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A USER GUIDE FOR OPTEX VERSION4 R. Chambon

1. Main records and sub directories in stepdir optimize in the particular case of module GPTVRF The sub directory varpertdir in optimize ili Chapter 1 OPTEX MODULES IGE 314 2 1 Fuel Management Optimization In this section modules used for fuel management optimization will be described 1 1 The FOBJCT module The FOBJCT module is used to define the different parameters for an optimization calculation These parameters can be decision variables contraint zone definitions constraint limits This module can also evaluate the objective function and the constraints values The calling specifications are Table 1 1 Structure FOBJCT OPTIM FOBJCT OPTIM MAPFL FLUX FLUXP MACRO TRACK INDEX descfobjct where OPTIM character 12 name of the extended OPTIMIZE If OPTIM appears on the RHS the information previously stored in OPTIM is modified if necessary and stored MAPFL character 12 name of the extended MAP If MAPFL appears on the RHS the infor mation in it will be read for many parameters initialisation FLUX character 12 name of the FLUX linked list This object is used for the function evaluation It is recommended to provide it even if no function evaluation is done for many parameter reading FLUXP character 12 name of the FLUX linked list This object is used for some function evaluation su
2. o _ fl P40 0 22 ax T 44 BA ja AA f x9 EO AX Gey TE ec ied The calling specifications are Table 1 13 Structure PERTUR OPTIMIZE PERTUR OPTIMIZE FLUX SYS SYSP TRACK MACRO MACROP pertur data where GPT character 12 name of the SOURCE containing the source terms If GPT appears on the RHS the previous values will be updated FLUX character 12 name of the FLUX containing the unperturbed flux direct or adjoint SYS character 12 name of the SYSTEM containing the reference system matrices SYSTEM must be a linked list SYSP character 12 name of the SYSTEM containing the perturbation of the system matrices TRACK character 12 name of the TRACK type L TRIVAC containing the tracking informa tions TRACK must be a linked list OPTIMIZE character 12 name of the OPTIMIZE containing the optimization informations GPT pertur data must appear on the RHS to be able to updated the previous values structure containing the data to the second choice for the module PERTUR IGE 314 20 1 3 1 Data input for module PERTUR EDIT iprint Table 1 14 Structure pertur data VARMUN 4 vari var2 ALL D LAMBDA D LAMBDA DX D LAMBDA V D LAMBDA V DX eval data where EDIT iprint VARNUM Varl Vvar2 ALL D LAMBDA D LAMBDA DX D LAMBDA V D LAMBDA V DX eval data key word used to set iprint index used to control the printin
3. WRITE fvalpert A9 I3 F C VAL P p for 1 X p Ner IGE 314 Crab 4 Cnu 4 Cs 4 Leoni 30 Lett 30 Lexp 30 Lmett 30 Lconv 26 Lgp 28 29 Lgi 28 29 Lpro 26 Nitmar 28 29 Rn 29 Ry 29 Ri 29 Rn 28 Rp 28 Ri 28 a 16 18 37 EGPT 37 cst 16 18 Eert 16 17 inn 16 17 Ened 28 29 Pv Fc 9 6 Ew 4 burnmar 3 4 burnmin 3 4 CStiim 9 6 CStiupe 9 6 enfima 4 enfimin 3 4 GPT from 10 gprto 10 gTP from 11 grpto 11 best 30 testi 0 7 14 16 18 test2 6 7 14 16 18 ifeni 24 25 ifenz 24 25 fetu 37 38 ifet2 37 38 liter1 14 16 tneig 26 21 plan 5 ivari 14 15 20 22 24 37 38 isara 14 15 20 22 24 37 38 Tiara l4 15 ban 9f 51 Turat 30 zonel 5 6 zone2 5 6 izone 5 Jplan 5 keff 5 krefs T m 16 18 Ncha 5 imas 26 17 Nsurv_zones 5 num 14 16 dmoys T tenr 4 5 tobt 4 val 14 16 x 11 xx 11 kol 11 true 14 27 7 01 OLD VALUE 48 stepdir 48 49 2 13 19 21 23 26 31 34 37 z 2 13 19 21 23 26 31 34 37 i d A 8 9 A PHI 10 14 15 ABS 11 37 ADD 16 18 31 33 addflu 31 addflu_data 31 33 addmac 31 addmac_data 31 32 ADDOBJ 31 ADFLUX 33 ADJ ONLY 33 ADJOINT 8 9 21 22 35 AFLUX 9 33 AFLUX2 9 ALL 3 5 10 11 14 16 20 22 24 28 29 37 ALLSAME 5 6 16 17 ALMOST FSBLE 14 15 ANALYT
4. key word used to define the cost of the uranium is the core structure containing the data to the option FUEL COST DF key word used to specify that the distribution of the average exit burnup for each volume will be pre calculated key word used to specify that the distribution of the average exit burnup will be stored in the OPTIM object key word used to define the constraint type value zone of influence structure containing the data to the option CST ZONE DF key word used to define and evaluate the objective and or constraints functions structure containing the data to the option EVAL OBJ CST This will be treated as a section in itself because other module will refer to it Table 1 3 Structure czdf data BURNUP ZONE burn in burNmax ALL Y N ju isl nbz ENRICH ZONE enrimin E Timar 4 4 Y N i t 1 nez y where IGE 314 BURNUP ZONE burn min burN max ALL Y N nbz ENRICH ZONE enTimin ENTimax Y N nez 4 key word used to specify that exit burnup decision variables will be set This exit burnup zone were defined previously and are stored in the MAP minimum value of the exit burnup maximum value of the exit burnup key word used to specify that all burnup exit zone will be a decision variable key word used to specify that a specific burnup exit zone will be a decision variable key word used to specify that a specific burnup exit zone will not be a decision variable
5. key word used to specify that the integration will be performed only on the energy for every point of the core key word used to specify that the integration will be performed only on the energy for every point of a control zone of one constraint key word used to define the energy part of the integration key word used to specify that the integration will be performed on all energy groups number of the first energy group for the integration number of the last energy group for the integration key word used to specify that the definition of the integral over energy is finished key word used to specify that the definition of the integral is finished key word used to specify that the definition of the function is finished Table 1 9 Structure data 4 real VAR loc var name operator VARF loc_var_name where real VAR VARF loc var name operator real number key word used to specify that a local variable will be used key word used to specify that a local variable which depend with the functional will be used ex zone volume name of a local variable name Note it has to be loaded before name of a numerical operator The name must be one of these PLUS MINUS TIMES x DIVISION POWER xx MAX MIN LOG LN EXP SIN COS TAN ABS SORT 1 1 3 Examples of function definition We will now give a few examples which will permit users a better understanding of the procedure to define t
6. Structure GPTSRC GPT GPTSRC GPT OPTIMIZE FLUX SYS SYSP TRACK MACRO MAPFL gptsrc_data where GPT character 12 name of the GPT linked list file containing fuel regions description and burnup informations If GPT appears on the RHS the information previously stored in GPT is modified if necessary and stored OPTIMIZE character 12 name of the extended OPTIMIZE linked list FLUX character 12 name of the FLUX linked list This object is used for the function evaluation It is recommended to provide it even if no function evaluation is done for many parameters reading file MACRO character 12 name of the MACROLIB linked list file containing fuel regions description and burnup informations If it appears on RHS is means it will be necessary for a function evaluation objective or constraint MAPFL character 12 name of the extended MAP If MAPFL appears on the RHS the infor mation in it will be red for many parameters initialisation TABFL character 12 name of the TABLE linked list file containing fuel regions description and burnup informations If it appears on RHS is means it will be necessary for a function evaluation objective or constraint gptsrc_data structure containing the data to module GPTSRC 1 4 1 Data input for module GPTSRC Table 1 16 Structure gptsrc_data EDIT iprint DIRECT ivar var2 ALL J l ADJOINT eval data OTHER 4 DIRECT ADJOINT i 4
7. modules o s cosis aoa aara OR UE a A an E Sadna E 232 1 Data input for module MATLAB 2 44 2586 Li 44 ra bus 2 3 The GPTVRE module 20 0820 ooo aN RR ee bo eG RA ue 2 3 1 Data input for module GPTVRF xxm 2 OPTEX STRUCTURES 1 Contents of a tabu data structure 1 1 The sub directories in tabu 2 Contents of a optimize data structure 2 1 The sub directory OLD VALUE in optimize 2 2 The sub directory stepdir in optimize 2 3 Contents of a optimize data structure for module GPTVRF unt MSN c r OE ji IGE 314 Ll 1 2 1 8 1 4 1 5 1 6 1 7 1 8 19 1 10 1 11 1 18 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 26 1 27 1 28 1 29 1 30 1 31 2 1 2 3 2 3 2 4 2 5 2 6 2 2 8 List of Tables Surustuse PUBJOTS aii ea o XU MESE GU d a See a AK uk cR b E Structure descfobjet oss ss seoid DEB RR RR meet eR ee Structure ezdf data 32203 aace 4 8 eoo dhe Rhe mob RR A ce Structure CA data 2 2 xp ue mora LEK RA eee b ib Reb LASS SS Structure estzdf data 4 4 cuo ode UR A Rom ved SO e ee i Structure evaldnta s sej hin cde ee bn ee SEXE REGE ee x ee DE me Structure vardef data sir cbure seg data s LU DE ss ROIVER REX So Reise Structure data ee 2 044844 8 PERG ie ENS SE a
8. 1 eval data IGE 314 where EDIT iprint DIRECT Varl Vvar2 ALL ADJOINT eval data 22 key word used to set iprint index used to control the printing in module key word used to calculate a direct source term for decision variables S O A AB App Ap Ad B 6 Bo OO fp E gt BA 1 2 OX AX AX Pew AX 500 number of the first decision variable number of the second decision variable kev wod used to specifv that the direct source terms calculations will be done for all the decision variables key word used to calculate a adjoint source term for decision variables 57 _ 0G s Tm 1 21 see explainations in the module FOBJCT key word EVAL OBJ CST Some prede fined function are described too IGE 314 23 1 5 The GPTGRD module The GPTGRD module is used to compute the gradient of functions using the generalized perturbation theory To do that the user must precalculate the sources terms module GPTSRC and the generalized adjoints module GPTFLU The GPTGRD module also allows to define directly values of gradient of functions The calling specifications are Table 1 17 Structure GPTGRD OPTIMIZE GPTGRD OPTIMIZE FLUXP SYS SYSP SYS2 SYS2P TRACK MACRO FLUX MATEX MAPFL direct data gptgrd data OPTIMIZE GPTGRD OPTIMIZE direct data where OPTIMIZE FLUXP TRACK MACRO FLUX GPT MATEX MAPFL dire
