EPORCK V1.8 User's Guide Evolutionary Procedure for the
Contents
1. e sep a EO e 12 Running EPORCK 13 41 Run check list 2 42 ar shine ele Meath ee Ban 13 4 2 Getting started ss sa aed pal A A A EL 13 4 5 Outpt files x oa a AN En alee A A ds 14 4 4 Specific mools an s ee ee ee ee 18 Problem sample 19 1 Methodolgy of GA applied to chemical scheme fi tting This section decribes the different methods used in EPORCK 1 1 Chemical scheme defi nition Parameters AY FYo Cexp E RT A CGS Nr No st S No ON 010 a e Reaction N Figure 1 Chemical scheme representation Chemical schemes are caracterised for each reaction see Fig 1 by a four real numbers set This allows to define the Arrhenuis law Thus a N step chemical scheme requires to fit 4N parameters 1 2 The optimisation problem cost function minimisation The fit of scheme parameters can be seen as an optimisation problem The aim is to find the complete parameters set that let the corresponding scheme fits some predefined reference ouputs This kind of problem are often reduced to a minimisation one The idea is to minimise a cost function that represent the error or the distance between the reference or target scheme s ouputs and actual ones The function to minimise is presented in Sec 2 2 The set of methods that solve the optimsation problems can be split into two main types e Gradient based methods e GA based methods Gradient based methods are theoretically more efficie2. Generation 49 0 12382746 Generation 51 0 12382442 Generation 57 0 12312602 Generation 60 0 12272412 Generation 67 0 12264616 Generation 82 0 12264499 Generation 83 0 12261784 Generation 86 0 12261014 Generation 88 0 12259977 Generation 91 0 12259902 Generation 94 0 12259635 Generation 0 12259579 Generation 100 0 12259553 Best solution was found at generation 100 solution value 0 12259553 Best solution found XE 1 18 39402390 EL 2 28957 59765625 X 3 1 09906709 XL 4 1 56450987 X 5 9 85662270 6 16572 35156250 X 7 7 22574282 X 8 32858 76171875 X 9 1 13119853 X 10 0 90438539 EPORCK gt Corresponding scheme file writen premix scheme Total run time 5185 seconds The eporck out file contains a run summary and information about each individual evaluation Essentially used for debuging EPORCK V1 8 gt premix job file does not exists generating premix job K R R R R R R akak OR aak k ak ak ae k R R ak ak ae a k k k SR R ak k k k k k ak k k k k k k k k k k k k k kkk kkk EPORCK SESSION ote aot kkk k k k k k k k k k Evolutionary Procedure for the Optimisation of Chemical Kinetic schemes VERSION V1 80 EPORCK 71 82 RUN SUMMARY EPORCK V1 8 gt Number of constraints 7 V1 8 gt Number of operating points mixture composition 4 EPORCK V1 8 gt Index of premix output selecte
3. and b is a parameter determining the degree of non unformity The non uniform operators are responsible of fine tunning capabilities of the system whole non uniform mutation This operator has the same behavior than the simple non uniform mutation The mutation is applied on the whole chromosom i e each gene simple arithmetical crossover The operator selects randomly a gene lo cation of two individuals g and g2 There are two offsprings with the same genom exept for the crossing gene location 81 ag l a g g ag2 1 a g This operator uses a random value a 0 1 Arithmetical crossovers must be selected anyway They have a stabilisation effect on the evolutionary processes whole arithmetical crossover This operator has the same behavior than the simple arithmetical crossover The crossover is applied on the whole chromosom 1 e each gene heuristic crossover This operator is a unique crossover for the folowwing reasons it uses values of the objective function in determining a direaction of search it produces only one offspring and may produce no offspring at all This operator behaves acording to the rule a FEU x FP i e individual 2 is better than 1 4 onild parent my with r A random number from 0 1 If after some attemtps varying r the generated offspring is still not feasible i e out of boundaries then no offsprig is produced Its major responsabili
