directive is specified then the initial basis is instead read from the file 1 which must also be in t
42. bjective involving division by 0 nonlinear objective without CPLEX Barrier option for QPs CPLEX MIP option needed to handle piecewise linear terms quadratic constraint involves division by zero bug no quadratic terms in nonlinear constraint error in cplex options surprise return from a CPLEX routine perhaps a driver bug constraint is not convex quadratic logical constraint is not an indicator constraint CPLEX licensing problem Following optimization CPLEX also returns an individual status for each variable and constraint This feature is intended mainly for reporting the basis status of variables after a linear program is solved either by the simplex method or by an interior point barrier method followed by a crossover routine In addition to the variables declared by var statements in an AMPL model solvers also define slack or artificial variables that are associated with constraints Solver statuses for these latter variables are defined in a similar way ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 89 The major use of solver status values from an optimal basic solution is to provide a good starting point for the next optimization run possibly after a data change You can refer to a variable s solver status by appending sstatus to its name Initially when no problem has yet been solved all variables have the status none After an invocation of a simplex solver the same display lists the statuses of the variables
43. can view each of these directives as corresponding to a particular decision faced at each step in the branch amp cut procedure To be specific imagine that an LP QP QCP subproblem has just been solved The sequence of decisions and the corresponding directives are then as follows Branch next from which node in the tree backtrack nodesel Branch by constraining which fractional variable at the selected node mip_priorities ordertype varselect refer to the discussion on setting priorities by variable in Algorithmic Control on page 77 Investigate which of a fractional variable s two resulting branches first branch refer to the discussion on setting branching preference by variable in Algorithmic Control on page 77 Solve the resulting new subproblem by which LP algorithm mipalgorithm Explore rounded subproblem solutions how often heuristicfreq 62 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE It is often hard to predict which combination of directives will work best Some experimentation is usually required your knowledge of the problem structure may also suggest certain choices of branch amp cut strategy The first directive you may wish to consider is the mipemphasis directive which guides the overall balance between seeking optimality and feasibility by setting many of the other directives to achieve this overall balance mipemphasis i default 0 This directive guides CPLEX s branch amp cut strategy
44. cific location for the temporary files by setting option TMPDIR to a valid path On a PC you might use ampl option TMPDIR D temp On a Unix machine a typical choice would be ampl option TMPDIR tmp ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 25 26 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Command Line Switches Customizing AMPL Certain AMPL options normally set with the option command during an AMPL session can also be set when AMPL is first invoked This is done using a command line switch consisting of a hyphen and a single letter followed in some cases by a numeric or string value You will find these switches most useful when you have one or more model data or run file that you want AMPL to process using different option settings at different times without actually editing the files themselves The table below summarizes the command line switches and their equivalent names when set with the AMPL option command Table 4 1 AMPL Option Names for Command Line Switches Switch AMPL Option Description Cn Cautions n n 0 suppress caution messages n 1 report caution messages default n 2 treat cautions as errors en eexit n n gt 0 abandon command after n errors n 0 abort AMPL after Inl errors n 0 report any number of errors ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 27 Switch AMPL Option Description f funcwarn 1 do not t
45. city solutions are generated 1 0 keeps only the newest solutions 1 1 keeps the solutions with the best objective values and 1 2 keeps the solutions that are most diverse poolstub f The directive specifies the stub for solution files in the MIP solution pool The solutions that remain in the solution pool after some are replaced if more than poolcapacity solutions are found are written to files f amp 1 f amp n where n is the number of solutions in the solution pool That is file names are obtained by appending 1 2 nto f The value of n is returned in suffix npoo1 on the problem populate i default 0 This directive tells CPLEX to run its populate algorithm in order to generate more solutions When i 0 only the usual MIP optimization is run When i 1 populate is run after MIP optimization When i 2 populate is run instead of MIP optimization populatelim i default 20 Limits the number of solutions added to the solution pool by the populate algorithm ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 73 Directives for Controlling Output When invoked by solve CPLEX normally returns just a few lines to your screen to summarize its performance The following directives let you choose more output which may be useful for monitoring the progress of a long run or for comparing the effects of other directives on the behavior of the branch amp cut algorithm Output normally comes to the screen but may be redirected to a
46. ctive determines whether primal reductions dual reductions or both are performed during preprocessing By default CPLEX performs both Set this directive to 0 to prevent all reductions 1 to only perform primal reductions and 2 to only perform dual reductions While the default usually suffices performing only one kind or the other may be useful when diagnosing infeasibility or unboundedness presolve i default 1 Prior to invoking any simplex algorithm CPLEX applies transformations that reduce the size of the linear program without changing its optimal solution In this presolve phase constraints that involve only one non fixed variable are removed either the variable is fixed and also dropped for an equality constraint or a simple bound for the variable is recorded for an inequality Each inequality constraint is subjected to a simple test to determine if there exists any setting of the variables within their bounds that can violate it if not it is dropped as nonconstraining Further iterative tests attempt to tighten the bounds on primal and dual variables possibly causing additional variables to be fixed and additional constraints to be dropped ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE AMPL s presolve phase as described in Section 14 1 of the AMPL book also performs many but not all of these transformations To see how many variables and constraints are eliminated by AMPL s presolve set option show stats to 1 To suppre
47. ctives for Preprocessing 0 0c cece eee eee eee eee hn n 59 Directives for Algorithmic Control seseseseeeeeee eee 62 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Chapter 8 Chapter 9 Directives for Relaxing Optimality 00 c eee eee RII 70 Directives for Halting and Resuming the Search 000 eee eee eee eee 72 Directives to Manage the Solution Pool 0 cece eee eee eee 72 Directives for Controlling Output 0 0 0 0 eee eee III 74 Common Difficulties 0 cee eR hh huh 74 R nnirig Qut of MeMO i esna e AAA ap E adc bi dotes 74 Failure To Prove Optimality llle RII 75 Difficult MIP Subproblems oooococcccco ee I RH s 76 Defined Suffixes for CPLEX 20 00 cece eens 77 Algorithmic Control cia 22 jose ull eed aa ai 77 Sensitivity Ranging 5 3232 em uera a RE ae ee 80 Diagnosing Infeasibilities llcleeeeeeeee RII 81 Direction of Unboundedness ocooccccco ee n n nn nnn 83 CPLEX Status Codes in AMPL essesseeeee eene 85 Solve Codes uve eos a AEN ad uA se cd edicere esce RE e rm RE 85 Basi Status A A uve EE PN NU 89 E Dre cud dE E E aee o riesci ed rere 93 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 5 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 3 1 4 1 6 1 6 2 6 3 6 4 7 1 7 2 7 3 7 4 7 5 8 1 9 1 9 2 A 1 List of Tables Auxiliary Files iii Lr akt eher race EIE ERR E OUR EN each les
48. default 0 cliquecuts i1 default 0 covercuts i2 default 0 disjcuts i3 default 0 flowcuts i4 default 0 flowpathcuts i5 default 0 fraccuts i6 default 0 gubcuts i7 default 0 impliedcuts i8 default 0 mircuts i9 default 0 zerohalfcuts i10 default 0 Integer programming solve times can often be improved by generating new constraints or cuts based on polyhedral considerations These additional constraints tighten the feasible region reducing the number of fractional variables to choose from when CPLEX needs to select a branching variable CPLEX can generate cuts based on different combinatorial constructs corresponding to the directives listed above By default CPLEX decides whether to generate cuts Typically the default setting yields the best performance To disable a particular family of cuts set its directive to 1 To enable moderate cut generation set the appropriate directive to 1 To enable aggressive cut generation set it to 2 To set all these classes of cuts to one common value for instance 1 to disable all cuts use the directive mipcuts Cuts directives are applied in the order in which they are encountered so for instance mipcuts 1 fraccuts 2 first turns off all cuts and then turns fractional cuts back on The reverse case of fraccuts 2 mipcuts 1 results in all cuts being disabled as though the raccuts 2 directive is not present ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Using more aggressive cut g
49. directive 73 poolreplace directive 73 poolstub directive 73 populate directive 73 populatelim directive 73 predual directive 44 preprocessing directives 43 directives integer programs only 59 prereduce directive 44 prerelax directive 61 presolve directive 44 presolvenode directive 61 prestats directive 45 pretunefile directive 36 pretunefileprm directive 36 pricing directive 48 primal directive 40 primal simplex algorithm 39 primal dual barrier algorithm 39 primalopt directive 41 priorities directive 68 priority suffix 77 probe directive 61 probetime directive 61 problem file ASCII format 23 binary format 23 problem files 21 Q qcpconvergetol directive 50 quadratic programming 32 R RAM requirement for linear programs 40 readbasis ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 99 directive 53 readvector directive 53 refactor directive 48 relax optimality 70 relax directive 43 relobjdiff directive 71 repairtries directive 68 repeatpresolve directive 61 requirements AMPL 10 rinsheur directive 68 round directive 69 S save output 22 saving temporary files 22 Scale directive 45 search directives for stopping and starting 72 sensitivity directive 54 siftopt directive 41 simplex algorithm basic solution 40 directives 45 singular directive 53 solution display information 22 save output 22 saving a solution 22 solution command 22
50. dle The transformation to a linear program can be done if the following conditions are met Any piecewise linear term in a minimized objective must be convex its slopes forming an increasing sequence as in 1 1 3 5 5 1 0 1 5 3 gt gt x j Any piecewise linear term in a maximized objective must be concave its slopes forming a decreasing sequence as in 1 3 1 5 0 5 0 25 x j Any piecewise linear term in the constraints must be either convex and on the left hand side of a constraint or equivalently the right hand side of a constraint or else concave and on the left hand side of a constraint the right hand side of a constraint In all other cases the transformation is to a mixed integer program AMPL automatically performs the appropriate conversion sends the resulting linear or mixed integer program to CPLEX and converts the solution into user defined variables The conversion has the effect of adding a variable to correspond to each linear piece when the above rules are not satisfied additional integer variables and constraints must also be introduced Quadratic Programs This user guide provides but a brief description of quadratic programming In effect it is assumed that you are familiar with the area Interested users may wish to consult a good reference such as Practical Optimization by Gill Murray and Wright Academic Press 1981 for more details A mathematical description of
51. e and solve result by a message string In the example shown solve result numis set to 0 and solve result to solved indicating normal termination The AMPL option solve result table lists the valid combinations of Solve result num and solve result for CPLEX These combinations should be interpreted as shown below Table 9 1 Interpretation of Numeric Result Codes Number String Interpretation 0 99 solved optimal solution found 100 199 solved optimal solution indicated but error likely 200 299 infeasible constraints cannot be satisfied 300 399 unbounded objective can be improved without limit 400 499 limit stopped by a limit such as on iterations 500 599 failure stopped due to solver error Status ranges are normally used to control algorithmic flow in AMPL scripts where solve result numcan be tested to distinguish among cases that must be handled in different ways It is occasionally useful however to make fine distinctions among different solver termination conditions All valid solve codes with the corresponding termination message from CPLEX are listed in the table below Table 9 2 Solve Codes and Termination Messages Number Message at termination O optimal solution 1 primal has unbounded optimal face 2 optimal integer solution 3 optimal integer solution within mipgap or absmipgap 100 best solution found primal dual feasible 110 optimal with unscaled infeasibilities 111 integer optimal with unscaled infe