9. 2 13 19 21 23 26 37 OPTIMV 37 OTHER 21 OUT STEP EPS 16 17 OUT STEP LIM 16 17 54 OUT STEP NMX 16 17 PARABOLIC 16 18 PENAL METH 16 17 PERTUR 19 PERTUR 19 45 pertur data 19 20 PERTURB VAR 14 15 PLAN 5 PLQ 45 PLUS 11 POWER 11 POWER CHA 14 16 POWER CHA 2 14 16 POWER CHA 3 14 16 POWERLIMIT 7 PREDEF 8 9 predef_func 6 7 predef_var 8 9 PREVIOUS 14 15 PROM LIST LG 28 29 PROMIS RAD 28 29 PROMISE AREA 26 27 PROMISE TEST 26 27 PUT 14 PUT CURRENT 28 29 QLPUTL 13 QUAD CST 14 16 RANGE 5 6 14 16 17 REACTOR 10 16 18 real 11 RECOVER 14 RECTANGLE 27 28 REL 24 37 repertory 8 9 RESET BEST 28 29 RESTORE 14 15 SAME 5 SAVE GPT 37 SAVE PERT 37 SCAT O 18 SCAT 1 18 seed 27 28 seg data 6 10 SIGW O 9 18 SIGW 1 10 18 SIMPLEX 16 17 SIN 11 SOURCE 19 SQRT 11 STEP 31 32 IGE 314 step 16 17 STEP INTERP 14 STEP REDUCT 16 17 STEP VALID 14 SUB 31 33 SURV ZONE 5 SYS 13 19 21 23 SYS2 23 SYS2P 23 SYSP 13 19 21 23 SYSTEM 13 19 TABFL 21 TABLE 21 TABU 27 29 tabu 40 41 TABU 26 TABU LIST LG 28 29 TABU RAD 28 29 TABU 26 TABUSH 26 27 29 TAN 11 test 14 TEST CST VLD 14 testl 14 test2 14 TIMES 11 TOTAL 9 18 TRACK 2 13 19 21 23 34 TRACK 13 19 23 34 TRACKING 2 TYP BURNUP 16 17 TYP ENRICH 16 17 UCOST 7 UPDATE 26 27 USPLIT 23 VAL
10. Ne dat s Structure QLPUILS 22 444 dak wa gE IDA a A eee eee bh un A BOR Structure descglputl eee ee a eee Structure def dat 2 4 8 54 2 6e Kaw ane de ol ee Rom AR we die structure PERTUR 24k ma xor LUN Pu OPE RUE eee wes Structure pertur data Structure GPTSBROS 1 4 4 a bobo d o eoe a RUE FOE OE a OR yo dort RO Eos otrlieliire PPESECASTA L 2 noe dE be oe em vob b Rn de e he Sebe Pda ts arica GEIGROY la Log IA od LR ee ee Ab EIE b A deu E Structure desetabu 4 2 dios cup bba beni Re e OS Sube x vue ao der wav des Structure det daba 004 64S uma oe Ron owe COR Ros wo gre tee Structure nelder data 1 44 eR ardore e Structure ADDOBJe s ee os ydo dod RR d REGE ok eee Ne ae RR gos Structure addmac data Structure addflu data mol eRe ES deb A EG we Structure MATLAB o e sir ai 4 l e e ene ERREUR e Re ee vedejo E e dedo Structure desemiatlerd oi so zan A made Structure desematlflu 5o se s b e Ron mm OR RA a ee DOUCHE G IRA CT DULUCHUIIS PBUVET Cate tal i rue i eoe de An a ae de dc E edd Main records and sub directories in tabu Main records in sub directories Additional records in NELDER MEAD directory Main records and sub directories in optimize Main records and sub directories in OLD VALUE
11. are stored in the TABU object key word used to specify the initial elements of the promising list are selected and evaluated and not the neighbors key word used to specify the initial elements of the polytope for the Nelder Mead simplex algorithm are selected and evaluated and not the neighbors integer value for a neighbor point to be which has been evaluated key word used to check the neighbors results The best neighbor result is compared to the fittest solution ever found An update is performed if necessary Tests for global convergence and promising area detection can be done The tabu list is updated key word used to verify if global convergence is achieved logical value for the global convergence Lconv equals true if Nit is greater than Nitmax key word used to verify if a promising area has been detected key word used to specify that no threshold limits the acceptance of promising areas logical value for the promising area detection key word used to specify that calculation based on gradient methods will be performed on a promising area previously detected key word used to specify the Nelder Mead simplex algorithm is used instead of the gradient method key word used to define the area for the local gradient method optimization algorithm A backup of original decision variable limits is done in TABUSH object and new smaller ones are stored in OPTIM object key word used to set the gradient method result
12. default 1073 4th int limit for internal convergence default 1073 5th E4 limit for convergence for the quadratic constraint 6th expected value for the objective function calculated with the linearized problem 7th EAX relative variation of the decision variables for the epsilon method of pertur bation default 1072 8th m Exponent for a objective function min P P default 8 0 9th a multiplication factor for constraint weight if S8 4 or 5 default 2 0 10th Ea limit of the error of the constraints for which function penaltv weight have to be adjust 11th Veore Volume of the core 12th Vreactor Volume of the reactor The other value of the record are not used and set to 0 0 Notes related with the perturbated material properties In the record BKP PERT XS 1 and 0 means that the corresponding perturbated material properties will be backuped or not respectively The available perturbated material properties are 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th DIFFX diffusion coefficient along x axes D DIFFY diffusion coefficient along y axes D DIFFZ diffusion coefficient along z axes D TOTAL total cross section 34 SCATO compressed isotropic component of the scattering matrix SIGWO isotropic component of the within group of the scattering of the scattering cross section SCAT1 compressed linearly anisotropic component of the scattering matrix SIGW1 linearly a
13. kg 45 continued from last page Comment The actual values of the objective function first value and the contraints the following values The number of the constraints are assigned in the order they have been defined The different limits and values for the iterative calculations of the optimization problem The first value is the volume where the ob jective function applies and the followingones correspond to the volumes where the con straints apllie The indexes of the perturbated material prop erties to backup The fixed fuel cost of each enrichment zone if S 1 0 or the parameters to calculate the enrichment dependant cost if S7 2 0 The fuel cost distribution corresponding to each point of the neutrons flux unknowns MW d tThe average exit burnup distribution corre sponding to each point of the neutrons flux unknowns The gradients or the absolute variation de pending of the keyword used in the PERTUR module of the eigenvalue with the decision variables The gradients or the absolute variation de pending of the keyword used in the PERTUR module of the eigenvalue for the coolant voided reactor with the decision variables The gradients of the objective function and the constraints The gradients of the objec tive for all the decision variables are in first position then follow the gradients of the con straints Directory containing differents informations of the previous iterations the values o
14. number of average exit burnup zone key word used to specify that exit burnup decision variables will be set This exit burnup zone were defined previously and are stored in the MAP minimum value of the exit burnup maximum value of the exit burnup key word used to specify that a specific enrichment zone will be a decision variable key word used to specify that a specific enrichment zone will not be a decision variable number of enrichment zone Table 1 4 Structure fcdf data FIXED cost i 1 nez DEPENDANT Cnu Cs Crap interest tobt tenr MEMORY where FIXED cost nez DEPENDANT Ew CNu Cs CrAB interest tobt key word used to specify that the price of the fuel is fixed for each enrichment zone cost of the fuel number of enrichment zone key word used to specify that the price of the fuel is dependant of the enrichment for each enrichment zone U 35 concentration of waste uranium after the separation work natural uranium cost kg cost of a separation work unit SWU cost of fabrication of the bundles kg interest rate y71 time to obtain uranium y IGE 314 5 tone time for enrichment y MEMORY key word used to specify that the distribution of the purchase cost of uranium actually in the reactor will be pre calculated and stored in the OPTIM object Table 1 5 Structure cstzdf_data KEFF kefy MAXPOWER ss ZONE DEF SURV ZONE Nsurv zone PL
15. represents e The number of decision variables N ar S The number of constraints Nest 3 The type of optimization S where So 1 minimization 3 NE 1 maximization The test for external convergence S where So 0 not converged A 1 converged The number of external iterations SS The type of reduction for external step S where ge 1 half 6 2 parabolic The number of inner iterations 57 The number of outer iterations S e The resolution s method for the linearized problem Sj where SIMPLEX LEMKE LEMKE LEMKE MAP Augmented Lagragian Penalty Method S II NANA e The type of perturbation for the decision variables S15 where So 1 epsilon 107 2 previous e The type of fuel cost definition S where So 1 dependent of the enrichment Il 2 fixed IGE 314 44 e The test for a realistic decision vector Sfo where so 0 do not respect all constraints 12 1 do respect all constraints A flag for unsuccessful resolution in QLP Sf where D 0 successful at last iteration 13 gt 1 number of iteration with unsuccessful resolution The number of regions N S 6 The number of channels in the core Nen 5S1 The number of bundles per channel Nk Ss e The number of unknowns per energy group Nu Sis The number of energy groups G 55 Table 2 4 Main records and sub directories in optimize Condition Units Comment SIGNATURE uu Cx12 Signature of the
16. the neutrons will be used A AB 0 key word used to specify that the system matrix corresponding to the production of the neutrons will be used A AB 0 name of the object L FLUX key word used to specify that the adjoint flux will be used instead of the flux default value In this case the adjoint system matrix are used automatically key word used to specify that a predefined variable will be load name of the predefined variable The predefined variable name are define below contents size neutron flux distribution nun X ngrp adjoint flux distribution of the second provided L FLUX nun X ngrp neutron flux distribution of the second provided L FLUX nun X ngrp adjoint flux distribution nun X ngrp average flux distribution by channel nch x ngrp x nzone axial average flux distribution nz X ngrp diffusion coefficient along X abcisse nun X ngrp diffusion coefficient along Y abcisse nun X ngrp diffusion coefficient along Z abcisse nun X ngrp total cross sections nun X ngrp fission cross sections nun X ngrp number of neutrons per fission time fission cross sections nun X ngrp fission cross section times the energy recovered by fission nun X ngrp fission spectrum nun X ngrp isotropic component of the within group of the scattering ofthe nun x ngrp scattering cross sections IGE 314 SIGW 1 D TOTAL D CHI D DIFFX D DIFFY D DIFFZ D NUSIGF D NFTOT D HFACT D SIGWO D SIGWI AxPHI BxPHI APxPHI BP PHI FU