4. whole to the chromosom simple uniform mutation The operator selects randomly a gene and mute it randomly with a uniform probability distribution This operators plays an important role in the early phases of evolution process as the individuals are allowed to move freely within the search space This operator is essential when starting with a clone population as it introduces novetly phase space exploration boundary mutation The operator selects randomly a gene g and mute it to one of its upper or lower boundary This operator is usefull in early stage of the optimisation when user defined parmeters boundary may limit the optimisation process If the best individual has one of its gene at one boundary the optimisation is restricted by search space definition simple non uniform mutation The operator selects randomly a gene and mute it to g randomly with a non uniform probability distribution defined by g A t upper_bound g g or with equal probability g A t lower_bound g The function A f y returns a value in the range 0 yl such that the prob ability of A t y being close to O increases as the generation number in creases This property causes this operator to search the space uniformly initially exploration and very locally at later state focus on the most promising region Alt y yr 1 3also convex where r is a random number from 0 1 T is the maximum generation number
5. restart 2 multiple restart 3 6 parameter for non unifrom mutation do not modify 10 parameter for simple cross over do not modify 1 test case number not used input_eporck dat file The sample file coments describe the file structure Note the line numbering is added only for convenience This file is read via a parser Any comment can be inserted The numerical values are only read after recognition of the folowing key words all are finalised with e Constraints number Constraints indexes Constraints weights e OP number OP weights e Target values Tere is no input order since the file is rewinded for each keyword 4 O O aun t LA DNDN RRR RR a Fei bh GA ra VO OC JA Ch LN PLN k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k k ale k k INPUT DATA FOR EPORCK V1 8 a fe fe ae ae ae SR SR R R R SR SR SR SR R K R SR SR SR SR SR R K k 3k 3k 3k SR R K R K SR k SR ae SR K R K R ak ak k k Constraints number 4 Constraints indexes 1 26 7 Constraints veights 5 0 1 0 2 0 2 0 OP number 3 OP weights 1 0 1 0 1 0 Reference values 1 line per OP 1 column per constraint OP1 s T2 Y_CO Y_C02 Target values 5 877000e 01 1 779800e 03 3 073600e 05 7 718800e 02 P2 Target values 8 907000e 01 1 956100e 03 2 0370
6. 00e 04 9 213200e 02 OP3 Target values 1 172400e 00 2 113700e 03 9 499800e 04 1 058500e 01 11 26 This input file means that The optimisation will use 4 contraints wich are Sz se lector 1 7 4 selector 2 the third species outlet mass fraction selector 6 and the fourth species outlet mass fraction selector 7 The Ga weights coefficients see Sec 2 2 are respectively 5 0 1 0 2 0 and 2 0 Each scheme is evaluated with PREMIX on three operating points OP An OP is defined by the fresh mixture temperature and the mixture composition defined in the equil job file see Sec 3 5 The pressure is assumed to have the the same value for all the OP The weights are all equal to 1 0 Finally the target values are tabulated 3 4 restart eporck fi le This file is only needed when a single or multiple restart is specified in input_genocop dat see Sec 3 2 For single restart the information reduced to a unique line filled by the genes floats separated by tabulation or space For multiple restart the files contains as much lines as a generation size Each line defines an individual 3 5 equil job file The user must only check the equil job content It must contatains the same number of chained CNTN solutions ie same of operating points than declared in the input_eporck dat file At the initilisation equil job is read to generate the premix com mad file premix job This taking into acount pressure inlet temper