52. e format as outlined below With this feature you may be able to solve AMPL models with a solver that reads its problem input in MPS file format If you choose to use this feature you will find AMPL s ability to produce auxiliary files very useful since these files can be used to relate the MPS file format information to the sets variables constraints and objectives defined in the AMPL model However you will not be able to bring the solution variable values dual values and so on back into AMPL further work with the solution must be performed outside of AMPL To translate your model into MPS file format use the write command as outlined above with m as the first letter of the ilename To illustrate the command shown below creates a file named steel mps ampl write msteel In most cases you will need to run your solver separately to obtain the solution Note that the MPS format does not provide a way to distinguish between objective maximization and minimization However CPLEX assumes that the objective is to be minimized There is no standardization on this issue other solvers may assume maximization Thus it is incumbent upon the user of the MPS format to ensure that the objective sense in the AMPL model corresponds to the solver s interpretation Temporary Files Directory If the TMPDIR option is not set AMPL writes the problem and solution files and other temporary files to the current directory You can give a spe
53. e start algorithm 11 1 or the infeasibility constant start algorithm 11 2 may improve numerical stability possibly at the cost of speed Setting 11 3 selects the standard barrier algorithm bargrowth r default le 12 This directive is used to detect unbounded optimal faces At higher values the barrier algorithm will be less likely to conclude that the problem has an unbounded optimal face but more likely to have numerical difficulties 1f the problem does have an unbounded face Any positive number is acceptable input barcorr i default 1 CPLEX may perform centering corrections if it encounters numerical difficulties during the barrier method optimization By default 1 1 the barrier solver automatically computes an estimate for the maximum number of centering corrections done at each iteration If the automatic estimate is computed to be 0 setting the value to a positive integer may improve the numerical stability of the algorithm probably at the expense of computation time ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 49 barobjrange r default le 20 This directive sets the maximum absolute value of the objective function CPLEX s barrier algorithm looks at this value to detect unbounded problems Any positive value is acceptable input However care should be taken to avoid choosing a value so small that CPLEX will conclude a problem is unbounded when it is not barstart i default 1 This directive controls the starting poin
54. ective controls whether CPLEX should perform probing before solving the MIP Probing can lead to dramatic reductions in the problem size but can also consume large amounts of time By default 1 0 CPLEX automatically decides whether to perform probing To disable probing set i 1 To enable probing set it to a value of 1 2 or 3 A larger value results in an increased level of probing More probing can lead to greater reductions in problem size but also significant increases in probing time probetime i default le 75 This directive limits the amount of time in seconds spent probing repeatpresolve i default 1 Tells CPLEX whether to re apply presolve with or without cuts to a MIP model after processing at the root is otherwise complete The default of i 1 lets CPLEX choose Set i 1 to represolve without the generated cuts and set 1 2 to represolve using the generated cuts Set 1 3 to represolve with the generated cuts and allow new cuts Set 1 0 to prohibit represolve sosi i default 1 An optimization problem containing restrictions that at most one of a specified group of variables can take a nonzero value is a form of discrete optimization that can be handled by an equivalent mixed integer program When i is at its default value of 1 this conversion is ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 61 performed using a structure known as a special ordered set of type 1 If i is changed to 0 the conversion is made instead to an
55. eneration causes CPLEX to make more passes through the problem to generate cuts The disjcuts cliquecuts and covercutsdirective also supports a setting of 3 for very aggressive cut generation option mip priorities v1 i1 v2 i2 From CPLEX 7 0 onwards the nip priorities option has been superseded by the priority suffix Please refer to Algorithmic Control on page 77 for a discussion of setting priorities by individual variable mipsearch default 0 This directive tells CPLEX what type of tree search to use With the value of 0 CPLEX will decide based on problem characteristics With a value of 1 traditional branch and bound search is used and with a value of 2 dynamic search is used migcpstrat default 0 This directive applies when the integer program has quadratic constraints that is when the problem is an MIQCP CPLEX can either solve a linear program at each node of the branch and bound tree which is faster but only gives an approximate solution to the underlying quadratically constrained program QCP and thus will usually require more nodes or CPLEX can solve a QCP The default value of 0 allows CPLEX to decide which strategy to use based on problem characteristics A value of 1 directs CPLEX to solve a QCP at each node and a value of 2 directs CPLEX to solve an LP nodefile i default 1 workfilelim r default 128 workfiledir f The list of unprocessed nodes in the branch amp cut tree typically dominates CPLEX s memor
56. equires more time for each node but usually fewer nodes to solve the problem This strategy works especially well on binary problems where the number of binary variables is significantly greater than the number of rows It is also useful when memory is limited creating fewer nodes requires less memory Pseudo reduced costs 1 4 are related to pseudocosts 1 2 but are less expensive to compute They may therefore be advantageous on models whose LP relaxation contains many hundreds or thousands of fractional variables that are potentially to be branched upon Directives for Relaxing Optimality In dealing with a difficult integer program you may need to settle for a good solution rather than a provably optimal one The following directives offer various ways of weakening the optimality criterion for CPLEX s branch and bound algorithm absmipgap r1 default 0 0 mipgap r2 default 1 0e 4 The optimal value of your integer program is bounded on one side by the best integer objective value found so far and on the other side by a value deduced from all the node subproblems solved so far The search is terminated when either best node best integer r1 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE or best node best integer 1 0 best node lt r2 Thus the returned objective value will be no more than rl from the optimum and will also be within about 100 r2 percent of the optimum if the optimal value is significant
57. er of iterations required The following directives select and control these preprocessing features aggregate il1 default 1 aggfill i2 default 10 When i1 is left at its default value of 1 CPLEX looks for constraints that possibly after some rearrangement define a variable x in terms of other variables two variable constraints of the form x y b constraints of the form x Xj yj where x appears in less than 12 other constraints Under certain conditions both x and its defining equation can be eliminated from the linear program by substitution In CPLEX s terminology each such elimination is an aggregation of the linear program When i1 is 1 CPLEX decides how many passes to perform Set i1 to 0 to prevent any such aggregations Set 11 to a positive integer to specify the precise number of passes Aggregation can yield a substantial reduction in the size of some linear programs such as network flow LPs in which many nodes have only one incoming or one outgoing arc If 12 2 however aggregation may also increase the number of nonzero constraint coefficients resulting in more work at each simplex iteration The default setting of 12 10 usually makes a good tradeoff between reduction in size and increase in nonzeros but you may want to experiment with lower values if CPLEX reports that many aggregations have been made If CPLEX consistently reports that no aggregations can be performed on the other hand you can set il to 0
58. er optimization certain computations that require a basis that has been factored for example for the computation of the basis condition number may be unavailable The workfilelim directive specifies the maximum amount of RAM that may be used for the Cholesky factorization of the barrier optimizer before files are used for the remainder of memory needs The default is 128 which means CPLEX will use 128 megabytes of RAM before using disk space These temporary barrier files are created in the directory specified by the value of the workfiledir directive If no value is specified the directory specified by the TMPDIR on Unix or TMP on Windows environment variable is used If TMPDIR or TMP are not set either the current working directory is used Temporary barrier files are deleted automatically when CPLEX terminates normally threads i default 0 This directive specifies a global thread limit that is a default thread count for the parallel MIP parallel barrier and concurrentopt optimizers The value 0 tells CPLEX to use as many threads as are allowed by the license when the parallelmode directive is 1 A value of 0 when the parallelmode is 0 or 1 tells CPLEX to use as many threads as possible subject to maintaining a deterministic algorithm A positive value for i specifies that i threads should be used netopt i default 1 CPLEX incorporates an optional heuristic procedure that looks for pure network constraints in your linear progra
59. er r seconds of computation time and returns its current solution whether or not it has determined that the solution is optimal ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 53 Directives for Controlling Output When invoked by solve CPLEX normally returns just a few lines to your screen to summarize its performance The following directives let you choose a greater amount of output which may be useful for monitoring the progress of a long run or for comparing the effects of other directives on the detailed behavior on CPLEX s algorithms Output normally comes to the screen but it may be redirected to a file by specifying solve gt filename bardisplay i default 0 The default choice of 1 0 produces a minimal few lines of output from CPLEX summarizing the results of a barrier method run When i 1 a log line recording the barrier iteration number primal and dual objective values and infeasibility information is displayed after each barrier iteration When i 2 additional information about the barrier run is provided This level of output is occasionally useful for diagnosing problems of degeneracy or instability in the barrier algorithm file f1 This directive instructs CPLEX to write a copy of the model it receives for solution into a file named 1 logfile f1 This directive instructs CPLEX to create a log file named 1 that will contain output from the optimization The amount of output in the log file will depend on other di
60. escendants of one node however before backtracking to a better part of the tree The default value of 9999 gives a moderately breadth first search and represents a good compromise Lower values often pay off when the LP subproblems are expensive to solve Setting 12 to 0 chooses a pure depth first strategy regardless of r CPLEX automatically uses this strategy to search for an initial feasible integer solution at the outset of the branch amp cut procedure ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE branch i1 default 0 The branch directive determines the direction in which CPLEX branches on the selected fractional variable When branching on a variable x that has fractional value r CPLEX creates one subproblem that has the constraint x gt ceil r and one that has the constraint x lt floor r these are the up branch and down branch respectively By default i1 0 CPLEX uses an internal heuristic to decide whether it should first process the subproblem on the up branch or on the down branch You may instead specify consistent selection of the up branch 11 1 or down branch i1 1 Sometimes one of these settings leads the algorithm to examine and discard the poorer branches high in the tree reducing the tree size and overall solution time Branching control can also be exercised using the direction suffix described in Algorithmic Control on page 77 fpheur i3 default 0 This directive tells CPLEX whether or not to app
61. ff the default scaling by setting i 1 A value of 1 invokes a modified more aggressive scaling method that can produce improvements on some problems Since CPLEX has internal logic that determines when it need not scale a problem setting the scale directive to 1 rarely improves performance Directives for Controlling the Simplex Algorithm Several key strategies of the primal and dual simplex algorithms can be changed through CPLEX directives If you are repeatedly solving a class of linear programs that requires substantial computer time experimentation with alternative strategies can be worthwhile ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 45 advance i default 0 By default 1 0 the advanced basis indicator is off You can set it according to Table 6 2 Table 6 2 Settings for the advance Directive Setting Effect 0 This is the default value The advanced basis indicator is off 1 The advanced indicator is on ILOG CPLEX uses an advanced basis supplied by the user Preprocessing is skipped 2 The advanced indicator is on and ILOG CPLEX will crush an advanced basis or starting vector supplied by the user If this parameter is set to 1 or 2 ILOG CPLEX uses advanced starting information when optimization is initiated If you anticipate the advanced basis to be a close match for your problem so that relatively few iterations will be needed or if you are unsure then setting 1 is a good choice bec