17. the record GRA DIENT of the optimize data structure on the RHS continued on next page IGE 314 50 optimize in the particular case of module GPTVRF continued from last page Condition UnitsComment GRADIENT EXP R N ar Nest 1 The gradients calculated numerically of the objective function and the constraints The gradients are stored the same way as for the record GRADIENT of the first description varpertdir Dir Directory containing the perturbation values and the corresponding values of the functions for a decision variable z Notes related with the perturbated decision variables directory The directories varpertdir will be composed using the following FORTRAN instructions WRITE varpertdir A8 I4 VAR PERT i for 1 lt N 4 Each directory contains also the records described in the following table Table 2 8 The sub directory varpertdir in optimize Condition Units Comment EPSILON ua R Nei The value of the perturbation of the decision variable i fvalpert R Nest 1 The values of the objective function and con straints for the perturbation p of the decision variable i The number of perturbation Ne can include the unperturbated case e 0 0 and can be different for each decision variable i Moreover the values of the perturbation do not have to be in increasing or decreasing order The records fvalpert will be composed using the following FORTRAN instructions
18. AN plan Vsonejii5l Neha SAME Jotan BUNDLE 4 ALL PLAN ipian 4 0 1 j Lena SAME jptan J CHANNEL ALL 0 1 5 j 1 ncna y ifs sl VALUE DEF 4 Leonel Cstlim RANGE 2 onel tzone2 1 CStlimj Uzonel tzone2 ALLSAME cstrim Ji END MAX POW VOID REACT FC py rc ANALYTIC FCT cstiype CStlim where KEFF key word used to defined kerf keff neutron multiplication factor aimed this is a constraint of type equal MAXPOWER key word used to defined a maximum power in a zone this is a constraint of type inferior ZONE DEF key word used to specify that the definition of the zone will be provided SURV ZONE key word used to specified that the zone will be defined manually TWsuruszone total number of surveillance zone Leone number of the zone that the bundle is part of 0 if no surveillance zone for this bundle BUNDLE key word to specified that surveillance zone are bundles CHANNEL key word to specified that surveillance zone are channels PLAN key word to specify that the definition of surveillance zone for plan will follow plan numbers of the plan to be defined SAME key word used to specify that the definition of surveillance zone in the plan iptan Will be the same one as in the plan jpian Jolan number of the plan already defined ALL key word used to specify that the power in all bundles or channels will be a constraint Neha number of channels VALUE DEF key word used to speci
19. CONSTRAINT fent fent jsl ivar2 isi tvarl 1 ifen2 S feni 1 where NEW VALUE REL DIRECT VALUE ivari twar2 FOBJ CONSTRAINT ifeni fen2 grad key word used to specify that the value of gradient is set to zero key word used to recover the epsilon in record OPT PARAM R of object OPTIMIZE key word used to specify that the value of gradient will be directly given by the user first decision variable for which the gradient will be defined last decision variable for which the gradient will be defined If it is not defined the default value is 4 444 key word used to specify that the gradient of the objective function will be defined key word used to specify that the gradient of conctraints will be defined first constraint for which the gradient will be defined last constraint for which the gradient will be defined value of the gradient this key word has to be provided if gptgrd data is not used Table 1 19 Structure gptgrd data GPT DIRECT 4 ivar tvar2 ALL eval data L INDIRECT EXPLICIT IMPLICIT 4 vari ivar2 ALL 4 FOBJ CONSTRAINT iyeni ifen2 where DIRECT vari twar2 ALL kev word used to specifv that the direct part of the gradient will be calculated first decision variable for which the gradient will be defined last decision variable for which the gradient will be defined kev word used to specifv that the gradient will be calc
20. COST 7 10 EDIT 3 14 20 22 26 31 35 37 END 10 11 END ENERGY 10 11 END INTEGRAL 10 11 END MAX POW 5 6 ENERGY 10 11 ENRICH ZONE 3 4 EPS 14 15 epsilon 14 15 epsilon4 16 18 EVAL OBJ CST 3 eval data 3 6 20 22 24 25 EXIT B DIST 3 EXP 11 EXPAN VLD 30 EXPLICIT 24 25 F ADJOINT 33 F C VOLUME 16 18 F EVAL 14 15 fact 28 fedf_data 3 4 feas 14 15 FIND NEW 30 IGE 314 FIXE 18 FIXED 4 FLUI 31 FLU2 31 FLUNEW 31 FLUX 2 8 13 19 21 23 34 FLUX 9 33 35 FLUX 2 13 19 21 23 31 34 FLUX AV 9 FLUX AX 9 FLUX2 9 FLUXP 2 8 23 FOBJ 6 16 18 24 25 FOBJCT 2 3 6 fracl 31 33 frac2 31 33 FROM 2 PARTS 33 FROM MP 32 FUEL COST DF 3 FUNCT PREDEF 6 FUNCVALUE 10 FUNCZVOL 10 GEOM 34 GEOM 34 GEOMETRIC 28 GET CURRENT 28 29 GPT 19 21 23 GPT 24 GPT 21 23 GPT ADJOINT 35 GPT FLU 35 GPTGRD 23 gptgrd_data 23 24 gptgrd_data 24 GPTSRC 21 gptsrc data 21 gptsrc data 21 GPTVRF 34 37 43 49 50 gptvrf data 37 gptvrf data 37 grad 24 GREP 6 8 9 H FACTORS 9 18 HALF 16 18 HARMONIC 35 HISTORY 14 16 igal 33 iga2 33 iga3 33 ihrm 35 ilev 31 32 53 IMPLICIT 24 25 IN 8 9 33 INDEX 2 34 INDEX 2 34 INDIRECT 24 25 INIT 10 NIT PRO LIST 26 29 NITIAL 14 15 NITIALIZE 28 29 NN STEP EPS 16 17 NN STEP LIM 16 17 NN STEP NMX 16 17 NTEGRAL 10 interest 4 i
21. IC FCT 5 6 AP PHI 10 14 15 ASCII MAT 34 35 AUG LAGRANG 16 17 B 8 9 IGE 314 B PHI 10 14 15 BALL 27 28 BEST AS CURR 28 29 BKP MACRO P 14 15 BKP MCR P XS 16 18 BP PHI 10 14 15 BUNDLE 5 BURNUP ZONE 3 4 CENTER GRID 35 36 CHANEL GRID 35 36 CHANNEL 5 CHI 9 18 COEF UPDATE 14 15 COMPARE 37 COMPARE NEW 30 COMPLETE 28 29 CONSTRAINT 6 14 16 18 24 25 CONTRACTION 30 conv 14 15 CONV TEST 14 15 26 27 CORE 10 16 18 cos 11 cost 4 CREATION 26 27 CST QUAD LIM 16 18 CST VIOL EPS 16 18 CST WEIGHT 16 17 CST WGT MFAC 16 18 CST ZONE 10 11 CST ZONE DF 3 cstzdf data 3 5 CTRL ZONE DF 3 czdf data 3 D CHI 10 D DIFFX 10 D DIFFV 10 D DIFFZ 10 D HFACT 10 D KEFF 7 8 D KEFF KREF 7 8 D LAMBDA 10 20 D LAMBDA V 10 20 D LAMBDA V DX 20 D LAMBDA DX 20 D MINPCMAX 7 8 D NFTOT 10 D NUSIGF 10 D SIGWO 10 D SIGWI 10 D TOTAL 10 D VOID R FC 7 8 data 10 11 52 data_name 8 9 DBL ZONE 11 DDIFF 32 def data 14 16 26 28 DEFINITION 14 26 DEPENDANT 4 descfobjct 2 3 descmatlflu 34 35 descmatlgrd 34 descalputl 13 14 desctabu 26 DFLUX 33 DIFFX 9 18 DIFFY 9 18 DIFFZ 9 18 DIRECT 14 16 21 22 24 DIRECT VALUE 24 direct_data 23 direct_data 24 DISCRETE ALL 10 11 DISCRETE COR 10 11 DISCRETE CST 10 11 DIVISION 11 DOWN 8 9 DPHI POWER 7 DPHI UCOST 7 DX METHOD 14 DX POWER 7 DX U
22. Lu Index corresponding to the summit of the polytope with the worst value of tabu search fonction IWORST2 uuu Index corresponding to the summit of the polytope with the second worst value of tabu search fonction IBEST iuuuuuu Index corresponding to the summit of the polytope with the worst value of tabu search fonction XAVERGuuuuua R Nvar The average values of the decision variables for all the points of the polytope REFLECT VAL R Njar Nest 2 The reflection of the worst point of the poly tope with the centroid given by XAVERG It also includes the corresponding objective func tion constraints and tabu search values after their evaluation EXPAN VLDouu R Noar Nest 2 The reflection of the centroid of the polytope given by XAVERG with the worst point It also includes the corresponding objective func tion constraints and tabu search values after their evaluation IGE 314 43 2 Contents of a optimize data structure The optimize specification is used to store the optimization variables and functions values and definitions limits and options It is also used in a particular case with the module GPTVRF to store the functions for many perturbated values of the decision variables and the gradients calculated numerically and analytically In any case the signature variable for this data structure must be SIGNAL OPTIMIZE The dimensioning parameters for this data structure which are stored in the state vector S
23. MFAC a CST VIOL EPS cost MIN PCMX 2N m IGE 314 METHOD SIMPLEX LEMKE MAP AUG LAGRANG PENAL METH MAXIMIZE MINIMIZE INN STEP LIM step VAR WEIGHT CST WEIGHT lesti weight RANGE best2 ALLSAME TYP BURNUP TYP ENRICH weight OUT STEP LIM INN STEP NMX OUT STEP NMX max INN STEP EPS Eert OUT STEP EPS Einn STEP REDUCT 17 key word used to define the guasi linear programming method key word used to specify that the SIMPLEX method will be used key word used to specify that the LEMKE method will be used key word used to specify that the MAP method will be used key word used to specify that the augmented lagrangian method will be used key word used to specify that the penalty method will be used key word used to specify that the optimization problem will be a maximization key word used to specify that the optimization problem will be a minimization de fault key word used to limit the inner step of the optimization problem limit for a step key word used to set the weight of the different types of the decision variables for the guadratic limit of the outer step of the optimization problem NX lt Sk 1 16 key word used to set the weight of the constraints number of the first constraint to set the weight weight of the constraint s key word used to specify that several constraint weights will be set number of the last constraint to set the weight key word