7. 8917 Constraint 4 OP 0 R 0 0759388 Ropt 0 077188 OP 1 R 0 0904783 Ropt 0 092132 OP 2 R 0 104097 Ropt 0 10585 OP 3 R 0 115009 Ropt 0 11708 Fitness 4 0 0171888 Constraint 5 OP 0 R 0 0645338 Ropt 0 063805 OP 1 R 0 0769769 Ropt 0 075733 OP 2 R 0 0891545 Ropt 0 08725 OP 3 R 0 101003 Ropt 0 098111 Fitness 5 0 0197823 Constraint 6 OP 0 R 0 000306608 Ropt 3 8648e 06 OP 1 R 0 000389734 Ropt 1 4029e 05 OP 2 R 0 000416907 Ropt 4 8887e 05 OP 3 R 0 000378165 Ropt 0 00014535 Generation 0 Fitness 1 27353 etc The evaluation log file contains the evalutation history For each generation an individual evaluation is summarised on a line by its ANEO e generation number e the cost function evaluation genotype i e the gene parameter sequence The best scheme file is a CHEMKIN scheme format file updated at each improvement It describes the best scheme at the moment ELEMENTS H 0 N END SPECIES CH4 02 CO C02 H20 NO N2 END REACTIONS CH4 1 502 gt CO 2H20 2 477885E 18 0 0 29281 8 FORD CH4 1 108466 FORD 02 1 564027 CO 0 502 C02 7 491749E 09 0 0 14106 0 FORD CO 1 000000 FORD 02 0 500000 17 N2 02 gt 240 1 047884E 09 0 88 60693 5 FORD N2 1 803871 FORD 02 0 620011 END The premix scheme file is aCHEMKIN scheme format file updated at the end of the run It describes the best scheme of all 4 4 Specific tools These tools aim to facilitate
8. EPORCK V1 8 User s Guide Charles MARTIN May 19 2004 o x H O SC e 1 d m co co cee 1 8 _ 0 20 0 00 0 20 0 40 x Evolutionary Procedure for the Optimisation of Chemical Kinetics Introduction EPORCK has been developed in order to ease the fitting procedure of reduced chemical schemes This is achieved by automating the optmisation procedure Thus EPORCK is devoted to finding scheme parameters set that fits the user s require ments EPORCK 15 a GA Genetic Algorithm based software Nevertheless future developements will include Gradient based methods in order to accerate final conver gence ess than fi ve reactions Contents 1 Methodolgy of GA applied to chemical scheme fitting 1 1 1 Chemical scheme definition 1 1 2 The optimisation problem cost function minimisation 1 1 3 basic principles 2 EPORCK architecture and requirements 4 SS Mamirame ee ec E e dE eech A 2 2 Reference criteria and cost function 5 23 EPORCK TEQUES cela we akan ah Aba doe ns 5 EPORCK input files description 7 scheme le ee GN ble eS ae 8 3 2 input genocop dat file 10 3 3 input eporck dat file 11 3 4 Testarteepofek ne ine an ana a e AL M kon B 12 3 5 equal job 0000000007 12 3 6 Sept shell
9. ainations Each interger refers to the number of individuals involved in a GOp The selection order is defined by the list of the GOp below There are two important points to keep in mind e For crossover GOp the number of individuals involed must be a multiple of 2 since 2 parents are needed to produce an offspring e The sum of the number of individuals involed must be stricly inferior to the half of the population size The selection order is 1 simple uniform mutation 2 boundary mutation 3 simple non uniform mutation whole arithmetical crossover simple arithmetical crossover Gu A whole non uniform mutation 7 heuristic crossover See Sec 2 3 for a full definition of the GOp 1 8 0 0 8 N_param 0 0 N_param 2 3 12 0 1 18 0 lower_bnd param_ upper_bnd 4 15000 0 2 35000 0 lower_bnd param_ upper_bnd 5 0 8 3 1 2 lower_bnd param upper_bnd 6 1 0 4 2 0 param_ upper 7 6 0 5 15 0 param_ upper_bnd 8 10000 0 6 20000 0 lower_bnd param_ upper_bnd 9 1 0 1 2 param_ upper bond 10 0 5 8 1 0 lower_bnd param_ upper_bnd 11 12 17 50 population size generations number 13 14 0 0 1 2 2 1 genetic operators selection 15 16 0 10 1 selective pressure coeff do not modify 17 18 0 minimisation 0 maximisation 1 19 10 20 21 22 23 24 25 26 27 3 3 1 RESTART FLAG multiple random 0 single random 1 single