62. he standard MPS basis format This basis determines the initial solution If the writebasis directive is specified CPLEX writes a record of the final simplex basis to the file named 2 in the standard MPS basis format Normally this is an optimal basis but it may be otherwise if an optimum does not exist or could not be found by the chosen algorithm or if the iterations were terminated prematurely by one of the directives described below readvector f1 writevector f2 These directives are used to take a barrier algorithm solution and write it to or read it from a CPLEX vec file Because AMPL always instructs CPLEX to take its barrier method solution and apply a hybrid method to obtain a basic solution this feature can only be used if a barrier iteration limit is exceeded If the readvector directive is specified CPLEX will read in a vec file named 1 and use it to initiate the hybrid crossover method that results in an optimal basic solution Note that CPLEX will not perform additional barrier iterations after reading in the vec file Similarly if the writevector directive is specified CPLEX will write out vec file named 2 singular i default 10 CPLEX will attempt to repair the basis matrix up to i times when it finds evidence that the matrix is singular Once this limit is exceeded CPLEX terminates with the current basis set to the best factorizable basis that has been found timelimit r default 1 0e 75 CPLEX stops aft
63. ich a linear program s basic variables may violate their bounds You may wish to lower r1 after finding an optimal solution if there is any doubt that the solution is truly optimal but if it is set too low CPLEX may falsely conclude that the problem has no feasible solution Valid values for x1 lie between 1e 9 and 0 1 The Markowitz threshold r2 lt 1 influences the order in which variables are eliminated during basis factorization Increasing r2 may yield a more accurate factorization and consequently more accurate computations during iterations of the simplex algorithm Too large a value may produce an inefficiently dense factorization however Valid values for r2 lie between 0 0001 and 0 99999 The optimality tolerance r3 gt 0 specifies how closely the optimality or dual feasibility conditions must be satisfied for CPLEX to declare an optimal solution Valid values for x3 lie between 1e 9 and 0 01 Directives for Starting and Stopping Normally CPLEX uses an internal procedure to determine a starting point for the simplex algorithm then iterates to optimality The following directives override these conventions so that you can start from a saved basis and can stop when a certain criterion is satisfied Command line versions of CPLEX for AMPL can also be stopped by using break typically by pressing the Control and C keys simultaneously The best solution found so far is returned bariterlim i default 2100000000 CPLEX stops after i
64. imizing This forces the mixed integer optimization to ignore integer solutions that are not at least r1 better than the one found so far As a result there tend to be fewer nodes generated and the algorithm terminates more quickly but the true integer optimum may be missed if its objective value is within r1 of the best integer objective found If r1 0 r2 is used to adjust the objective function value during the optimization For a maximization problem r2 times the absolute value of the objective function value is added to the best feasible objective value obtained so far Similarly if the objective is to be minimized r2 times the absolute value is subtracted from the best so far feasible objective value Subsequent nodes are ignored if their linear relaxations have optimal values worse that this adjusted value Positive values of r2 usually speed the search but may cause the true optimum to be missed ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 71 Directives for Halting and Resuming the Search There is usually no need to make exhaustive runs to determine the impact of different search strategies or optimality criteria While you are experimenting consider using one of the directives below to set a stopping criterion in advance In each case the best solution found so far is returned to AMPL As mentioned earlier using break on command line versions of CPLEX for AMPL will return the best known solution for integer programs that
65. in memory when the nodefile directive is used Storing part of each node in files will allow more nodes to be explored once the work ilelim amount of memory has been used See the discussion of the nodefile directive This feature may be especially useful if you use steepest edge pricing for subproblem simplex pricing strategy because the pricing information consumes a lot of memory The best approach to reduce memory usage is to modify the solution process Switching to a higher backtrack parameter value and best estimate node selection strategy or depth first search node selection which is even more extreme often works Depth first search rarely generates a large unexplored node list since CPLEX will be diving deep into the branch amp cut tree rather than jumping around within it This narrowly focused search also often results in faster individual node processing times Overall efficiency is sometimes worse than with best bound node selection since each branch is exhaustively searched to the deepest level before fathoming it in favor of better branches Another memory conserving strategy is to use strong branching variable selection using the varselect directive When using strong branching substantial computational effort is made at each node to determine the best branching variable As a result many fewer nodes are generated reducing the overall demand on memory Often strong branching is faster as well as using less memory On some pr
66. ing a text editor 15 96 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE end AMPL session 15 F feasibility directive 52 feasopt directive 35 feasoptobj directive 35 file creating auxiliary 23 predefined commands 28 file directive 54 files load several files 17 temporary directory 25 flowcuts directive 66 flowpathcuts directive 66 fpheur directive 65 fraccand directive 60 fraccuts directive 66 fracpass directive 60 G global thread limit 42 gubcuts directive 66 H heuristicfreq directive 65 iis suffix 81 iisfind directive 35 impliedcuts directive 66 infeasible problems directives 43 installation 10 AMPL and Parallel CPLEX 11 Unix 10 Windows 11 integer programs 31 integrality directive 71 L launching AMPL 15 lazy directive 65 78 licensing 11 linear programs 31 CPLEX solution method 39 logfile directive 54 lowercutoff directive 71 lowerobj directive 53 lpdisplay directive 54 lpiterlim directive 53 markowitz directive 52 Markowitz threshold 52 Markowitz tolerance 52 maximize directive 43 memory requirement for linear programs 40 running out 74 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 97 memory usage execute solver outside AMPL 24 memoryemphasis directive 41 messages termination 86 minimize directive 43 MIP difficult subproblems 76 mip priorities option 67 mipalgorithm directive 65 mipcrossover directive 65 mipcuts directive 66 mipdisp
67. ion 10 up suffix 80 uppercutoff directive 71 upperobj directive 53 usage notes 12 user cuts 65 79 V varselect directive 70 version directive 55 WwW Windows installation 11 workfiledir directive 41 67 workfilelim directive 41 67 write command 22 23 writebasis ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 101 directive 53 writevector directive 53 102 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE
68. ions of acceptable quality Table 7 2 recapitulates the settings of this parameter Table 7 2 Settings for the mipemphasis Directive Setting Effect O default Balance optimality and feasibility 1 Emphasize feasibility over optimality 2 Emphasize optimality over feasibility 3 Emphasize moving best bound 4 Emphasize hidden feasibles ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 63 backtrack r default 0 9999 bbinterval i1 default 7 nodeselect i2 default 1 These directives determine the criterion for choosing the next node from which to branch once a feasible integer solution has been found Depending on whether 12 is set to 1 2 or 3 CPLEX associates a value with each node and chooses a node based on these values For 12 1 a node s value is the bound on the integer optimum that is given by solving the LP subproblem at that node For 12 2 or i2 3 a node s value is an estimate of the best integer objective that can be achieved by branching from that node estimates of node objective values are derived from so called pseudocosts which are in turn derived from the solutions to the LP subproblems Settings 2 and 3 differ regarding the exact nature of the estimated objective Depending on the value at the current most recently created active node CPLEX either branches from that node or else backtracks to the node that has the best bound 12 1 or best estimate 12 2 or 12 23 among all active n
69. is 2 those with suffix of 2 are treated at user cuts and all others are treated as ordinary constraints mipalgorithm i1 default 0 mipcrossover i2 default 1 This directive specifies the algorithm or combination of algorithms that CPLEX will apply to solve the LP subproblem at each branch amp cut node The recognized values of i1 are Table 7 3 Settings for the mipcrossover Directive 0 Automatic 1 Primal simplex ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 65 or 2 Dual simplex 3 Network simplex 4 Barrier 5 Sifting The default strategy chooses the algorithm by using an internal heuristic based on the type of subproblem Typically CPLEX will use the dual simplex method when the problem is linearly constrained and the barrier method when it is a quadratically constrained program For linear programming subproblems the default settings usually perform well but other strategies may significantly reduce the time per node except for the quadratically constrained case where barrier is the only available choice These settings do not significantly affect the number of nodes that must be visited during the search When the Barrier algorithm is used to solve subproblems i1 4 by default 12 1 CPLEX uses primal simplex for the crossover In certain cases dual simplex may be faster When the subproblems are quadratically constrained programs CPLEX does not perform a crossover so this directive has no effect mipcuts i
70. itional steps when solve is invoked and the problem is infeasible The easopt and easoptobj directives tell CPLEX to relax constraints and bounds to find a feasible solution The iisind directive tells CPLEX to try to refine the conflict among the constraints and bounds to a smaller set of constraints and bounds These directives can also be applied to integer programs conflictdisplay i default 1 This directive controls the amount of output during conflict refinement Set 1 0 for no output i 1 for summary output and i 2 for a detailed display feasopt i default 0 Whether to find a feasible point for a relaxed problem when the problem is infeasible With the default setting of 0 no feasible point is found Set i 1 to find a feasible point and i 2 to find an optimal feasible point among all those that require only as much relaxation as is needed to find the first feasible point feasoptobj i default 1 This directive sets the objective to use in measuring minimality of a relaxation Set i 1 for minimizing the sum of the relaxations of constraints and bounds Set i 2 for minimizing the number of constraints and bounds that must be relaxed Set 1 3 to minimize the sum of squares of the required relaxations of constraints and bounds iisfind i default 0 When i 1 for an infeasible problem CPLEX returns an irreducible infeasible subset IIS of the constraints and variable bounds By definition members of an IIS have no feasible solution but d
71. itor that saves files in ASCII format Windows command line DOS users can use edit or notepad and Unix users vi or emacs If you are using edit under DOS for instance you can type ampl shell edit steel dat Use editor menus and commands to edit your file then save it and exit the editor At the ampl prompt you can type new AMPL commands such as ampl reset data ampl data steel dat Note that editing a file in a text editor does not affect your AMPL session until you explicitly reload the edited file as shown above Running AMPL in Batch Mode If you have previously developed a model and its data and would like to solve it and display the results automatically you can create a file containing the commands you would like AMPL to execute and specify that file at the command line when you run AMPL For example you might create a file called steel run containing the commands model steel mod data steel dat option solver cplexamp solve display Make steel ans Note that this assumes that steel run is in the same directory as the model and data files and that AMPL can be found on the path You can then run AMPL as follows C gt ampl steel run A more flexible approach which is a commonly followed convention among AMPL users is to put just the AMPL commands the last three lines in the example above in a file with the run extension You can then type C gt ampl steel mod steel dat steel run
72. ive 64 baralg directive 49 barcorr directive 49 bardisplay directive 54 bargrowth directive 49 bariterlim directive 52 barobjrange directive 50 baropt directive 41 barrier algorithm directives 49 barstart directive 50 basic solution simplex algorithm 40 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Index 93 basis simplex algorithm 40 batch mode 16 bbinterval directive 64 bestnode suffix 79 binary format problem and solution files 23 boundstr directive 59 branch directive 65 C cliquecuts directive 66 clocktype directive 52 72 coeffreduce directive 59 command let 90 option 20 27 option solver 19 predefined commands 28 solution 22 write 22 23 command line switches 27 commands display 22 comptol directive 50 concurrentopt directive 41 configuration 10 conflictdisplay directive 35 covercuts directive 66 CPLEX append directives 35 barrier algorithm 31 barrier algorithm QP extension 33 choice of algorithm 39 cplex options option 34 linear programs 39 memory requirement for linear programs 40 mixed integer algorithm 57 optimization methods 39 problems handled by CPLEX 31 specifying CPLEX directives 34 crash directive 46 crossover directive 50 current suffix 80 cutpass directive 60 cuts generate 66 polyhedral 66 cutsfactor directive 60 D densecol directive 50 dependency directive 44 devex pricing 48 dgradient directive 47 direction suffix 77 directive