24. NCVALUE FUNCZVOL KEFF KEFF VOID D LAMBDA D LAMBDA V INIT data linearly anisotropic component of the within group of the scat tering of the scattering cross sections derivative of total cross sections derivative of fission spectrum derivative of diffusion coefficients along X abcisse derivative of diffusion coefficients along Y abcisse derivative of diffusion coefficients along Z abcisse derivative of fission cross sections derivative of number of neutrons per fission time fission cross sections derivative of fission cross section times the energy recovered by fission derivative of isotropic component of the within group of the scattering of the scattering cross sections derivative of linearly anisotropic component of the within group of the scattering of the scattering cross sections A system matrix times neutron flux vector B system matrix times neutron flux vector perturbated A system matrix times neutron flux vector perturbated B system matrix times neutron flux vector value of the function usually used when the derivative func tion is calculated see the definition of the DX UCOST predifined function for example value of the volume on which the function is defined inte grated keff keff corresponding to a pertubated flux derivative of the eigenvalue derivative of the eigenvalue corresponding to a pertubated flux Table 1 8 Structure seq data nun X ngrp nun X ngrp nun X ngrp nun X ngr
25. TECHNICAL REPORT IGE 314 A USER GUIDE FOR OPTEX VERSION4 R CHAMBON Institut de g nie nucl aire D partement de g nie m canique Ecole Polytechnique de Montr al July 4 2015 IGE 314 Contents COMEN dase k e ee a ee oe REO Au haa NUE Mes Magan AER Lie Ae ncn ee a a RE Hee ee c TT 1 OPTEX MODULES 1 Fuel Management Optimization Ll The FOBICI modules o c ropu a dox caede ROG Sch e drm AR me th e E eR 1 1 1 Data input for module FOBJOT o o a oa w we bee RR RA 1 1 2 Data input for module functions definition 113 Examples of function definition 12 The QLPUTL module 24 ww 4 iwa KA da a je aa ow Ro du xoxo 1 2 1 Data input for module QLPUTL 1 3 The PERTUR module 0008 cedo 9 om POR UR JE obe hohem eR box ee LS Data input for module PERTUR 1 4 The GPTSRC module gt o s cs s seo Rec a a EUR dre a dodo 1 4 1 Data input for module GPTSRGE 02219 Rex wes ec m pu six 1 5 The GPTGRD module e oro UR RR Roe bomo b RR ru Lol Data input for module GTPGRD 1 6 The TABU module e a cc 0060 0 Ee a be der ope a ee 161 Data input for module TABU 5 424 21448 xo m RB ERS aje 2 Output Data Treatment bee doo nx dik ee do doe eee Sore a POP Re seji The ADDOBI MOdUIe 6 ou ce ERM RRR AR 2 1 1 Data input for module ADDOBI 2 9 e ee eee Pina The MATLAB
26. The ADDOBJ module The ADDOBJ module is used to perform the differences between two objects or to add two objects For the MACROLIB and FLUX this is possible only if they contain the same energy group and material mixture numbers The calling specifications are Table 1 24 Structure ADDOBJ MACNEW ADDOBJ MACNEW MACRO1 MACRO addmac data FLUNEW ADDOBJ FLUNEW FLU1 FLU2 addflu data where MACNEW character 12 name of the MACROLIB containing either the nuclear increments from the calculation of MACRO1 MACRO or the sum of properties from MACRO1 MACRO 2 Be aware the order of MACROLIB is important even for addition option MACRO1 character 12 name of a MACROLIB MACRO2 character 12 name of a MACROLIB When addition is performed it must contain incremental nuclear properties addmac structure containing the data to module ADDOBJ with the options for MACROLIB op erations FLUNEW characterx12 name of the FLUX which will be the result of the addition or the sub traction of the two old one This object has to be in create mode only FLU1 characterx12 name of the first FLUX FLU2 characterx12 name of the second FLUX addflu structure containing the data to module ADDOBJ with the options for FLUX addition 2 1 1 Data input for module ADDOBJ Table 1 25 Structure addmac data EDIT iprt STEP ilev ADD fracl frac2 SUB continued on next page IGE 314 32 St
27. UE DEF 5 VAR 11 VAR WEIGHT 16 17 VAR ZONE 10 11 var name 8 9 VARDEF 6 vardef data 6 8 VARF 11 VARMUN 20 VARNUM 20 varpertdir 50 VOID REAC FC 6 8 VOID REACT FC 5 weight 16 17 XS_name 16 18 XSM 34 Y 4 3 ZONE 16 18 ZONE DEF 5 55
28. ber of decision variables Nyar Sto e The number of constraints Nest St e The first number for the random point generation algorithm S TIME e The number of generated random numbers S Table 2 1 Main records and sub directories in tabu Condition UnitsComment SIGNATURE uu Cx12 Signature of the data structure SIGNA STATE VECTOR I 40 Vector describing the various parameters as sociated with this data structure S and the tabu search optimization integer options continued on next page IGE 314 41 Main records and sub directories in tabu continued from last page Condition UnitsComment TABU PARAM R Vector containing various tabu search opti mization real options and several current val ues CURRENT VAL The values of the current decision variables the corresponding functionals and the tabu function BEST VALuuuu F The values of the decision variables the cor responding functionals and the tabu function for the best point ever found NEIGHBORHOOD i Directory containing the neighbor decision variable set TABU LIST u i Directory containing the tabu decision vari able set PROMISE LIST i Directory containing the decision variable set corresponding to promising areas NELDER MEAD i Directory containing the decision variable set corresponding to the polytope for Nelder Mead Simplex method Notes related with the different limits and values for the iterative calculations of th
29. ch as void reactivity MACRO character 12 name of the MACROLIB linked list file containing fuel regions description and burnup informations If it appears on RHS it means it will be necessary for a function evaluation objective or constraint TRACK character 12 name of the TRACKING linked list file containing the tracking informa tions If it appears on RHS it means it will be necessary for a function evaluation objective or constraint or to memorize the average exit burnup or the fuel cost dis tribution INDEX character 12 name of the INDEX linked list file containing the index informations If it appears on RHS it means it will be necessary for a function evaluation objective or constraint or to memorize the average exit burnup or the fuel cost distribution descfobjct structure containing the data to module FOBJCT IGE 314 1 1 1 Data input for module FOBJCT EDIT iprint CTRL ZONE DF czdf_data FUEL COST DF fcdf data Table 1 2 Structure descfobjct CST ZONE DF cstzdf data EVAL 0BJ CST eval data where EDIT iprint CTRL ZONE DF czdf data FUEL COST DF fcdf data EXIT B DIST MEMORY CST ZONE DF cstzdf data EVAL 0BJ CST eval data l EXIT B DIST MEMORY l key word used to set iprint index used to control the printing in module key word used to define the decision variables and their zones of influence structure containing the data to the option CTRL ZONE DF
30. ct data gptgrd data character 12 name of the OPTIMIZE containing the optimization informations GPT must appear on the RHS to be able to updated the previous values characterx12 name of the FLUX containing the generalized adjoint flux explicit or implicit character 12 name of the TRACK linked list file containing tracking information cor responding to FLUXP character 12 name of the MACROLIB linked list file containing fuel regions description and burnup informations character 12 name of the FLUX containing the unperturbed flux direct or adjoint If it appears on RHS is means it will be necessary for a function evaluation objective or constraint character 12 name of the GPT linked list file containing fuel regions description and burnup informations If it appears on RHS is means it will be necessary for a function evaluation objective or constraint character 12 name of the MATEX object created by the USPLIT module and con taining the complete reactor material index including devices character 12 name of the MAP linked list file containing the fuel map informations structure containing the data to the direct definition of gradient for the module GPTGRD structure containing the data to the generalized theory based gradients choice for the module GPTGRD IGE 314 24 1 5 1 Data input for module GTPGRD Table 1 18 Structure direct data NEW VALUE REL DIRECT VALUE ivari ivar2 4 FOBJ
31. data structure SIGNA STATE VECTOR 1 40 Vector describing the various parameters as sociated with this data structure S VAR VALUE 4 R Njar The values of the decision variables VAR TYPE uuu R Noar The type of the decision variables Vartype var zone IV The definition of the zone where th deci sion variable have an influence on the material properties VAR MAX VAL R Njar The maximum values of the decision variables can be VAR MIN VAL R Njar The minimum values of the decision variables can be VAR WEIGHT R Naar The weight of the decision variables w in the quadratic constraint CST VOL TYPE I Nest Record containing the type for the zone where the constraints apply CST 0BJunuuua R Nest The limit value of the contraints The units depends with the type of the constraint type CST TYPE nju I Nest The type of the contraints 1 for gt lt 0 for misl for lt cst zone I Nz c The definition of the zone where the constraint j apply CST WEIGHT R Nest The weight of the constraint 7 and y for the duals and meta heuristic methods continued on next page IGE 314 Main records and sub directories in optimize Condition FOBJ CST VAL OPT PARAM R R 40 FUNC ZON VOL R Nest 1 BKP PERT XS I 13 FUEL COST uu R dependant FUEL C DIST Nu BURN C DIST Nu D LAMBDA uuu Noar D LAMBDA V R Nvar GRADIENT uuu RC Near Nest 1 OLD VALUE uu Units
32. defined by 29 09 qj OZPPF qj OH OX ZPPF OX oa H dv Gx Avd qj OH 1 I t 1 control zone TH dw ox Y te 1 etj n trol DPHI POWER is defined by 22 DN ZPPF y H F aj H 09 H v H rev 0 otherwise j 1 Neontrol zone where H r 1 1 1 2 1 3 1 4 1 5 1 6 IGE 314 8 KEFF is defined by ke f keff is directly taken in the FLUX object D KEFF is defined by dkeff PE dA dX IX 1 7 where AM is the derivative of the eigenvalue previously calculated with the PERTUR module VOID REAC FC is defined by py 1 1 S 1 8 keff keff v PV Av where kerf and k ry y are directly taken in the FLUX and FLUXP object respectively s d D VOID R FC is defined by del dpy d d y 1 dX dX dX 1 9 where is the derivative of the eigenvalue previously calculated with the PERTUR module and e is the derivative of the eigenvalue previously calculated for a voided reactor with the PERTUR module KEFF KREF is defined by Aker Akegg kej kref 1 10 where kres is the required reference multiplication factor D KEFF KREF is defined by dAk ff MI mec x kept kre IX x keff f dX 2 where kref is the required reference multiplication factor and is the derivative of the eigenvalue previously calculated with the PERTUR module MINPCMAX is defined by test2 EPmoy y q din