10. ated randomly respect to parame ters bounds or generated by previous EPORCK run restart or pre existing scheme Restart as random initialisation may be so called single or multiple e single only one scheme is generated then replicated to obtain an initial popula tionof clones e multiple cach generated scheme differs a prori from its brothers Note that EPORCK use a constant population number of schemes in the running generation Once the initial population enters the main loop each scheme is evaluated population loop by PREMIX or SENKIN in ignition version Note that PREMIX EPORCK coupling uses exchange files on disk so avoid network file system NFS that are much slower than local hard disks Nevertheless this weak coupling does not affect global performance since 95 of CPU time is consumed by PREMIX Then the GA core take the popuplation as input to operate on it selected genetic operators and selective pressure some die some live but population remain constant The main loop is thus closed Note that the process stops when reaching a specified generation number 2 2 Reference criteria and cost function The selectable criteria R are extracted from a laminar flame structure S the laminar flame speed To the burnt gas temperature 5 Luli the flame thermal thickness max r 24 the k species outlet mass fraction k D The fitness or cost function E is defined as follows F Y ob k
11. ature and mixture composition in order to setup temperature profiles and chained premixed computation Note that mixture composition unit is mole fraction equil job HP PRES 1 0 TEMP 300 0 REAC CH4 0 500 REAC 02 2 000 REAC N2 7 520 TEST 1800 CNTN END REAC CH4 0 800 REAC 02 2 000 REAC N2 7 520 CNTN END REAC CH4 1 100 REAC 02 2 000 REAC N2 7 520 END 3 6 Script shell fi les The user must only check the Chemkin executables and databases paths equil sh bin sh Path to Chemkin executables CK local chemkin36 bin Premix scheme name DO NOT MODIFY scheme premix scheme 12 Swap chemout path to file or no output chemout dev null chemout chem out chemlink chem asc Path to thermodynamic database file chemdat local chemkin36 data therm dat Equil command file name DO NOT MODIFY equilinput equil job Swap equilout path to file or no output equilout dev null equilout equil out Equil solution file name DO NOT MODIFY equilbin equil bin chemkin interpreter CK chem i scheme o chemout c chemlink d chemdat Equil CK equil i equilinput o equilout b equilbin c chemlink exit premix sh bin sh Path to Chemkin executables CK local chemkin36 bin Premix scheme name DO NOT MODIFY scheme premix scheme chemlink chem asc Swap tranout path to file or no output tranout dev null tranout tran out Path to transport database file trandat local chemki
12. cal vocab is naturaly used to describe GA For our problem we can make the following bijection a chromosom lt gt a chemical scheme representation a gene gt a chemical scheme parameter an individual lt gt one chemical scheme a population gt a set of chemical schemes e a generation gt a set of breeded schemes 2110501101 2 795 SIDJOWIVICY Figure 2 Animal genes vs scheme parameters set GA and more generally the evolutionary processes are centered onto an evolu tionary loop Fig 3 This iterative procedure lets evolve a population generation by generation under a selective pressure i e keep alive individuals that fits our require ments The selective critierion is usually called fitness function or objective function In our case the fitness is kind of distance between the individual and a target point in the search space So be carreful not to do some confusion small value of the fitness function caracterises a well fitted individual For this reason the fitness function term is often replaced here by cost function New individulals are the offspring of a single parent mutation or a cross over between a couple of parents The balance between do main exploration Fig 3 GENETIC OPERAORS block and optimum determination Fig 3 SELECTION block is one of the key to success e Strong selective pressure by decrasing population diversity leads to premature convergence i e th