73. l from Section 4 3 of the AMPL book ampl model steelT mod ampl data steelT dat ampl option solver cplexamp ampl option cplex options sensitivity ampl solve CPLEX 11 0 0 sensitivity CPLEX 11 0 0 optimal solution objective 515033 18 iterations 1 in phase I suffix up OUT suffix down OUT suffix current OUT The three lines at the end show the suffix commands executed by AMPL in response to the results from CPLEX These commands are invoked automatically you do not need to type them For variables suffix current indicates the objective function coefficient in the current problem while down and up give the smallest and largest values of the objective coefficient for which the current simplex basis remains optimal CPLEX returns 1e 20 for down and 1e 20 for up to indicate minus infinity and plus infinity respectively ampl display Sell down Sell current ampl Sell up Sell down Sell current Sell up bands 1 23 3 25 1e 20 bands 2 25 4 26 1e 20 bands 3 24 9 27 215 bands 4 10 27 29 1 coils T 29 2857 30 30 8571 coils 2 33 35 1e 20 coils 3 35 2857 37 1e 20 4 35 2857 39 1e 20 coils 7 80 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE For constraints the interpretation is similar except that it applies to a constraint s constant term the so called right hand side value ampl display time down time current ampl time up time down time current time up i 1 37 8071 40 66 3786 2
74. lay directive 74 mipemphasis directive 63 mipgap directive 70 mipinterval directive 74 mipsearch directive 67 mipstartstatus directive 60 mipstartvalue directive 60 miqcpstrat directive 67 mircuts directive 66 N netfind directive 49 netopt directive 42 network primal simplex algorithm 39 nodefile directive 67 nodelim directive 72 nodeselect directive 64 nonlinear quadratic programs 31 numeric result codes interpretation 86 O objdifference directive 71 optimality directives for relaxing 70 optimality directive 52 optimization methods available in CPLEX 39 option cautions 27 eexit 27 funcwarn 28 gentimes 28 linelim 28 mip_priorities 67 outopt 28 presolve 28 randseed 28 substout 28 times 28 version 28 options add options 21 persistent settings 28 preserve settings 29 set options 27 specify solver options 20 ordering directive 50 ordertype directive 68 out of memory 24 output directives for controlling 72 74 98 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE directives for controlling output 54 P Parallel CPLEX installing with AMPL 11 parallelmode directive 42 paramfile directive 36 paramfileprm directive 36 persistent option settings 28 perturbation directive 51 perturblimit directive 51 pgradient directive 46 piecewise linear programs transformation 32 polishtime directive 68 poolagap directive 73 poolcapacity directive 73 poolgap directive 73 poolintensity
75. lgorithm will be very slow Given adequate memory CPLEX s performance is relatively insensitive to changes in refactorization frequency For a few extremely large difficult problems you may be able to improve performance by reducing i from the value that CPLEX chooses netfind i default 1 This directives governs the method used by the CPLEX network optimizer to extract a network from the linear program The value of i influences the size of the network extracted potentially reducing optimization time The default value 1 1 extracts only the natural network from the problem CPLEX then invokes its network simplex method on the extracted network In some cases CPLEX can extract a larger network by multiplying rows by 1 reflection scaling and rescaling constraints and variables so that more matrix coefficients are plus or minus 1 Setting the netfind directive to 2 enables reflection scaling only while setting it to 3 allows reflection scaling and general scaling Directives for Controlling the Barrier Algorithm Several key strategies of the barrier algorithm can be changed through CPLEX directives If you are repeatedly solving a class of linear programs that requires substantial computer time experimentation with alternative strategies can be worthwhile baralg i1 default 0 The automatically determined choice of barrier algorithm 11 0 is usually the fastest However on primal or dual infeasible problems the infeasibility estimat
76. llel mode Licensing ILOG License Manager ILM access keys are needed for both AMPL and CPLEX If you have already activated a license for the CPLEX Suite on this machine you only need to activate an AMPL license to use the AMPL CPLEX System Updating an Existing License If you are upgrading from a previous version of CPLEX please refer to the ILM license update procedures provided separately or contact ILOG Sales Administration You should skip any installation steps that would establish a new license New Installation If you are installing CPLEX or AMPL for the first time you will receive an ILOG License Manager ILM manual and a license key that enables the use of AMPL and or CPLEX Follow the instructions in that manual for details on how to install the license key ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 11 12 Usage Notes The CPLEX solver for AMPL is named cplexamp cplexamp exe on Windows This version of AMPL will use this solver by default Older versions of the CPLEX solver for AMPL were simply named cplex cplex exe on Windows Some users of that version may have specified the solver in their model or run files like this option solver cplex If you have models containing settings like this you will encounter errors or the old version of the solver might be invoked There are two ways to fix this Ideally you should change these lines to option solver cplexamp If that is not practical yo
77. lternatively you can list several strings which AMPL will automatically concatenate ampl option cplex options crash 0 dual ampl feasibility 1 0e 8 scale 1 ampl lpiterlim 100 In this form you must take care to supply the space that goes between the directives here we have put it before feasibility and iterations If you have specified the directives above and then want to try setting say optimality to 1 0e 8 and changing crash to 1 you could use ampl option cplex options ampl optimality 1 0e 8 crash 1 However this will replace the previous cplex options string The other previously specified directives such as feasibility and iterations will revert to their default values 34 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE CPLEX supplies a default value for every directive not explicitly specified defaults are indicated in the discussion below To append new directives to cplex options use this form ampl option cplex options cplex options ampl optimality 1 0e 8 crash 1 A in front of an option name denotes the current value of that option so this statement just appends more directives to the current directive string As a result the string contains two directives for crash but the new one overrides the earlier one Directives for Handling Infeasible Problems The following directives are useful when CPLEX finds that your problem is infeasible Setting these options directs CPLEX to take add
78. ly greater than 1 in magnitude Increasing r1 or r2 allows a solution further from optimum to be accepted The search may be significantly shortened as a result Valid values for r2 lie between 1e 9 and 1 0 integrality r default 1 0e 5 In the optimal solution to a subproblem a variable is considered to have an integral value if it lies within r of an integer For some problems increasing r may give an acceptable solution faster This parameter may be set to 0 to improve the robustness of MIP solutions most commonly with little if any impact on the performance of the optimizer lowercutoff r1 default 1 0e75 uppercutoff r2 default 1 0e75 These directives specify alternative cutoff values a node is fathomed if its subproblem has an objective less than r1 for maximization problems or greater than r2 for minimization problems As a result any solution returned by CPLEX will have an optimal value at least as large as rl or as small as 12 This feature can be useful in conjunction with other limits on the search but too high a value of r1 or too low a value of r2 may result in no integer solution being found objdifference r1 default 0 0 relobjdiff r2 default 0 0 This directive automatically updates the cutoff to more restrictive values Normally the incumbent integer solution s objective value is used as the cutoff for subsequent nodes When r1 gt 0 the cutoff is instead the incumbent s value r1 if minimizing or r1 if max
79. ly the feasibility pump heuristic and to what effect The default strategy is specified with 0 and allows CPLEX to decide whether or not to apply the heuristic The value of 1 specifies that the feasibility pump heuristic should not be applied The value of 1 directs CPLEX to seek any solution while the value of 2 directs CPLEX to seek a solution with a good objective value The feasibility pump heuristic can be quite expensive but it is sometimes able to find solutions on problems where otherwise CPLEX will not find a solution heuristicfreq i default 0 Use the heuristicfreq directive to specify the frequency with which CPLEX applies a heuristic at the nodes This can help find solutions missed using other settings The default value 1 0 instructs CPLEX to use internal logic to decide when to apply the heuristic To suppress application of the heuristic at all nodes let i 1 To specify the node frequency with which CPLEX applies the heuristic set i to a positive integer lazy i default 3 This directive tells CPLEX how to treat constraints with the lazy suffix At the default value constraints with lazy suffix of 1 are treated as lazy constraints and those with lazy suffix of 2 are treated as user cuts When the value is 0 all constraints with the Lazy suffix are treated as ordinary constraints When the value is 1 those with suffix of 1 are treated as lazy constraints and all others are ordinary constraints and when the value
80. m If this procedure finds sufficiently many such constraints CPLEX applies its fast network simplex algorithm to them Then if there are also non network constraints CPLEX uses the network solution as a start for solving the whole LP by the general primal or dual simplex algorithm whichever you have chosen The default value of 1 1 invokes the network identification procedure if and only if your model uses node and arc declarations and CPLEX sets up the primal formulation as discussed above Setting 1 0 suppresses the procedure while 1 2 requests its use in all cases You can have CPLEX display the number of network nodes constraints and arcs variables that it has extracted by setting the prestats directive described with the preprocessing options below to 1 CPLEX s network simplex algorithm can achieve dramatic reductions in optimization time for pure network linear programs defined entirely in terms of node and arc declarations For a pure network LP every arc declaration must contain at most one from and one to phrase and these phrases may not specify optional coefficients In the case of linear programs that are mostly defined in terms of node and arc declarations but that have some side constraints defined by subject to declarations the benefit is highly dependent on problem structure it is best to try experimenting with both i 0 and i 1 parallelmode i default 0 This directive sets the type of parallelism used by CPLE
81. ms may outweigh the performance gains from the tighter problem formulation In such cases use this directive to limit the number of cuts that CPLEX generates CPLEX will generate no more than r times the number of rows in the problem eachcutlim i default 2100000000 This directive limits the number of cuts of each type that may be generated This directive may be useful on models where such a large number of one type of cut are generated that the overall limit on cuts is reached before generating all types of cuts By default there is no limit on cuts of each type only an overall limit on cuts as specified with the cutsfactor directive fraccand i default 200 This directive limits the number of candidate variables CPLEX will examine when generating fractional cuts on a MIP model For most purposes the default of 200 will be satisfactory fracpass i default 0 This directive controls the number of passes CPLEX performs when generating fractional cuts on a MIP model The default of 0 instructs CPLEX to automatically determine the number of passes and should suffice for most problems Set it to a positive integer to specify a particular number of passes mipstartstatus i1 default 1 mipstartvalue i2 default 1 These directives control how existing MIP solution information is used by CPLEX The default value of 11 1 tells CPLEX to use incoming variable and constraint statuses Incoming statuses can be ignored by setting 11 0 Note howe