33. e 1 12 j icsti ldj gt moy where Gmoy is the average power zone m can be changed with the module QLPUTL The sum is performed from constraint iesti tO est2 D MINPCMAX is defined by dAEPmoy 2m 1 44 2m qj Imo 1 1 dX m dj dmoy ix 1 13 j icstildj 4moy where qmoy is the average power zone m can be changed with the module QLPUTL The sum is performed from constraint iesti tO 6542 Table 1 7 Structure vardef data II LOAD object DOWN repertory GREP data name IN var_name II MSYS FLUX object_sys A B object flux ADJOINT IN var name PREDEF predef var IGE 314 where LOAD object DOWN repertory GREP data name IN var_name MSYS FLUX object_sys A object_flux ADJOINT PREDEF predef_var key word FLUX AFLUX FLUX2 AFLUX2 FLUX AV FLUX AX DIFFX DIFFY DIFFZ TOTAL NFTOT NUSIGF H FACTORS CHI SIGW O key word used to define the object where the data are stored name of the object key word used to go in a sub directory name of the repertory key word used to define the name of the data to load name of the data to load key word used to define the name of the local variable name of the local variable name key word used to specify that a local variable will be calculated by the product of a system matrix and a flux or adjoint name of the object L SYSTEM key word used to specify that the system matrix corresponding to the lost of
34. e optimization problem Ist Ra neighborhood radius fraction 0 1 of the total decision space default 0 01 2nd R radius around tabu list decision variable set within points are also tabu fraction 0 1 of the total decision space default 0 001 3rd R radius around promising area list decision variable set within points are also tabu fraction 0 1 of the total decision space default 0 002 4th fact factor in case of a geometric discretisation of the neighborhood default 2 5th best tabu search function value ever achieved The other value of the record are not used and set to 0 0 1 1 The sub directories in tabu The sub directories are NEIGHBORHOOD TABU LIST PROMISE LIST and NELDER MEAD They all have two main records in common NELDER MEA D has several additional records Those two types of records are presented in the two following tables IGE 314 42 Table 2 2 Main records in sub directories Type Condition Units Comment ITEM LLLLLLU RO List of decision variable set its corresponding functional and tabu search function values TABU F VAL y R Neig The tabu search function values of the neigh bors The length of the ITEM list is given by e Neig for NEIGHBORHOOD directory e min Lf L1 for TABU LIST directory e minfLi Lp for PROMISE LIST directory e Noar 1 for NELDER MEAD directory Table 2 3 Additional records in NELDER MEAD directory Condition UnitsComment IWORST
35. elder Mead convergence criterium default 0 01 IGE 314 30 Table 1 23 Structure nelder data FIND NEW gt gt tworst lt lt COMPARE NEW gt gt Leap lt lt gt gt Letr lt lt gt gt Leonv lt lt EXPAN VLD gt gt Leo lt lt CONTRACTION gt gt Let lt lt gt gt tbest lt lt gt gt Leconv lt lt where FIND NEW worst COMPARE NEW Lexp Lett Leono EXPAN VLD CONTRACTION Lett Ubest key word used to find the worst point of the polytope for the Nelder Mead simplex algorithm and compute its reflected point integer value for the index of the worst point of the polytope key word used to compare the reflected point of the worst point of the polytope with the other points Next geometrical transformation is decided according to the results of the comparison logical value for the expansion move logical value for the contraction move logical value for convergence key word used to validate the expansion point comparison of its results with the reflection point key word used to compare the contraction point comparison of its results with the reflection point Next geometrical transformation is decided according to the results of the comparison logical value for the multi contraction move integer value for the index of the best point of the polytope IGE 314 31 2 Output Data Treatment In this section input of output data treatment modules will be given 2 1
36. f both MACROLIB have a perturbed level it must the same The resulting properties will be stored on root directory DDIFF keyword to specify a correct treatment of diffusion coefficients If SUB is specified the resulting incremental diffusion coefficient will be 1 als ee Di Dz AD where Di is taken from the first MACROLIB and D from the second If ADD is specified the resulting diffusion coefficient will be 1 D 1 Di AD where D is taken from the first MACROLIB and AD from the second NODIF keyword to specify that no addition or substraction of diffusion coefficients will be done This is the default option IGE 314 EDIT iprt 33 Table 1 26 Structure addflu data ADD fracl frac2 SUB F ADJOINT ADJ ONLY ROM 2 PARTS FLUX AFLUX DFLUX igal ADFLUX igal fracl FLUX AFLUX DFLUX iga2 ADFLUX iga2 frac2 IN FLUX AFLUX DFLUX iga2 ADFLUX iga2 where EDIT iprt ADD fracl frac2 SUB F ADJOINT ADJ ONLY FROM 2 PARTS FLUX AFLUX DFLUX ADFLUX igal iga2 IN iga3 key word used to set iprt index used to control the printing gt 1 structure of the resulting object is printed keyword to specify that the two objects will be added This is the default option first real that will multiply the value of the first object default 1 0 second real that will multiply the value of the second object default 1 0 keyword to specify that the two objects
37. f the deci sion variables the objective function the con straints and the gradients of these functions for the previous external iteration This reper tory will be created by the module PLQ unless it is specified to not do continued on next page IGE 314 46 Main records and sub directories in optimize continued from last page Condition Units Comment BKP VALUE uu Dir Directory containing a backup of the values of the decision variables the objective function the constraints and the gradients of these func tions for this external iteration This reper tory will be created if the interpolation of the objective function in the middle point is cal culated stepdir Dir Directory containing the perturbated proper ties and the 4 9 and Bpo vectors Notes related with the decision variables definition The type of the decision variable are given by Variype which is defined by Variype ttype 1000 izone where 1 average exit burnup i P 2 enrichment type 3 number of bundles shift 4 device thickness izone for the number of the corresponding zone in the L MAP for the decision variable The zones definition information records var zone will be composed using the following FORTRAN instructions WRITE var zone A8 14 VAR ZONE i for 1 lt i lt Ny The size N of the records depends of the type of the decision variable For average exit burnup enrichment and number of bundles s
38. for the promising area as the new current decision variable An update of the best point ever found is done is necessary The promising list is also updated key word used to specify the Nelder Mead simplex algorithm is selected structure containing the data to the option NELDER MEAD corresponding to the different geometric transformations Table 1 22 Structure def_data NEIGHBOR NB ngh NEIGHBOR TYP 4 RECTANGLE BALL continued on next page IGE 314 Structure def data NEIGHBOR DIS 4 GEOMETRIC fact LINEAR ISOVOLUME NEIGHBOR RAD R TABU RAD R PROMIS RAD R NIT MAX CONV Nitmas TABU LIST LG 4 ALL ILg PROM LIST LG 4 ALL Lgp GET CURRENT COMPLETE PUT CURRENT INITIALIZE INIT PRO LIST RESET BEST BEST AS CURR 28 continued from last page NELDER EPS neg where ISEED key word used to define the seed for random number generation seed seed integer value for the seed default given by CLETIM NEIGHBOR NB ngh NEIGHBOR TYP RECTANGLE BALL NEIGHBOR DIS key word used to define the number of neighbors ngh integer value for the number of neighbors default 5 key word used to specify the type of the neighborhood key word used to specify that the neighborhood will be hyperrectangle crowns default key word used to specify that the neighborhood will be hypersphere crowns key word used to specify that the type of discretisation within the nei
39. fy that the limit of maximum zone power will be provided done first number of surveillance zone IGE 314 6 cstiim constraint limit RANGE key word used to specify that the constraint limit will be specified for several zones iones second number of surveillance zone ALLSAME key word used to specify that all the constraint will have the same limit for the zone number between zone and zone2 END MAX POW key word used to specify that the definition of the maximum power surveillance zones is finished VOID REAC FC key word used to define the full core void reactivity PV EC full core void reactivity ANALYTIC FCT key word used to specify that the corresponding constraint will be defined analytically Csttype type of the analytic constraint 1 for lt 0 for and 1 for gt 1 1 2 Data input for module functions definition Because the functions definition is common with other modules its description will be grouped in this section as a independent part of the FOBJCT module description The functions definition is based on inverted polish notation logic Some functions are predefined but if it is not the case new functions can be defined manually In this particular case variables may be required Some of them are predefined also otherwise the user can get them with the same logic as the module GREP For the functions representing the constraints the user need to specify its number So it is important to know the order in whic