13. d as target criteria Criterion 1 selected Criterion 2 selected Criterion 3 selected Criterion 6 selected Criterion 7 selected Criterion 8 selected Criterion 9 selected EPORCK V1 8 gt Response weigts sum to 29 000000 normalizing EPORCK V1 8 gt Response s weight Weight 1 0 413793 Weight 1 0 413793 Weight 2 0 137931 Weight 3 0 034483 Weight 4 0 034483 Weight 5 0 034483 Weight 6 0 310345 15 EPORCK EPORCK EPORCK EPORCK EPORCK EPORCK EPORCK EPORCK EPORCK EPORCK EPORCK Weight 7 0 034483 V1 8 gt veigts sum to 12 000000 normalizing V1 8 gt weights Weight 1 0 333333 Weight 2 0 166667 Weight 3 0 166667 Weight 4 0 333333 V1 8 gt Target responses operating point OP OP 1 Target response 1 0 587700 Target response 2 1779 800049 Target response 3 0 000580 Target response 4 0 000031 Target response 5 0 077188 Target response 6 0 063805 Target response 7 0 000004 OP 2 Target response 1 0 890700 Target response 2 1956 099976 Target response 3 0 000441 Target response 4 0 000204 Target response 5 0 092132 Target response 6 0 075733 Target response 7 0 000014 OP 3 Target response 1 1 172400 Target response 2 2113 699951 Target response 3 0 000373 Target response 4 0 000950 Tar
14. e minimum found is only local e Weak selective pressure and too much mutation in population slow down opti mum determination by wasting CPU time in the evaluation of unfitted indi viduals distant form the optimum The search is uneffective The other main key to succes in GA performing is the definition of the cost func tion This definition determines directly the shape of the search space hyper surface so may greatly influence the convergence rate of GA methods Actually the cost func tion represents a norm of the distance that seprates the individual from a reference point This reference point is the target to reach It must be realistic i e reachable For example it makes no sense to fit a 1 step scheme on Sz for both lean and rich operating points See 2 2 for our cost function implemetentation y nn Evolution loop nn Figure 3 GA general principle 2 EPORCK architecture and requirements 2 1 Mainframe Random Restart lst Generation G1 K Chemkin input files v Premix Senkin system calls Postprocess Chemkin binary files v Evaluate Fitness function v GENOCOP III core uonejndod doo SUODE T U S 1940 40071 v Nevv generation u Figure 4 EPORCK general frame Fig 4 presents EPORCK structure The evolutionary loop is initialised by a scheme population This initial set may be gener
15. feature allows to stop properly EPORCK before the maximum number of generations in order to complete all output files properly 4 3 Output files The genocop out file see Sec 4 2 contains convergence information Each time a new individual is the best a line is appended It contains generation number and cost function value Fri Jul 25 11 22 40 2003 Equalities Inequalities Domains 15 00 lt 1 lt 15000 00 lt 40000 00 X3 lt 0 40 XA lt 2 00 6 0 X5 lt 5000 00 X6 lt 20000 00 3 0 lt X7 lt 5000 00 X8 lt 40000 00 0 00 lt X9 lt 0 00 lt 10 3 00 Test case number 1 Number of operators 4 0 4 2 4 1 2 Number of generations 100 Population size 40 Parameter B 6 Parameter Q 0 100000 k k k US NG RESTART 4x USING SINGLE POINT INITIAL POPULATION Generation Solution Value Generation 1 1 27352941 Generation 2 0 35373634 Generation 3 0 28377339 Generation 8 0 28145617 Generation 0 5012270 Generation 0 25018328 10 1 EPROCK gt WARNING PAUSE UNDER USER REQUEST EPROCK gt TO GO AHEAD TYPE touch GO_EPORCK IN RUNNING DIRECTORY EPROCK gt THINK TO REMOVE PAUSE_EPORCK BEFORE 1 EPROCK gt WARNING Ee AHEAD UNDER USER REQUEST Generation 0 18954715 Generation 30 0 18917012 14 Generation 31 0 16416746 Generation 35 0 16402860 Generation 39 0 14888197 Generation 41 0 14788626 Generation 42 0 14654692 Generation 43 0 13493264