82. nd CPLEX may be able to solve it more efficiently The primal and dual directives instruct CPLEX to set up the primal or the dual formulation respectively The dualthresh directive makes a choice the dual LP if the number of constraints exceeds the number of variables by more than i and the primal LP otherwise autoopt dualopt baropt primalopt siftopt concurrentopt The autoopt directive instructs CPLEX to select an appropriate algorithm to solve the problem You can specify a particular algorithm by the dualopt baropt and primalopt directives which invoke dual simplex barrier and primal simplex methods respectively The autoopt directive will most frequently select the dual simplex method The two simplex variants use similar basis matrices but employ opposite strategies in constructing a path to the optimum Any of the algorithms can be applied regardless of whether the primal or the dual LP is set up as explained above in general the six combinations of primalopt dualopt baropt and primal dual perform differently Consider trying the barrier method or the primal simplex method if CPLEX s dual simplex method reports problems in its display or if you simply wish to determine whether another algorithm will be faster Few linear programs exhibit poor numerical performance in both the primal and the dual algorithms In general the barrier method tends to work well when the product of the constraint matrix and its transpose remains spar
83. nd has been designed to avoid problems such as degenerate stalling and numerical inaccuracy that can occur in the simplex algorithm However some linear programs can benefit from adjustments to the following directives if difficulties are encountered numericalemphasis i default 0 This directive lets you indicate to CPLEX that it should emphasize precision in numerically difficult or unstable problems with consequent performance trade offs in time and memory When set to its nondefault value of 1 CPLEX will choose tactics that emphasize numerical stability Try setting this directive before trying any of the other settings in this section doperturb i1 default 0 perturbation r default 1 0e 6 perturblimit i2 default 0 The simplex algorithm tends to make very slow progress when it encounters solutions that are highly degenerate in the sense of having many basic variables lying at one of their bounds rather than between them When CPLEX detects degenerate stalling it automatically introduces a perturbation that expands the bounds on every variable by a small amount thereby creating a different but closely related problem Generally CPLEX can make faster progress on this less constrained problem once optimality is indicated the perturbation is removed by resetting the bounds to their original values The value of r determines the size of the perturbation If you receive messages from CPLEX indicating that the linear program has been
84. near MIP models also apply to mixed integer QP models MIQP In cases where the nature of QP dictates different behavior from a directive usually the result is that the directive is ignored and default behavior remains in effect An example of this would be the dual directive to specify that CPLEX solves the explicit dual formulation for QP the default primal formulation will be used anyway In almost every case such differences will result in best performance and will require no user intervention Quadratic Constraints A model containing one or more quadratic constraints of the form T ax tx Ox Sr is called a Quadratically Constrained Program QCP and can be solved using the CPLEX barrier algorithm Linear constraints may also be present in a QCP and a positive semi definite quadratic term in the objective function is permitted If discrete variables are present then the model is termed Mixed Integer QCP or MIQCP The Q matrix for each quadratic constraint must be positive semi definite just as for a quadratic objective function to ensure that the feasible space remains convex Most of the comments regarding CPLEX features in section Quadratic Programs above also pertain to QCP with the additional observation that only the barrier optimizer applies to continuous models that have any quadratic constraints and therefore barrier is also the only choice for subproblem solution of MIQCP models ILOG AMPL CPLEX SYSTEM 11 0 USE
85. ng temporary files AMPL deletes the temporary problem n1 and solution 01 files after a solver is finished so no permanent record of the solution is kept unless you save the output yourself for example using display with redirection as illustrated above To override the deletion of temporary files you can use the AMPL write command For example C gt ampl ampl model steel mod data steel dat ampl write bsteel ampl solve CPLEX 11 0 0 optimal solution objective 192000 2 iterations 0 in phase I ampl quit The first letter b in the filename portion of the write command is interpreted specially as explained below If you now display the files in the current directory with a command such as dir steel you will find the problem file steel n1 and the solution file steel sol To later view the solution values you would use the solution command For example C gt ampl ampl model steel mod data steel dat ampl solution steel sol CPLEX 11 0 0 optimal solution objective 192000 2 iterations 0 in phase I ampl display Make Make bands 6000 coils 1400 ampl quit You must include the model and data statements as shown above so that AMPL knows the definitions of symbolic names like Make But solution then retrieves the earlier results from steel sol without running a solver ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE if you use b as the first character of the ilename
86. nts the idea is to keep the node subproblems small and easy and only add the user cuts as they are found to be needed The way in which a constraint is handled depends on the value of the lazy setting and the value of the lazy directive Table 8 1 Settings for the lazy Directive 0 Treat constraints with lazy of 1 or 2 as ordinary constraints 1 Treat constraints with lazy of 1 as lazy constraints 2 Treat constraints with lazy of 2 as user cuts 3 Treat constraints with lazy of 1 as lazy constraints and treat constraints with lazy of 2 as user cuts Another form of algorithmic control is provided by the suffix bestnode of your model s objective function which returns the best node value at the present state of optimization after control is returned to AMPL from the solve command If the optimization terminates for some reason other than a proved optimum such as a time limit or other limit the bestnode suffix in comparison with the solution value may provide some indication of the quality of the solution or the nearness of a proof of optimality ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 79 Sensitivity Ranging When the sensitivity directive described in Directives for Controlling Output on page 54 is included in CPLEX s option list classical sensitivity ranges are computed and are returned in the following three suffixes current down up Let us illustrate the use of these suffixes using an example mode
87. oblems the automatic generation of cuts results in excessive use of memory with little benefit in speed In such cases it is expedient to turn off cut generation by setting the covers and cliques directives to 1 Failure To Prove Optimality One frustrating aspect of the branch amp cut technique for solving MIP problems is that the solution process can continue long after the best solution has been found In these situations the branch amp cut tree is being exhaustively searched in an effort to guarantee that the current integer feasible solution is indeed optimal Remember that the branch amp cut tree may be as large as 2 nodes where n equals the number of binary variables A problem containing ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 75 76 only 30 binary variables could produce a tree having over 1 billion nodes If no other stopping criteria have been set the process might continue until the search is complete or your computer s memory is exhausted In general you should set at least one limit on the number of nodes processed number of improved solutions found or total processing time using the CPLEX directives given above Setting limits ensures that the tree search will terminate in reasonable time You can then inspect the solution and if necessary re run the problem using different directive settings Consider some of the shortcuts described above for improving performance particularly those for relaxing optimalit
88. odes When used in conjunction with best estimate node selection 12 2 the bbinterval setting 11 controls the interval for selecting the best bound node Decreasing this interval may be useful when best estimate finds good solutions but makes little progress moving the bound Conversely increasing i1 may help when the best estimate node selection does not find any good integer solutions The backtracking decision is made by comparing the value bound or estimate at the current node with the values at parent nodes in the tree If the value of the current node has degraded increased for a minimization decreased for a maximization by at least a certain amount relative to the values at parent nodes then a backtrack is performed The cutoff for degradation is determined by an internal heuristic that is regulated by the value of r Lower values of r which can range from 0 to 1 favor backtracking resulting in a strategy that is more nearly breadth first The search jumps around fairly high in the tree solving somewhat dissimilar subproblems Good solutions are likely to be found sooner through this strategy but the processing time per node is also greater Higher values of x discourage backtracking yielding a strategy that is more nearly depth first Successive subproblems are more similar nodes are processed faster and integer solutions are often quickly found deep in the search tree Considerable time may be wasted in searching the d
89. of the file paramfile f1 paramfileprm f2 These directives are used to import the settings contained in either the 1 or 2 files The 1 file uses AMPL directive names and the 2 file is a CPLEX PRM file tunefix 1 This directive tells CPLEX which parameters to keep fixed during the tuning algorithm The tuning algorithm starts with all parameters at their default values except those specified in 1 1 is a list of directives and values either enclosed in single or double quotes or separated by commas with no white space if more than one The list 1 is combined with any settings from the tunefixfile directive Example tunefix mipgap 0 tunefixfile f The name of a file with AMPL directives which CPLEX should leave fixed during the tuning algorithm The tuning algorithm starts with all parameters at their default values except those specified in The set of parameters in is combined with any settings from the tunefix directive tunedisplay i default 1 This directive controls the amount of output from the tuning algorithm No output is produced when i 0 A minimal amount is produced when i 1 The parameters being tried are printed when i 2 and full logs are printed when i 3 36 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE tunerepeat i default 1 CPLEX can tune on several variations of the problem The variations are obtained by permuting the rows and columns of the problem Tuning on several variations may give more robu
90. olve 6 42 CPU 6 42 Wall Output 0 05 CPU 0 05 Wall Input is the time that CPLEX takes to read the problem from a file that has been written by AMPL Solve is the time that CPLEX spends trying to solve the problem Output is the time that CPLEX takes to write the solution to a file for AMPL to read CPU values provide processor time whereas wa11 values provide elapsed time Setting 1 2 writes the timing information to standard error and setting 1 3 directs the information to both the standard output and the standard error The latter two options are only interesting for Unix CPLEX for AMPL users version This directive causes the display of the CPLEX version being used to solve the problem ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 55 56 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Using CPLEX for Integer Programming CPLEX Mixed Integer Algorithm For problems that contain integer variables CPLEX uses a branch amp cut approach The optimizing algorithm maintains a hierarchy of related linear programming subproblems referred to as the search tree and usually visualized as branching downward oN O e Figure 7 1 CPLEX Mixed Integer Algorithm the Search Tree There is a subproblem at each node of the tree and each node is explored by solving the associated subproblem ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 57 The algorithm starts with just a top or root node whose associated subproblem is
91. omputational time per iteration and the number of iterations As a rule of thumb if the number of iterations to solve your linear program exceeds three times the number of constraints you should consider experimenting with alternative pricing procedures The recognized values of i are as follows ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Table 6 3 Settings for the pgradient Directive 1 Reduced cost pricing Hybrid reduced cost devex pricing Devex pricing Steepest edge pricing Steepest edge pricing in slack pace A OUO N O Full pricing The reduced cost procedures are sophisticated versions of the pricing rules most often described in textbooks The devex and steepest edge alternatives employ more elaborate computations which can better predict the improvement to the objective offered by each candidate variable for entering the basis Compared to the default of i 0 the less compute intensive reduced cost pricing i 1 may be preferred if your problems are small or easy or are unusually dense say 20 to 30 nonzeros per column Conversely if you have more difficult problems which take many iterations to complete Phase I consider using devex pricing i 1 Each iteration may consume more time but the lower number of total iterations may lead to a substantial overall reduction in time Do not use devex pricing if your problem has many variables and relatively few constraints however as the number of calculations re