40. g in module key word used to define the decision variable for which the perturbation theory calcu lations will be done number of the first decision variable number of the second decision variable key word used to specify that the perturbation theory calculations will be done for all the decision variables key word used to specify that absolute variation of the eigenvalue perturbation will be calculated for the corresponding perturbated decision variables key word used to specify that derivative of the eigenvalue perturbation will be calcu lated for the corresponding perturbated decision variables key word used to specify that absolute variation of the eigenvalue perturbation will be calculated for the corresponding perturbated decision variables and that the provided system matrix correspond to the voided reactor or an other configuration of the reactor key word used to specify that derivative of the eigenvalue perturbation will be cal culated for the corresponding perturbated decision variables and that the provided system matrix correspond to the voided reactor or an other configuration of the re actor see explanations in the module FOBJCT key word EVAL OBJ CST 1 1 2 Some predefined function are described too IGE 314 21 1 4 The GPTSRC module The GPTSRC module is used to calculate the sources terms direct and or adjoint for generalized perturbation theory The calling specifications are Table 1 15
41. ghborhood GEOMETRIC key word used to specify that the radius of the crowns are given by a geometric serie The radius are given by m Po acto with 1 ngh fact real number gt 1 for the geometric serie for the radius determination LINEAR key word used to specify that the radius of the crowns are given by a linear serie default The radius are given by rj e with i 1 ngh ngh ISOVOLUME key word used to specify that the radius of the crowns are chosen to have a constant volume for all crowns The radius are given by Ti Rn vej NI with 1 ngh IGE 314 NEIGHBOR RAD Rn TABU RAD ki PROMIS RAD Rp NIT MAX CONV Nitmaz TABU LIST LG PROM LIST LG ALL Lg Lgp GET CURRENT COMPLETE PUT CURRENT INITIALIZE INIT PRO LIST RESET BEST BEST AS CURR NELDER EPS Ened 29 key word used to set the radius R of the neighborhood real number for neighborhood radius This radius is a fraction of the total limits and then must be between 0 0 and 1 0 key word used to set the radius R of the hyperrectangle ball around tabu values All the points within this small domain are tabu as well real number for tabu list radius This radius is a fraction of the total limits and then must be between 0 0 and 1 0 key word used to set the radius Rp of the hyperrectangle ball around tabu values All the points within this small domain are tabu as well real number for promising lis
42. h constraints where defined Table 1 6 Structure eval_data FOBJ CONSTRAINT ics est2 VARDEF vardef data seg data FUNCT PREDEF predef func where FOBJ key word used to specify that the objective function will be evaluated CONSTRAINT key word used to specify that constraint functions between number test and ic s 2 will be evaluated Testi first number of constraint dest2 second number of constraint VARDEF key word used to define the variables needed for the function evaluation vardef data structure containing the data to the option VARDEF seg data structure containing the data used to defined a function directly by the user FUNCT PREDEF key word used to specify that a predefined function will be evaluated IGE 314 predef func name of the predefined function The predefined function name are UCOST DX UCOST DPHI UCOST POWERLIMIT DX POWER DPHI POWER KEFF D KEFF VOID REAC FC D VOID R FC KEFF KREF kref D KEFF KREF kref MINPCMAX moy lesti best D MINPCMAX may Testi Tenia Where UCOST is defined by Fc S52 H 0 ir acteur H Q r acteur OFc DX UCOST is defined by 257 Fo ore _ Gg gom Cu Ba e Am OX i H d v H d v 3L dyy F 1 var ay oe DPHI UCOST is defined by 272 BEG ou a Su H F Fo H F Ob e H 6 v POWERLIMIT is defined by q ZPPF I lt TT flim z V Hey P DX POWER is
43. he function for optimization in DONJON IGE 314 12 1 Predefined function OPTIMIZE FOBJCT OPTIMIZE FLUX MACRO EVAL OBJ CST CONSTRAINT 2 10 PREDEF POWERLIMIT 2 Function defiend by user For example we suppose that a functional u defined by the user is Frost 2 keff f cv dE dV 1 14 CORE allenergygroups Where Cu is the fuel cost 9 the flux distribution OPTIMIZE FOBJCT OPTIMIZE FLUX MACRO FUEL COST DF MEMORY EVAL OBJ CST FOBJ VARDEF LOAD FLUX GREP K EFFECTIVE IN KEFF PREDEF FLUX 2 0 VAR KEFF INTEGRAL CORE VAR FUELCOST ENERGY ALL VAR FLUX END ENERGY END INTEGRAL END IGE 314 13 1 2 The OLPUTL module The QLPUTL module is used to define the optimization options and tools It is also used to do some pre calcultaion The calling specifications are Table 1 10 Structure OLPUTL OPTIM GLPUTL OPTIM FLUX MAPFL MACRO MACROP L SYS SYSP TRACK descqlputl where OPTIMIZE character 12 name of the extended OPTIMIZE FLUX character 12 name of the FLUX linked list This object is used for the function evaluation It is recommended to provide it even if no function evaluation is done for many parameters reading file MAPFL character 12 name of the extended MAP linked list file containing fuel regions de scription and burnup informations If MAPFL appears on the RHS the information in it will be red for many parameters initialisation MACRO characte
44. hift Nz Nen For device thickness Nz Nen Ny Notes related with the constraints definition The type of each constraint zones is defined by the following index one value for the whole reactor ex ker one value for all channels ex total power one value for one channel ex channel power one value for one bundle ex bundle power one value for one zone defined by many bundles void reactivity analytic function Jtype cO ER D N The zones definition information records cst zone will be composed using the following FORTRAN instructions WRITE cst zone A8 14 CST ZONE j for 1 lt j Nest The size N of the records depends of the type of the constraint 1 if jtype 3 the record contains the number of the channel N 2 if type 4 the record contains the number of the channel and the plan e Nen x Ne if jeype 5 the record contains one value for each bundle 0 out of the zone j 1 in the zone j IGE 314 47 If type 1 or 2 no record is necessary to define the volume because it is implicit with the type of the constraint reactor or core respectively Notes related with the different limits and values for the iterative calculations of the optimization problem Ist S external step limit It is used for the guadratic constraint if applicable default 1 0 2nd internal step limit for MAP method default 0 1 3rd Eext limit for external convergence
45. lon PREVIOUS NEW VAL UPDT PERTURB VAR 4 ivar RESTORE BKP MACRO P ivar2 Table 1 11 Structure descqlputl MAT FLUX 4 A PHI B PHI AP PHI ivars BP PHI ivar3 LA PNLT INITIAL F EVAL COEF UPDATE CONV TEST gt gt conv lt lt ALMOST FSBLE gt gt feas lt lt HISTORY ijter1 POWER CHA K EFFECTIVE QUAD CST CONSTRAINT ALL RANGE lt lt esti gt gt lt lt testg gt gt lt lt testi gt gt DIRECT lt lt num gt gt 1 val i 1 num POWER CHA 2 POWER CHA S key word used to set iprint index used to control the printing in module key word used to define the optimization options structure containing the data to the option DEFINITION key word used to verify if the new 4 X ends with a better objective function key word used to verify if the new 4 X respects the constraints logical value for the validition of the new decision variables test eguals true if Fo X is better than Fc X key word used to specify that an interpolation of the objective function for the midle point between XP and X 1 will be done key word used to calculate and store the middle value key word used to verify the middle value T logical value for the validation of interpolation If Fc ee is less than Fo er then the middle value is kept otherwise the new value is restored key word used to define which method will be used
46. merical gradient will be computed and compared to the analytical gradients number of the first decision variable for which the comparason will be done number of the last decision variable for which the comparason will be done number of the first functional for which the comparason will be done number of the last functional for which the comparason will be done key word used to specify that the comparason will be done for all decision variables and or all functionals Chapter 2 OPTEX STRUCTURES IGE 314 40 1 Contents of a tabu data structure The tabu specification is used to store the decision variable set used for a tabu search optimization method The different options of this method are also stored in the tabu data structure The signature variable for this data structure must be SIGNAL TABU The dimensioning parameters for this data structure which are stored in the state vector S represents e The number of neighbors Neig Si The type of neighborhood S where st 1 hyperrectangle E 2 ball e The type of discretisation of the neigborhood S where 1 geometric Si 4 2 linear 3 isovolume e The test for external convergence Nitmaz Si e The current number of iterations without improvement of the best value Nit Si e The tabu list maximum size L Si e The promising area list maximum size L Si e The tabu list current size Lf S e The promising list current size L e The num
47. nisotropic component of the within group of the scattering of the scattering cross section NFTOT fission cross section Xf NUSIGF product of the fission cross section Hy and the steady state number of neutron produced per fission v H FACTORS energy production coefficient H CHI the steady state energy spectrum of the neutron emitted by fission FIXE fixed sources Notes related with the fuel cost If the cost of the fuel is fixed the dimension of the record is given by the number of enrichment zones Otherwise the record contains the 7 parameters necessary to calculate the fuel cost which are Ist 2nd 3rd 4th 5th 6th Tth concentration in 7 U of the waste uranium w cost of natural uranium Cyy kg cost of a separation work unit Cs SWU cost of the bundle fabrication CraB kg interest rate int day time to obtain uranium days time for enrichment days IGE 314 48 The fuel cost is given by the equation Notes related with the perturbated materials properties directory The directories stepdir will be composed using the following FORTRAN instructions WRITE stepdir A4 I8 STEP i for 1 lt i N ar Each directory contains also the result of the multiplication of the perturbated system matrix and the flux 7 0 is used to stored the result of the unperturbated system matrix and the flux 2 1 The sub directory OLD VALUE in optimize Table 2 5 Main records and sub directo