16. get response 5 0 105850 Target response 6 0 087250 Target response 7 0 000049 OP 4 Target response 1 1 403600 Target response 2 2246 399902 Target response 3 0 000337 Target response 4 0 003192 Target response 5 0 117080 Target response 6 0 098111 Target response 7 0 000145 V1 8 gt Check PREMIX job file parameters v1 8 gt NPTS 5 v1 8 gt XSTR 1 50 cm v1 8 gt XEND 4 00 cm v1 8 gt XCEN 0 00 cm v1 8 gt TFIX 1073 0 K v1 8 gt WMIX 0 20 cm v1 8 gt END OF RUN SUMMARY aK kk k k k k k k k k k k k k ok k k ale ale ae k k k k k k k k k k k k ale ale ale k k ade k ale k ok ok EPORCK V1 8 gt RUN HAS BEGUN AT Fri Jul 25 11 22 40 2003 Constraint 0 OP 0 R 0 0514974 Ropt 0 5877 OP 1 R 0 0667286 Ropt 0 8907 OP 2 R 0 0810181 Ropt 1 1724 OP 3 R 0 0939793 Ropt 1 4036 Fitness 1 2 59005 Constraint 1 16 OP 0 R 1769 43 Ropt 1779 OP 1 R 1948 95 Ropt 1956 OP 2 R 2113 67 Ropt 2113 OP 3 R 2257 45 Ropt 2246 Fitness 1 0 00419652 Constraint 2 OP 0 R 0 00887623 Ropt 0 0005802 OP 1 R 0 00730358 Ropt 0 00044103 OP 2 R 0 00640637 Ropt 0 00037325 OP 3 R 0 00585811 Ropt 0 00033685 Fitness 2 2 80287 Constraint 3 OP 0 R 2 28689e 05 Ropt 3 0736e 05 OP 1 R 0 000171816 Ropt 0 0002037 OP 2 R 0 000864963 Ropt 0 00094998 OP 3 R 0 00313179 Ropt 0 0031922 Fitness 3 0 14
17. gr window 5 http www me berkeley edugri_mech 18 5 Problem sample 2 3 step scheme ideas e CH4 gt CO H2 H20 CO H20 gt CO H2 2H gt 2H 0 CH 202 gt CO 20H H20 CO H20 CO H2 H 20H 2 CH 202 gt CO 20H H20 CO 20H H20 C02 3 CH4 30 gt CO 2H 0 1 CO 3 lt CO 1 20 No e Jones amp Lindstedt like 19 CrHonyo 50 nCO n 1 H gt 1 H 292 lt HO CO H 0 C 0 e 4 step with Zeldovich simplified mechanism 1 1 3 CH4 202 CO 2H20 2 CO 02 gt CO O 3 N 0O0 gt NO N 4 N 02 4 gt NO O e 4 step with Zeldovich simplified mechanism 2a 1 5 CH4 50 gt CO 40H 2 2 CO 40H C0 2H 0 0 3 N O gt NO N 4 N 0 4 gt NO LO e 4 step with Zeldovich simplified mechanism 2b 1 CH4 302 gt CO 40H 2 CO 20H CO HO 3 N 0 gt NO N 4 N 02 4 gt NO O 20
18. n 1 line CH4 1 502 gt C0 2H20 t t fprintf scheme_file s line write A1 b1 Eal fprintf scheme_file E t 23 1f t 7 1 n pow 10 X 1 0 0 X 2 write non stoechiometric coefficients CH4 x line FORD CH4 fprintf scheme_file s line fprintf scheme file f An X131 02 x line FORD 02 fprintf scheme_file s line fprintf scheme file f n X 4 Reaction 2 x line C0 0 502 C02 t t fprintf scheme_file s line write A2 b2 Ea2 fprintf scheme_file E Vt 3 1 Xt 47 1 n pow 10 X 5 0 0 X 6 57 non stoechiometric coefficients CO line FORD CO fprintf scheme_file s line fprintf scheme_file f n X 7 warning impose reverse order to maintain equilibrium nu 1 0 rord X 7 nu line RORD CO fprintf scheme_file s line fprintf scheme file f n rord 02 line FORD 02 fprintf scheme_file s line fprintf scheme file f n X 8 warning impose reverse order to maintain equilibrium x nu 0 5 rord X 8 nu line RORD 02 fprintf scheme_file s line fprintf scheme file f n rord line END n fprintf scheme_file s line fclose scheme_file 3 2 input_genocop dat file In the sample file each line is defined by a coment Note the line numbering is only for only added for convenience Genetic operators GOp selection need some further expl