92. on in a few minutes are well known The lazy suffix is used to designate constraints which should be handled separately from the rest of the constraints in a mixed integer program Lazy constraints are constraints which are essential to defining the feasible region of the mixed integer program but that a user knows are unlikely to be violated Thus a reasonable way to handle these constraints is to apply them in a lazy way that is only as necessary Each time a potential integer solution is found it is checked against the lazy constraints If all the constraints are satisfied the integer solution is accepted ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE If any of the lazy constraints are not satisfied the potential integer solution is rejected and the constraints which were not satisfied are added to the problem as ordinary constraints The idea of lazy constraints is to keep the node subproblems small and easy as much as possible by leaving out constraints which are probably not going to be violated User cuts are constraints that are not necessary to define the feasible region of the integer program but tighten the model User cuts are checked periodically during the CPLEX branch and cut process If CPLEX finds a user cut which is violated by the solution to the node subproblem the user cut will be added to the problem as an ordinary constraint A user could add all the user cuts as ordinary constraints but as with lazy constrai
93. ons and a reference section Additional information can be found at the AMPL website at www ampl com AMPL is continuously undergoing development and while we strive to keep users updated on language features and capabilities the official reference to the language is the AMPL book which is naturally revised less frequently Installing AMPL Please read these instructions in their entirety before beginning the installation Remember that most distributions will operate properly only on the specific platform and operating system version for which they were intended If you upgrade your operating system you may need to obtain a new distribution All AMPL installations include cplexamp cplexamp exe on Windows the CPLEX solver for AMPL This combined distribution is known as the AMPL CPLEX system Note that cplexamp may not be licensed for a few users with unsupported solvers However most AMPL installations will include the use of cplexamp Requirements AMPL may be installed and run on many different hardware and software configurations A table of the currently supported configurations is available at http www ilog com products cplex product platforms cfm Unix Installation On Unix systems AMPL is installed into the current working directory We recommend that you perform the installation in an empty directory After installation make sure the executable files have read and execute privileges turned on for all users and
94. ore it reads any other files mentioned on the command line or prompts for any interactive commands ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE If you want AMPL to preserve all of your option settings from one session to the next you can cause AMPL to write the options into a text file named by setting the AMPL option OPTIONS INOUT ampl option OPTIONS INOUT c amplopt txt Before exiting AMPL writes a series of option commands to the file named by OPTIONS INOUT which when read will set all of the options to the values they had at the end of the session To use this text file set the corresponding environment variable to the same filename C gt set OPTIONS INOUT c Namplopt txt After you do this AMPL will read and execute the commands in amplopt txt when it starts up When you end a session AMPL will write the current option settings including any changes you have made during the session into this file so that they will be preserved for use in your next session If both the OPTIONS IN and OPTIONS INOUT environment variables are defined the file referred to by OPTIONS IN will be processed first then the file referred to by OPTIONS INOUT ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 29 30 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Using CPLEX with AMPL Problems Handled by CPLEX CPLEX is designed to solve linear programs as described in Chapters 1 8 and 15 16 of AMPL A Modeling Language for Ma
95. p sol display _varname var ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE CPLEX will add all the solutions it finds during the usual branch and cut algorithm to the pool with the default settings of the solution pool parameters The populate and poolintensity directives can be used to increase the number of solutions added to the pool poolagap r1 default le75 poolgap r2 default le75 These directives restrict solutions added to the pool based on their objective values relative to the best solution value currently in the pool Solutions will be added to the solution pool when best solution solution lt r1 or best solution solution 1 0 best solution lt r2 poolcapacity i default 2100000000 Specifies the number of solutions to keep in the solution pool poolintensity i default 0 This directive tells CPLEX how much effort to use in generating additional solutions with larger values specifying more effort The default of 0 is considered to be the value 1 if the populate directive is not also specified and 2 if it is Values of 3 and 4 can be quite time consuming value 4 directs CPLEX to enumerate all solutions that is to try all possible combinations of the integer variables which can also be quite memory intensive since there can be a large number of solutions poolreplace i default 0 This directive specifies the policy for replacing solutions in the solution pool if more than poolcapa
96. perturbed more than once r is probably too large reduce it to a level where only one perturbation is required The default doperturb value of i1 0 selects CPLEX s automatic perturbation strategy If an automatic perturbation occurs early in the solution process consider setting 11 1 to select perturbation at the outset This alternative will save the time of first allowing the optimization to stall before activating the perturbation mechanism but is useful only rarely for extremely degenerate problems The perturblimit parameter governs the number of stalled iterations CPLEX allows before perturbing the problem The default value of 1220 causes CPLEX to determine this number based on the characteristics of the particular problem being solved Setting 12 to a positive integer value identifies a specific number of stalled iterations to tolerate before perturbing the problem ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 51 feasibility r1 default 1 0e 6 markowitz r2 default 0 01 optimality r3 default 1 0e 6 If a problem is making slow progress through Phase I or repeatedly becomes infeasible during Phase II numerical difficulties have arisen Adjusting the algorithmic tolerances controlled by these directives may help Decreasing the feasibility tolerance increasing the optimality tolerance and or increasing the Markowitz tolerance will typically improve numerical behavior The feasibility tolerance r1 gt 0 specifies the degree to wh
97. portion of the write command AMPL uses a compact and efficient binary format for the problem and solution files If you use g instead AMPL writes the files in an ASCII format that may be easier to transmit electronically over systems like the Internet In technical support and consulting situations ILOG may ask you to send a file using this format If you use m AMPL writes the problem in MPS format and the filename ends in mps for example steel mps This is described further in Using MPS File Format on page 24 Creating Auxiliary Files AMPL can create certain human and program readable auxiliary files that help relate the various set variable constraint and objective names used in your AMPL model to the column and row indices that are written to the problem file and seen by the solver This is particularly valuable when the AMPL presolve phase actually eliminates variables and constraints before the problem is sent to the solver To create the auxiliary files you set the AMPL option auxfiles to a string of letters denoting the combination of auxiliary files you would like produced and then use the write command to create and save the auxiliary files along with the problem n1 file For example the command ampl option auxfiles cr will cause the write command to create auxiliary files containing the names of the variables columns and constraints rows as sent to the solver The table below shows the types of auxiliary
98. quired per iteration in this situation is usually too large to afford any advantage If devex pricing helps you may wish to try steepest edge pricing i 2 This alternative incurs a substantial initialization cost and is computationally the most expensive per iteration but may dramatically reduce the number of iterations so as to produce the best results on exceptionally difficult problems The variant using slack norms i 3 is a compromise that sidesteps the initialization cost it is most likely to be advantageous for relatively easy problems that have a low number of iterations or time per iteration Full reduced cost pricing i 4 is a variant that computes a reduced cost for every variable and selects as entering variable one having most negative reduced cost or most positive as appropriate Compared to CPLEX s standard reduced cost pricing i 1 full reduced cost pricing takes more time per iteration but in rare cases reduces the number of iterations more than enough to compensate This alternative is supplied mainly for completeness as it is proposed in many textbook discussions of the simplex algorithm dgradient i default 0 This directive governs the dual simplex algorithm s choice of a pricing procedure that determines which variable is selected to leave the basis at each iteration Your choice is likely to make a substantial difference to the tradeoff between computational time per iteration and the number of iterations As
99. reat unavailable functions of constant arguments as variable P presolve 0 turn off AMPLs presolve phase S substout 1 use defining equations to eliminate variables L linelim 1 fully eliminate variables with linear defining equations so model is recognized as linear T gentimes 1 show time to generate each model component t times 1 show time taken in each model translation phase ostr outopt str set problem file format b g m and stub name to display more possibilities use 0 S randseed use current time for random number seed sn randseed n use n for random number seed V version display the AMPL software version number If you type amp1 at the shell prompt AMPL will display a summary list of all the command line switches On some Unix shells is a special character so you may need to use with double quotation marks Persistent Option Settings If you have many option settings or other commands that you would like performed each time AMPL starts you may create a text file containing these commands in AMPL language syntax Then set the environment variable name OPTIONS IN to the pathname of this text file For example on a Windows PC you should type C gt set OPTIONS IN c Namplinit txt If you are using a C shell on a Unix machine you would type something like setenv OPTIONS IN ijr amplinit txt AMPL reads the file referred to by oPTIONS IN and executes any commands therein bef
100. rectives such as the display directive described above lpdisplay i default 0 The default choice of 1 0 produces a minimal few lines of output from CPLEX summarizing the results of the run When i 1 a log line recording the iteration number and the scaled infeasibility or objective value is displayed after each refactorization of the basis matrix Additional information on the operation of the network simplex algorithm is also provided if applicable This is often the appropriate setting for tracking the progress of a long run When i 2 a log line is displayed after each iteration This level of output is occasionally useful for diagnosing problems of degeneracy or instability in the simplex algorithm sensitivity When specified this directive instructs CPLEX to output sensitivity ranges corresponding to the optimal solution For variables the suffix current provides the corresponding objective function coefficient in the current problem and down and up specify the smallest and largest values for which the current basis remains optimal For constraints the suffixes apply to the constant value or right hand side Details on CPLEX defined suffixes are provided in Defined Suffixes for CPLEX on page 77 54 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE timing i default 0 When this directive is changed to 1 from its default value of 0 a summary of processing times is displayed to standard output Input 0 06 CPU 0 06 Wall S
101. rocedure 1 2 and the variant in slack space 1 23 have similar computational costs often their overall performance is similar as well though one or the other can be advantageous for particular applications e The variant using unit initial norms 1 4 is a compromise that sidesteps the initialization cost it is most likely to be advantageous for relatively easy problems that have a low number of iterations or time per iteration pricing i default 0 To promote efficiency when using reduced cost pricing in primal simplex CPLEX considers only a subset of the nonbasic variables as candidates to enter the basis The default of 1 0 selects a heuristic that dynamically determines the size of the candidate list taking problem dimensions into account You can manually set the size of this list to 1 0 but only very rarely will this improve performance refactor i default 0 This directive specifies the number of iterations between refactorizations of the basis matrix 48 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE At the default setting of 1 0 CPLEX automatically calculates a refactorization frequency by a heuristic formula You can determine the frequency that CPLEX is using by setting the display directive described below to 1 Since each update to the factorization uses more memory CPLEX may reduce the factorization frequency if memory is low In extreme cases the basis may have to be refactored every few iterations and the a