48. nstructions WRITE Aphi A5 I7 A x PHI g and WRITE Bphi A5 I7 B x PHI g respectively where g represent the energy group 2 3 Contents of a optimize data structure for module GPTVRF When the module GPTVRF is used a new optimize data structure can be created This new structure contains a copy of the STATE VECTOR record of the optimize data structure used on the RHS of the module Then only the bare minimum necessary datas for gradients verification will be stored This structure can also be deleted when a new point of the optimization procedure is calculated If the same optimize data structure is used in the module GPTVRF unnecessary data will be stored for the rest of the optimization calculations This is why we recommend to use a new optimize data structure on the LHS In both cases the optimize data structure will contain the data described in the following table Table 2 7 optimize in the particular case of module GPTVRF Condition Units Comment SIGNATURE uu Cx12 Signature of the data structure SIGNA STATE VECTOR 1 40 Vector describing the various parameters asso ciated with this data structure S same one or a copy of the previous description VAR VALUE RF R N ar The references values of the decision variables for which the gradients are numerically and analytically calculated GRADIENT GPT R N 4r Nest 1 The gradients calculated analytically This record is simply a copy of
49. onals If OPTIMV is the same as OPTIM then the perturbated datas will be stored in the same OPTIMIZE object OPTIM characterx12 name of the OPTIMIZE containing the curent values of the decision variables and of the functionals gptvrf data structure containing the data to module GPTVRF 2 3 1 Data input for module GPTVRF Table 1 31 Structure gptvrf data EDIT iprint SAVE PERT vay SAVE GPT ABS REL egpr COMPARE 4 ivari vara ALL ifeti foto ALL T where EDIT key word used to set iprint iprint index used to control the printing in module SAVE PERT key word used to store the current values of the functionals for the corresponding perturbation e of the decision variable ivar Von number of the perturbated decision variable amount of the pertubation ex e 0 01 corresponds to 1 of perturbation IGE 314 SAVE GPT ABS REL EGPT COMPARE tvarl lvar2 l fetl fct2 ALL 38 key word used to specify that the analytical gradient will be stored key word used to specify that the stored analytical gradient correspond to a absolute perturbation or that the derivative are already calculated key word used to specify that the stored analytical gradient will be devided by the corresponding amount of perturbation to obtain the relative gradient the derivative amount of the pertubation ex egpr 0 01 corresponds to 1 of perturbation key word used to specify that the nu
50. p nun X ngrp nun X ngrp nun X ngrp nun X ngrp nun X ngrp nun X ngrp nun X ngrp nun X ngrp nun X ngrp nun X ngrp nun X ngrp ncst 1 ncst 1 nun X ngrp nun X ngrp nun X ngrp nun X ngrp 10 INTEGRAL 4 REACTOR CORE CST ZONE VAR ZONE DBL ZONE DISCRETE ALL DISCRETE COR DISCRETE CST data ENERGY ALL gprfrom gprto data END ENERGY END INTEGRAL END where INIT data INTEGRAL REACTOR CORE key word used to specify that the function definition will follow structure containing the data used to defined parts of the function key word used to define an integral over one volume and energy key word used to specify that the integration volume is the reactor key word used to specify that the integration volume is the core all the bundles IGE 314 CST ZONE VAR ZONE DBL ZONE DISCRETE ALL DISCRETE COR DISCRETE CST ENERGY ALL GTP from 9TPto END ENERGY END INTEGRAL END Li kev word used to specifv that the integration volume is a control zone of one constraint kev word used to specifv that the integration volume is a zone where a decision variable applies kev word used to specifv that the integration volume is on the intersection of a control zone of one constraint and a zone where a decision variable applies key word used to specifv that the integration will be performed only on the energy for every point of the reactor
51. pecifv that the channel power distribution is also stored key word used to specify that ke value is also stored key word used to specify that guadratic constraint limit is also stored key word used to specify that some constraint values are also stored key word used to specify that all constraint values are stored key word used to specify that values of a range of constraint are stored integer representing the first or only number of constraint integer representing the second number of constraint key word used to specify that values provided by the user are stored integer representing the number of values provided by the user real representing the values provided by the user same key word as POWER CHA It can be used when channel power distribution for a perturbated state of the reactor is also stored same key word as POWER CHA 2 Table 1 12 Structure def data METHOD SIMPLEX LEMKE MAP AUG LAGRANG PENAL METH MAXIMIZE MINIMIZE INN STEP LIM step VAR WEIGHT 4 TYP BURNUP weight TYP ENRICH weight CST WEIGHT testi weight RANGE lesti dest2 ALLSAME weight weight J tcst1 esta ll OUT STEP LIM step INN STEP NMX Minas OUT STEP NMX nmaz INN STEP EPS cert OUT STEP EPS inn STEP REDUCT HALF PARABOLIC CST QUAD LIM epsilon4 BKP MCR P XS ADD NEW XS_name F C VOLUME FOBJ REACTOR CORE CONSTRAINT esri icstg REACTOR CORE ZONE CST WGT
52. print 3 14 20 22 26 34 35 37 iprt 31 33 iscr 35 ISEED 27 28 ISOVOLUME 28 isrc 35 F4 H H H H H H K EFFECTIVE 14 16 KEFF 5 7 8 10 KEFF VOID 10 KEFF KREF 7 8 LA PNLT 14 15 Lconv 27 LEMKE 16 17 LINEAR 28 LN 11 LOAD 8 9 loc_var_name 11 LOG 11 MACNEW 31 MACRO 2 13 19 21 23 MACRO I 31 32 MACRO2 31 32 macrolib 49 MACROLIB 2 13 21 23 31 32 MACROP 13 19 MAP 16 17 MAP 2 4 13 21 23 MAP FLUX 35 MAPEL 2 13 21 23 MAT FLUX 14 15 MATEX 23 MATEX 23 MATLAB 34 MAX 11 MAXIMIZE 16 17 MAXPOWER 5 MEMORY 3 5 IGE 314 METHOD 16 17 MIN 11 MIN PCMX 2N 16 18 MINIMIZE 16 17 MINPCMAX 7 8 MINUS 11 MSYS FLUX 8 9 N 4 nbz 3 4 nch 9 nest 10 NEIGHB BEST 26 27 NEIGHB CHOIC 26 27 NEIGHB CREAT 26 NEIGHB EVAL 26 27 NEIGHBOR DIS 28 NEIGHBOR NB 27 28 NEIGHBOR RAD 28 29 NEIGHBOR TYP 27 28 NELDER EPS 28 29 NELDER MEAD 26 27 nelder_data 26 30 NEW 16 18 NEW VAL UPDT 14 15 NEW VALUE 24 nez 3 4 NFTOT 9 18 ngh 27 28 ngrp 9 10 NIT MAX CONV 28 29 NO GRID 35 36 NO THRESHOLD 26 27 NODIF 32 nun 9 10 NUSIGF 9 18 nz 9 nzone 9 object 8 9 object flux 8 9 object sys 8 9 operator 11 OPT GRAD VRF 34 35 OPT PARAM R 24 OPTIM 2 3 5 13 26 27 29 34 37 OPTIMISATION 34 OPTIMIZE 13 19 21 23 24 optimize 43 46 49 50 OPTIMIZE
53. r 12 name of the MACROLIB linked list file containing the mixtures cross sections If it appears on RHS it means it will be necessary for a function evaluation objective or constraint MACROP character 12 name of the MACROLIB linked list file containing the mixtures pertur bated cross sections If it appears on RHS it means it will be necessary for a function evaluation objective or constraint SYS character 12 name of the SYSTEM containing the reference system matrices SYSTEM must be a linked list If it appears on RHS it will be necessary for system matrice times flux calculations SYSP character 12 name of the SYSTEM containing the perturbated system matrices SYS TEM must be a linked list If it appears on RHS it will be necessary for perturbated system matrice times flux calculations TRACK character 12 name of the TRACK type L_TRIVAC containing the tracking informa tions TRACK must be a linked list If it appears on RHS it will be necessary for system matrice times flux calculations descqlputl structure containing the data to module POLUTL IGE 314 14 1 2 1 Data input for module GLPUTL where EDIT iprint DEFINITION def data STEP VALID TEST CST VLD test STEP INTERP PUT RECOVER test2 DX METHOD EDIT iprint DEFINITION def data STEP VALID TEST CST VLD gt gt testi lt lt STEP INTERP PUT RECOVER gt gt test2 lt lt DX METHOD 4 EPS epsi
54. r ihrm will be drawn identifier for the harmonic number corresponding to the flux to be drawn IGE 314 36 NO GRID key word used to specify that no grid will be add on the map of the flux distribution An exemple of the results is presented on the figure a CENTER GRID key word used to specify that a grid will be add on the map of the flux distribution The nodes of the grid correspond to the center of the volumes where the flux are calculated An exemple of the results is presented on the figure b CHANEL GRID key word used to specify that a grid will be add on the map of the flux distribution The sguares of the grid correspond to the limits of the channels An exemple of the results is presented on the figure c a b c FLUX GRE2 Plans FLUX GR 2 Plan 49 FLUX GR 2 Plan 49 IGE 314 37 2 3 The GPTVRF module The GPTVRF module is used to verify the computation of the gradients with classical and generalized perturbation theories The analytical gradients calculated with the modules PERTUR and GPTGRD are compared with numerical gradients calculated with the Ceshino method using several values of the functionals for pertubated values of the decision variables The calling specifications are Table 1 30 Structure GPTVRF OPTIMV GPTVRF OPTIMV OPTIM gptvrf data where OPTIMV character 12 name of the OPTIMIZE containing the pertubated and unpertubated values of the decision variables and of the functi