19. n36 data tran dat tranlink tran asc premix command file DO NOT MODIFY job premix job Swap premixout path to file or no output premixout dev null premixout premix out Premix solution file DO NOT MODIFY savebin save bin tran CK tran o tranout d trandat c chemlink t tranlink premix CK premix i job o premixout b savebin c chemlink t tranlink exit 4 Running EPORCK 4 1 Run check list 4 2 Getting started The command line to launch EPORCK prompt gt eporck_V1 6 input_genocop dat genocop out input_eporck dat eporck out Note that these file names can be user re defined The user can pause continue or stop EPORCK before the normal program exit using the folwing procedures 13 PAUSE Simply create a file named PAUSE EPORCK in the running direc tory This easily done with the command touch PAUSE Note the program effectively pauses when the evaluation of the current genera tion is completed So it may not be instantaneous Check if eventually an old GO_EPORCK file is in the directory If any delete it before If you do not delete it the program pauses but restart within a short time e CONTINUE To continue the run after a pause Delete the PAUSE_EPORCK file Create a file named GO_EPORCK The program will restart within a minute e STOP Simply create a file named STOP_EPORCK in the running directory This easily done with the command touch STOP EPORCK This
20. nsistant with operating conditions It is used to generate runtime the premix job file See Sec 3 5 for details premix sh is a sh script shell file that launch the transport interpreter and PRE MIX See Sec 3 6 for details equil sh is a sh script shell file that launch the CHEMKIN interpreter and EQUIL See Sec 3 6 for details restart eporck optional file that contains chromosome s of individual s for restart procedure See Sec 3 4 for details scheme c file is the real vector of parameter to fit indexed from 1 include genocop h include extern h void write_scheme X file_sel Dummy VECTOR X int file_sel x Local x char filname char line float rord nu FILE scheme_file if file_sel 0 filname premix scheme else 4chemkin a chemkin_public a surface_chemkin a filname best scheme scheme_file fopen filname u if scheme_file NULL printf Open of s for output failed filname fclose input exit 1 rewind scheme_file SCHEME FILE EDITION line ELEMENTS n fprintf scheme_file s line line H Nu fprintf scheme_file s line line END n fprintf scheme_file s line line SPECIES n fprintf scheme_file s line line CH4 02 CO C02 H20 N2 n fprintf scheme_file s line line END n fprintf scheme_file s line line REACTIONS n fprintf scheme file s line Reactio
21. nt and less CPU time consum ing But global minimum research needs to use special multiple seeding technics since their main feature is to find local minima The main drawback of these meth ods is their poor robustness face to the difficulty to sometimes evaluate the function to minimise In other word when the evaluation of the cost function fails the classical gradient methods are unable to evaluate function gradients and then to step beyond the actual phase space position Additionally these methods are not suitable when the cost function shape is noisy or nearly chaotic On the other hand GA methods handle very well unconverged function evaluations and are very robust in a general sense Their main advantage resides in the way they balance domain exploration i e research of new solutions and optimum determi nation precise location of the minimum If this balance is well established they are quite unsensitive to inital conditions Their main drawback is perhaps the number of function evuluations face to efficient gradient methods This evaluation cost and general convergence may be grealty affected by GA s parmeters tunning 1 3 GA basic principles We introduce some basic considerations about GA A GA is used as a minimiser Fig 2 illustrates the direct relation between real life parameter the genes and our problem For our fit we deal with a monochromosmic animal whose genes are the scheme parameters The biologi