102. ropping any one of them permits a solution to be found to the remaining ones Clearly knowing the composition of an IIS can help localize the source of the infeasibility When iisfind is used CPLEX uses the iis suffix to specify which variables and constraints are in the IIS as explained in Diagnosing Infeasibilities on page 81 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 35 Directive for Tuning CPLEX can try various values for algorithmic directives to find a set of values that will reduce solution time The directives below are used to control the tuning algorithm The algorithm progresses by trying different sets of values in trial runs tunefile f1 tunefileprm f2 These directives tell CPLEX to do tuning and to write the results to file 1 using AMPL directive names or to file 2 in CPLEX PRM format The tuning algorithm can take up to six to ten times longer than a regular solve invocation but the results may save time in future runs pretunefile f1 pretunefileprm f2 These directives tell CPLEX to write out the current non default directive settings before starting tuning The files may be used to return to the pre tuning settings since CPLEX will change all settings to the tuned values as part of the tuning algorithm The file 1 uses AMPL directive names and the file 2 is written in CPLEX PRM format The pretunefileprm 2 file may contain some CPLEX display settings which are not included in the pretunefile 1 form
103. round Directive value meaning round nonintegral integer variables do not modify solve result AN do not modify solve_message 8 modify even if maxerr lt 1e 9 Modifications take place only if CPLEX assigned nonintegral values to one or more integer variables and for round 8 only if the maximum deviation from integrality maxerr exceeded the minimum integrality tolerance 1e 9 startalgorithm i default 0 This directive specifies the algorithm that CPLEX will apply to solve the initial LP relaxation The recognized values of i are Table 7 5 Settings for the startalgorithm Directive 0 Automatic Primal simplex Dual simplex Network simplex Barrier Sifting Concurrent oa fk OON strongcand i1 default 10 strongit i2 default 0 These two directives impact strong branching see varsel directive below The strongcand directive controls the size of the candidate list for strong branching The strongit parameter limits the number of iterations performed on each branch in strong branching The default setting of 12 0 which allows CPLEX to determine the iteration parameter will generally suffice You can use low values of 11 and i2 if the time per strong branching node appears excessive you may reduce the time per node yet still maintain the performance Conversely if the time per node is reasonable but CPLEX makes limited progress consider increasing the values ILOG AMPL CPLEX SYSTEM 11 0 USER
104. se The siftopt directive instructs CPLEX to use a sifting method that solves a sequence of LP subproblems eventually converging to an optimal solution for the full original model Sifting is especially applicable to models with many more columns than rows when the eventual solution is likely to have a majority of variables placed at their lower bounds The concurrentopt directive instructs CPLEX to make use of multiple processors on your computer by launching concurrent threads to solve your model in parallel The first thread uses dual simplex a second thread uses barrier a third thread if your computer has that many processors uses primal simplex and any additional processors are added to parallelizing barrier On a machine with enough memory this will result in a solution being returned by the fastest of the available algorithms on each problem eliminating the need to choose a single optimizer for all purposes memoryemphasis i default 0 workfilelim r default 128 workfiledir f This directive lets you indicate to CPLEX that it should conserve memory where possible When you set this parameter to its nondefault value of 1 CPLEX will choose tactics such as data compression or disk storage for some of the data computed by the simplex barrier and MIP optimizers Of course conserving memory may impact performance in some models ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 41 Also while solution information will be available aft
105. section In the branch amp cut algorithm however each active node of the tree requires additional memory The total memory that CPLEX needs to prove optimality for an integer program can thus be much larger and less predictable than for a linear program of comparable size ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Because a single integer program generates many LP subproblems even small instances can be very computation intensive and require significant amounts of memory In contrast to solving linear programming problems where little user intervention is required to obtain optimal results you may have to set some of the following directives to get satisfactory results on integer programs You can either change the way that the branch amp cut algorithms work or relax the conditions for optimality as explained in the two corresponding subsections below The first directive to consider for changing the behavior is the mipemphasis directive which directs the branch amp cut algorithm to focus on different balances of optimality and feasibility If memory consumption is an issue set the memoryemphasis directive it is described in the Continuous Optimization section but it also makes some changes for the branch amp cut algorithm notably using node files When experimenting with these possibilities it is also a good idea to include directives that set stopping criteria and display informative output these are described in the next two
106. solution file ASCII format 23 binary format 23 solution files 21 solutionlim directive 72 solve codes 85 86 solver add solver options 21 choosing 19 display solution information 22 execute outside AMPL 24 interface 19 multiline options 20 options 20 problem files 21 set initial values 21 solution files 21 specify options 20 use of initial values 21 sosl directive 61 sos2 directive 62 stability directives for improving 51 startalgorithm directive 69 starting directives 52 stopping directives 52 strongcand directive 69 strongit directive 69 submipnodelim directive 70 suffix bestnode 79 current 80 direction 77 down 80 iis 81 priority 77 100 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE unbdd 83 up 80 switches Cn 27 command line 27 en 27 28 L 28 ostr 28 P 28 S 28 s 28 sn 28 T 28 t 28 v 28 T temporary files directory 25 saving 22 termination messages 86 text editor using 15 text file predefined commands 28 threads directive 42 time to find solution 55 to read problem 55 to write solution 55 timelimit directive 53 72 timing directive 55 74 treememlim directive 72 troubleshooting common difficulties 74 tunedisplay directive 36 tunefile directive 36 tunefileprm directive 36 tunefix directive 36 tunefixfile directive 36 tunerepeat directive 37 tunetime directive 37 U unbdd suffix 83 Unix installat
107. solve phase typically improves CPLEX s performance on integer programs by speeding up the solve times of the LP subproblems solved in the branch and bound algorithm However while coefficient reduction will tighten the LP subproblems occasionally it makes them more difficult to solve So if CPLEX solves an ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 59 integer program in a modest number of nodes but the LP subproblem at each node consumes significant amounts of time solve time may improve by setting 1 0 to disable this feature The node count may increase but the savings in time per node may compensate for the increased node count The default setting of 1 2 causes CPLEX to perform coefficient reduction whenever possible while 1 1 will only reduce coefficients to integer values cutpass i default 0 This directive controls the number of passes CPLEX performs when generating cutting planes for a MIP model By default CPLEX automatically determines the number of passes to perform This setting should suffice for most problems Set the cutpass directive to 1 to stop all cut generation Set it to a positive integer to specify a particular number of passes cutsfactor r default 4 0 The cutsfactor directive controls the number of additional cuts generated by CPLEX While the constraints generated by CPLEX improve performance in most cases in some problems the additional memory to store them and time required to solve the larger LP subproble
108. ss AMPL s presolver so that all presolving is done in CPLEX set option presolve to 0 CPLEX s presolve can be suppressed by changing i to 0 from its default of 1 In rare cases the presolved linear program although smaller is actually harder to solve Thus if CPLEX reports that many variables and constraints have been eliminated by presolve you may want to compare runs with and without presolve On the other hand if CPLEX consistently reports that presolve eliminates no variables or constraints you can save a little processing time by turning presolve off To request a report of the number of eliminations performed by presolve see the prestats directive below prestats i default 0 When this directive is changed to 1 from its default of 0 CPLEX reports on the activity of the aggregation and presolve routines Presolve eliminated 1645 rows and 2715 columns in 3 passes Aggregator did 22 substitutions Presolve Time 1 70 sec During the development of a large or complex model it is a good idea to monitor this report and to turn on its AMPL counterpart by setting option show stats to 1 An unexpectedly large number of eliminated variables or constraints may indicate that the formulation is in error or can be substantially simplified scale i default 0 This directive governs the scaling of the coefficient matrix The default value of 1 0 implements an equilibration scaling method which is generally very effective You can turn o
109. st tuning results tunetime r default 10000 This directive limits the time per tuning trial This directive is meaningful only if x is less than the value of the time directive ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 37 38 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Using CPLEX for Continuous Optimization CPLEX Algorithms for Continuous Optimization For problems with linear constraints CPLEX employs either a simplex method or a barrier method to solve the problem Refer to a linear programming textbook for more information on these algorithms Four distinct methods of optimization are incorporated in the CPLEX package Aprimal simplex algorithm that first finds a solution feasible in the constraints Phase I then iterates toward optimality Phase II A dual simplex algorithm that first finds a solution satisfying the optimality conditions Phase I then iterates toward feasibility Phase II A network primal simplex algorithm that uses logic and data structures tailored to the class of pure network linear programs A primal dual barrier or interior point algorithm that simultaneously iterates toward feasibility and optimality optionally followed by a primal or dual crossover routine that produces a basic optimal solution see below CPLEX normally chooses one of these algorithms for you but you can override its choice by the directives described below For problems with quadratic constrain
110. t CPLEX uses to initiate the barrier method The default setting of 1 will suffice for most problems Consider other values 2 3 and 4 if the barrier method appears to converge slowly or when the predua1 directive is specified comptol r default 1e 8 This directive specifies the complementarity tolerance used by the barrier algorithm to test convergence The barrier algorithm will terminate with an optimal solution if the relative complementarity is smaller than this value Any positive number larger than 1e 10 is acceptable input crossover i default 1 On a linear problem by default 1 1 CPLEX initiates the crossover algorithm to convert the barrier solution to a basic or vertex solution using a primal simplex like method If i 2 a dual simplex like method is used for the crossover The crossover algorithm can be turned off by setting 1 0 densecol i default 0 CPLEX uses this directive to distinguish dense columns in the constraint matrix Because barrier algorithm performance can improve dramatically if dense columns are treated separately changing this value may improve optimization time Columns with more nonzeros than this setting are considered to be dense If left at the default value CPLEX will automatically determine a value considering factors such as the size of the problem Any nonnegative integer is acceptable input ordering i default 0 This directive selects the method used to permute the rows of the constraint
111. tage of these features solvers must be written to utilize AMPL s interface ILOG provides no support for the usage of AMPL with solvers not distributed by ILOG You choose a solver for a particular problem by giving its executable filename in the AMPL option solver command For example to use the AMPL compatible CPLEX solver type ampl option solver cplexamp Most solvers have algorithmic options such as CPLEX with its Mixed Integer and Barrier options In these cases you give the solver executable name to AMPL for example with option solver cplexamp the solver will determine from the problem characteristics as passed by AMPL for example a quadratic objective or integer variables as well as solver options you specify which algorithmic options will be used ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 19 Specifying Solver Options You can specify option settings for a particular solver through the AMPL option command CPLEX specific directives are described later in this document Since all solvers provide default settings for their options this is necessary only when your problem requires certain nondefault settings in order to solve or when certain settings yield improved performance or solution accuracy To specify solver options enter option solver options settings where solver is replaced by the name of the solver you are using This approach allows you to set up different options for each solver you use
112. te simple in this case ampl display Supply Price unbdd Supply Price unbdd 1 1 6 1 11 1 16 1 21 1 2 1 7 1 12 1 17 1 22 1 3 1 8 1 13 1 18 1 23 1 4 1 9 1 14 1 19 1 24 1 5 1 10 1 15 1 20 1 25 1 ampl display Demand Price unbdd Demand Price unbdd A3 1 A6 1 A8 1 A9 1 B2 1 B4 1 7 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE CPLEX Status Codes in AMPL Solve Codes When CPLEX returns control to AMPL after a solve command built in AMPL parameters and an AMPL option provide information on the outcome of the optimization as shown ampl model oil mod ampl data oil dat ampl option solver cplexamp ampl display solve result num solve result num 1 solve result ampl solve CPLEX 11 0 0 37 iterations optimal solution 0 in phase I ampl display solve result num solve result num 0 solve result solved ampl option solve result table option solve result table 0 solved 100 solved 200 infeasible 300 unbounded 400 limitN 500 failure re ILOG AMPL CPLEX SYSTEM 11 0 solve result objective 12 20834324 solve result USER S GUIDE 85 86 The session log shows that the built in AMPL parameter solve result numis 1 initially and parameter solve resultis The solve invocation resets these parameters however so that they describe CPLEX s status at the end of its run the solve result num parameter by a numeric cod
113. thematical Programming 2nd edition as well as the integer programs described in Chapter 20 Integer programs may be pure all integer variables or mixed some integer and some continuous variables integer variables may be binary taking values 0 and 1 only or may have more general lower and upper bounds For the network linear programs described in Chapter 15 CPLEX also incorporates an especially fast network optimization algorithm The barrier algorithmic option to CPLEX though originally designed to handle linear programs also allows the solution of a special class of nonlinear problems namely quadratic programs QPs as described later in this section However CPLEX does not solve general non QP nonlinear programs For instance if you attempt to solve the following nonlinear problem described in Chapter 18 of the AMPL book CPLEX will generate an error message ampl model models WNnltransd mod ampl data models WMnltrans dat ampl option solver cplexamp ampl solve at0 nl contains a nonlinear objective ampl ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 31 This restriction applies if your model uses any function of variables that AMPL identifies as not linear even a function such as abs or min that shares some properties of linear functions Piecewise linear Programs CPLEX does solve piecewise linear programs as described in Chapter 17 if AMPL transforms them to problems that CPLEX solvers can han
114. ts only the barrier method is used and there is no crossover algorithm ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 39 The simplex algorithm maintains a subset of basic variables or a basis equal in size to the number of constraints A basic solution is obtained by solving for the basic variables when the remaining nonbasic variables are fixed at appropriate bounds Each iteration of the algorithm picks a new basic variable from among the nonbasic ones steps to a new basic solution and drops some basic variable at a bound The coefficients of the variables form a constraint matrix and the coefficients of the basic variables form a nonsingular square submatrix called the basis matrix At each iteration the simplex algorithm must solve certain linear systems involving the basis matrix For this purpose CPLEX maintains a factorization of the basis matrix which is updated during most iterations and is occasionally recomputed The sparsity of a matrix is the proportion of its elements that are not zero The constraint matrix basis matrix and factorization are said to be relatively sparse or dense according to their proportion of nonzeros Most linear programs of practical interest have many zeros in all the relevant matrices and the larger ones tend also to be the sparser The amount of RAM memory required by CPLEX grows with the size of the linear program which is a function of the numbers of variables and constraints and the sparsit
115. u can copy the file cplexamp to cplex If you do the latter you must remember to copy it again the next time you upgrade cplexamp ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Installed Files Unix systems ampl cplexamp amplcplexi00userguide pdf examples README TXT Windows Systems ampl exe amplcplex100userguide pdf ampltabl dll cplex100 d11 cplexamp exe examples exhelp32 exe README TXT Examples models looping industries industries finance industries logistic industries product industries purchase industries schedule AMPL The CPLEX solver for AMPL User s manual for AMPL CPLEX Directory of examples see Examples below The notes on using CPLEX with AMPL provided by AMPL Optimization LLC AMPL User s manual for AMPL CPLEX Table handlers CPLEX DLL used by cplexamp exe The CPLEX solver for AMPL Directory of examples see Examples below Utility program invoked by AMPL for DOS shells The notes on using CPLEX with AMPL provided by AMPL Optimization LLC Sample AMPL models Most of these correspond to examples in the AMPL book More information on some of the examples is provided in the readme file in this directory Advanced sample AMPL models A description of each is provided in the readme file in this directory More samples The industries directory is sub divided into industry specific subdirectories The models have been brought together from a variety of so
116. urces Together they provide a palette of AMPL models that you may use as a starting point for your projects ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 13 14 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Using AMPL Running AMPL If you have added the AMPL installation directory to the search path you can run AMPL from any directory Otherwise run AMPL by moving to the AMPL directory and typing amp1 at the shell prompt At the amp1 prompt you can type any AMPL language statement or any of the commands described in Section A 14 of the book AMPL A Modeling Language for Mathematical Programming 2nd edition To end the session type quit at the amp1 prompt Using a Text Editor Generally you will edit your model and data both expressed using AMPL language statements in a text editor and type commands at the amp1 prompt to load your model and data solve a problem and inspect the results Although you could type in the statements of a model at the amp1 prompt AMPL does not include a built in text editor so you cannot use AMPL commands to edit the statements you have previously entered Microsoft Windows users on PCs and XWindows users on Unix systems should open separate windows for editing files and running AMPL ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE 15 If you cannot open multiple windows on your desktop you can use AMPL s shell command to invoke an editor from within AMPL You can use any ed
117. ution mixed integer solutions limit node limit with integer solution time limit with integer solution treememory limit with integer solution node file limit with integer solution unrecoverable failure aborted in phase II aborted in phase aborted in barrier dual infeasible aborted in barrier primal infeasible aborted in barrier primal and dual infeasible aborted in barrier primal and dual feasible aborted in crossover solution found numerical difficulties solution found inconsistent equations unrecoverable failure with no integer solution aborted no integer solution out of memory no tree no integer solution unrecoverable failure with integer solution aborted integer solution exists out of memory no tree solution may exist bug problem has no variables bug Error return from named CPLEX routine CPLEX SYSTEM 11 0 USER S GUIDE Table 9 2 Solve Codes and Termination Messages Continued Number 540 541 542 550 551 552 553 554 555 556 557 558 559 560 561 562 563 570 Basis Status Message at termination Diagonal QP Hessian has elements of the wrong sign QP Hessian has diag elements of the wrong sign QP Hessian is not positive definite problem has nonquadratic nonlinear constraints problem has a nonlinear objective problem has nonlinear integer variables problem has integer variables and a quadratic objective problem has unlinearized piecewise linear terms problem has a quadratic o
118. ver that nipstartstatus is normally overridden by the AMPL option send statuses which can take on the following values ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Table 7 1 Values of the AMPL Option send statuses 0 gt gt send no solver status values 1 default send statuses if there are no integer variables 2 gt send statuses even if there are integer variables By default 12 1 variable values are checked to see if they provide an integer feasible solution before the problem is optimized If an integer feasible solution is found the objective function value is used as a cutoff during branch amp cut To ignore existing values set 12 0 prerelax i default 1 Setting i 1 invokes the CPLEX presolve for the linear program associated with the initial relaxation of a mixed integer program All other presolve settings apply Sometimes additional reductions can be made beyond any previously performed MIP presolve reductions The default setting of i 1 lets CPLEX decide whether or not it should presolve the relaxation presolvenode i default 0 The presolvenode directive determines how CPLEX applies its presolve to the LP subproblems at the nodes of the branch and bound tree By default CPLEX decides automatically Set i 1 to force node presolve Set i 2 to also probe on integer infeasible variables at the nodes Set i 1 to prevent any node presolve The default setting usually works best probe i default 0 This dir
119. y They may provide you with an optimal or very nearly optimal solution even though a proof of optimality would require more computer resources than you have available Difficult MIP Subproblems Certain classes of MIP problems occasionally produce very difficult subproblems The subproblems may be dual degenerate Or an alternative algorithm such as primal simplex or barrier may perform better with the particular model If the subproblems are dual degenerate consider setting mipalgorithm to choose primal simplex for solving subproblems If the subproblems are taking many iterations per node to solve consider setting dgradient to use a stronger dual pricing algorithm Most often one would use dual steepest edge pricing In cases where the barrier algorithm is selected to solve the initial LP relaxation it may be useful to apply it to the subproblems as well However since the barrier algorithm cannot currently use a basis nor any other form of advanced start it will usually need to outperform the simplex solvers quite significantly on the subproblems before performance improves It is beneficial to set the barrier algorithm option to settings 1 or 2 Either of these nondefault choices is better at detecting infeasibility a frequent characteristic of MIP subproblems ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE Defined Suffixes for CPLEX The most common use of AMPL suffixes is to represent solver result values that correspond
120. y of the coefficient matrix The factorization of the basis matrix also requires an allocation of memory the amount is problem specific depending on the sparsity of the factorization When memory is limited CPLEX automatically makes adjustments that reduce its requirements but that usually also reduce its optimization speed The CPLEX directives in the following subsections apply to the solution of linear programs including network linear programs The letters i and x denote integer and real values respectively Directives for Problem and Algorithm Selection CPLEX consults several directives to decide how to set up and solve a linear program that it receives The default is to apply the dual simplex method to the linear program as given substituting the network variant if the AMPL model contains node and arc declarations The following discussion indicates situations in which you should consider experimenting with alternatives dualthresh i default 32000 primal dual Every linear program has an equivalent opposite linear program the original is customarily referred to as the primal LP and the equivalent as the dual For each variable and each constraint in the primal there are a corresponding constraint and variable respectively in the dual Thus when the number of constraints is much larger than the 40 ILOG AMPL CPLEX SYSTEM 11 0 USER S GUIDE number of variables in the primal the dual has a much smaller basis matrix a
121. y usage when solving integer programs A setting of 0 for the nodefile directive causes CPLEX to store all nodes in physical memory The default value of 1 creates a compressed version of the node file in memory Writing nodes to disk 1 2 3 enables CPLEX to process more nodes before running out of memory This is typically more efficient than relying on the operating system s generic swapping procedure If 1 2 an uncompressed node file is written to disk Compressing the file 1 3 adds computation time but allows more efficient use of memory When the nodefile directive instructs CPLEX to write nodes to a node file the workfilelim directive specifies the maximum size of RAM to be consumed before writing to disk takes place Although node files are designed for efficiency the speed of RAM is always superior to that of disk and you should take advantage of what memory your computer has The default value of 128 a reasonable value for most computers means that 128 megabytes of RAM will be devoted to storing the tree and requirements beyond that will begin to go to files on disk A related directive is treememl im described below which serves to place a limit on the total size of the tree The default value of the treememlim directive is effectively infinity which means CPLEX will continue to write nodes to disk until it solves the problem or exhausts available disk space or encounters some other limit ILOG AMPL CPLEX SYSTEM 11 0 USER

ILOG AMPL CPLEX System Version 11.0 User`s Guide

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