22. the generation of constraints target values The 1D laminar flames are computed with a complex chemical mechanism such as the GRI Mech for methane or natural gas The user must be able to extract reference quantities such as Ar Tour 5 yo Two essential tools help to extract these values from binary PREMIX V3 x solution file e makeref_V1X This fortran tool reads the binary PREMIX file and then edit an ASCII column file It contains one line per operating point i e for each equivalence ratio each line composed by one column per quantiy The quanties order is 6 Si Touts 5 and For outlet species mass fractions the order is the one declared in the premix scheme file There is a default input file called makeref choices composed of three lines 1 save bin 1 PREMIX binary soltion file name 2 0 4 first equivalence ratio point 3 1 5 last equivalence ratio point 4 0 1 equivalence ratio step e extcol This script tool extracts selected columns of an ASCII file ignoring lines begining with the character Example The user wants to extract columns 1 2 17 and 5 from a file called reference dat to a file called myrun_ref dat He types in an UNIX shell win dow extcol reference dat 1 2 17 5 gt myrun_ref dat pre2slt2 A fortran tool that postprocess PREMIX solution and plot S and Tow 0 in an xmgr window pre2yk2 A fortran tool that postprocess PREMIX solution and plot Y in an xm
23. ties are fine local tuning and search in most promis ing direction e adjustable selective pressure parameter It is not recommended to modify it e adjustable parameter for non uniform mutation operators It is not recommended to modify it e A restart functionality allows to restart an optimisation from the best individual of a previous optimisation It is also possible to restart from an entire generation See Sec 3 4 3 EPORCK input files description Here are the input files definition 3 1 scheme c No parser has been developped yet Thus PREMIX format scheme definition must be coded by user in C then linked with EPORCK binaries and CHEMKIN libraries See Sec 3 1 for details input_eporck dat contains information about operating points and also about constraints number type and value Cost function weights are also defined there See Sec 3 3 for details input_genocop dat contains information about parameters number range and also population size maximum generation number and genetic operators selec tion See Sec 3 2 for details premix job It is the PREMIX command files If this file does not exit it is automatically generated If premix job is present it must be consistant with equil job and input_eporck dat settings i e same number of operating points and operating condition with respect to reference constraint value See Sec 3 5 for details equil job It is the EQUIL command files It must be co
24. where 01 are the respective weights on the criterion set Rx Fe Y o In f 0 where Joe are respective weights on operating points R are respective reference or target values of selected criteria Criteria selection and weights settings are user defined 2 3 EPORCK features S Feasible domain Penalty applied Unfeasible domain LX y sv S 7 e s ey 4 QR parameter 1 Figure 5 non conex 2D search space EPORCK features concerning the definition of the problem e multi objective optimisation capability e arbitrary numbers of parameters to fit multi step schemes 24 tness is the term used by GA community in our case small fi tness function high scheme fi mess e all parameters are upper and lower bounded must be set by the user Theoret icaly aconex domain is needed Nevertheless unfeasible part s of the search space are well handled by EPORCK applying a penalty to unconverged solu tions cost function Fig 5 e limited number of target quantities S1 Tour 80 ye based on laminar flame structure Ignition delays also but in an another EPORCK version e arbitrary number of operating points depending on Pressure Temperature and or Mixture Composition EPORCK features concerning the resolution of the problem e arbitrary maximum number of generations e arbitrary number of individuals per generation e a selection of seven genetic operators Simple refers to one gene
Download Pdf Manuals
Related Search