55. ries in OLD VALUE Condition UnitsComment VAR VALUE u Naar The values of the decision variables of the last valid iteration FOBJ CST VAL Nest 1 The values of the objective function and the contraints of the last valid iteration GRADIENT uuu Nuar Nest 1 The gradients of the objective function and the constraints of the last valid iteration VAR VALUE2 y Nuar The values of the decision variables of the second last valid iteration BEST VAR LU The values of the decision variables corre sponding to the best valid solution ever found BEST FCT uuu The value of the objective function corre sponding to the best valid solution ever found 2 2 The sub directory stepdir in optimize Table 2 6 Main records and sub directories in stepdir Type Condition Units Comment The group dependent vectors representing the multiplication of a system matrix A and the unperturbated flux The group dependent vectors representing the multiplication of a system matrix B and the unperturbated flux continued on next page IGE 314 49 Main records and sub directories in stepdir continued from last page Type Condition Units Comment grpdir Dir The group dependent directory containing the perturbated properties The content is the same as for the macrolib but limited to the properties to be saved only see BKP PERT XS The records Aphi and Bphi will be composed using the following FORTRAN i
56. ructure addmac data continued from last page FROM MP 4 DDIFF NODIF where EDIT key word used to set iprt iprt index used to control the printing lt lt 2 minimum printing gt 3 macroscopic differ ences are printed ADD keyword to specify that the two objects will be added If only fracl is specifeid MACRO fracl MACRO2 will be performed using the options for the diffusions coefficients If fracl and fracl are specified fracl MACRO frac2 MACRO will be performed even for the diffusion coefficients fracl first real that will multiply the value of the first object default 1 0 frac2 second real that will multiply the value of the second object default 1 0 SUB keyword to specify that the two objects will be substracted This is the default option FROM MP keyword to specify that the two objects have been partially calculated by different CPU An addition will be performed to calculate the complete object fracl and frac2 equal 1 0 STEP key word used to set ilev ilev number of the perturbed level in MACROLIB In case of substraction of two MACROLIB If a single set of increments is stored it must be equal to 1 This step is used to later compute perturbation system matrices If this information is absent incremental cross sections are stored on root directory In case of addition of two MACROLIB ilev specifies the perturbed level where informations is stored in the two initial MACROLIB I
57. stored on a backup repertory of the L OPTIMIZE object for complementary infor mation see PQLUTL BKP MACRO P key word used to add name of cross section to be stored key word used to define a new list of name of cross section to be stored name of the cross section to be stored The list of available name is DIFFX DIFFY DIFFZ TOTAL NFTOT NUSIGF H FACTORS CHI SIGW O SIGW 1 SCAT O SCAT 1 CHI FIXE key word used to specify that the volume where the functionals apply will be calculated key word used to specify that the volume corresponding to the objective function will be computed key word used to specify that the volume corresponding to the constraints between number test and iesr2 will be computed number of the first constraint for which the volume will be calculated number of the last constraint for which the volume will be calculated key word used to specify that the volume of the functional is the whole reactor key word used to specify that the volume of the functional is the core represented by all the fuel channels key word used to specify that the volume of the functional is its corresponding zone key word used to set the multiplication factor a for the constraint weight update multiplication factor for the constraint weight update key word used to set the precision when the validation of a new point is done with the constraint validity precision for the constraint validity key word used to se
58. t radius This radius is a fraction of the total limits and then must be between 0 0 and 1 0 key word used to specify the number Nitmax of required external iteration without improvement of the best solution ever found for global convergence achievement integer value of required iterations for global convergence key word used to specify the maximum length of the tabu list key word used to specify the maximum length of the promising area list key word used to specify the values entering in a list are kept until the end of the optimization procedure integer value of maximum tabu list length integer value of maximum promising area list length key word used to specify the decision variable set in OPTIM object will be stored as the current one in TABUSH object key word used to specify the objective function the constraints and the penalty func tions will also be stored with the current values key word used to specify the current decision variable set in TABU object will be stored as the variable values in OPTIM object key word used to initialize chose a random value the starting decision variables in the decision space key word used to specify that the initial promising list is created key word used to reset the best value of the tabu search objective function key word used to set the best value as the current value key word used to set the convergence limit for the Nelder Mead simplex algorithm real value for the N
59. t the coefficient m of the power distribution optimization problem coefficient for channel having power greater than the average IGE 314 19 1 3 The PERTUR module The PERTUR module is used to compute gradients of function using the first order of perturbation theory Then it can be used to calculate the variation of reactivity of one reactor with a small perturbation of the cross sections There is two different approches to solve the problem of reactivity The first method uses in fact the module SORKEF of the previous version This part of the module computes source terms based on a first order perturbation theory over diffusion eguation The direct diffusion equation for system matrix perturbations AA and AB can be written for a linear perturbation of the flux o Ao A A Bo Ag AA AAB AAB o 1 17 The direct source term is then simply AA A AB AAB 4 where AA is the first order estimate of the eiganvalue variation Rayleigh formulation The adjoint source terms are easily obtained from a similar expression of the ajoint diffusion equation The second method is a part of the optimization modules package To calculate a the user has to precalculate system matrices flux It can be done easily and automaticaly by using the module POLUTL with the key word MAT FLUX For the specific case of the reactivity the variation of the inverse of k effective is given by the following equation
60. tabu structure containing the data to module TABU 1 6 1 Data input for module TABU Table 1 21 Structure desctabu EDIT iprint DEFINITION def data NEIGHB CREAT NEIGHB CHOIC INIT PRO LIST NELDER MEAD ineig NEIGHB EVAL INIT PRO LIST NELDER MEAD ineig NEIGHB BEST CONV TEST gt gt Lconv lt lt PROMISE TEST NO THRESHOLD gt gt Lpro lt lt PROMISE AREA NELDER MEAD 4 CREATION UPDATE NELDER MEAD nelder data where EDIT key word used to set iprint iprint index used to control the printing in module DEFINITION key word used to define the tabu search optimization options def data structure containing the data to the option DEFINITION NEIGHB CREAT key word used to create the neighborhood for the decision variable set stored as the current one in the TABUSH object IGE 314 NEIGHB CHOIC NEIGHB EVAL INIT PRO LIST NELDER MEAD Vneig NEIGHB BEST CONV TEST Lconv PROMISE TEST NO THRESHOLD Lconv PROMISE AREA NELDER MEAD CREATION UPDATE NELDER MEAD def data ISEED seed 27 key word used to specify the number neig within the neighbors which will be evaluated The corresponding decision variable values are copied in the OPTIM object as the current decision variables key word used to specify the number inejg within the neighbors which have been evaluated The corresponding functional values and the tabu function result
61. tion The result will be stored in L OPTIMIZE STEP HSIGN with WRITE HSIGN I8 ivars key word used to specify that a task related to the augmented lagrangian or penalty method is performed key word used to initialize the constraint weight if not already done and the la grangian coefficient when augmented lagrangian method is used key word used to calculate the augmented lagrangian or penalty function It can be also used with tabu search to evaluate the corresponding objective function key word used to update the constraint weights and lagrangian coefficients if neces sary in an external iteration key word used to specify that a convergence test for external iteration will be per formed logical value representing the result of the external convergence test key word used to specify that a test will be permorfed to check if the current point is almost feasible logical value representing the result of the almost feasible test The maximum error allowed to set feas to true is a relative difference between prescribed and current constraint values lower than the convergence crriterium IGE 314 HISTORY literi POWER CHA K EFFECTIVE QUAD CST CONSTRAINT ALL RANGE lesti test2 DIRECT num val POWER CHA 2 POWER CHA 3 where 16 key word used to store the decision vector and the functionnal values for iteration literl integer representing the iteration number kev word used to s
62. tion and produce the ASCII MAT file An exemple of the results is presented on the following figure Fobj Zone 2 T 0 144 F 0 143 F 0 142 F 0 141 F iw 0 14F 0 139 F 0 138 F 1 4 3 2 A 0 1 2 3 Pertubation 0 lt gt Burnup de sortie moyen 6478MWj t Table 1 29 Structure descmatlflu MAP FLUX FLUX ADJOINT GPT FLU isrc GPT ADJOINT isrc HARMONIC ihrm NO GRID CENTER GRID CHANEL GRID Hi where EDIT iprint MAP FLUX FLUX ADJOINT GPT FLU GPT ADJOINT iscr HARMONIC ihrm key word used to set iprint index used to control the printing in module XSFUEL 0 for no print default value 1 for minimum printing larger values produce increasing amounts of output key word used to select the flux distribution mapping option and produce the ASCII MAT file key word used to specify that the distribution of the flux will be drawn key word used to specify that the distribution of the adjoint will be drawn key word used to specify that the distribution of the explicit generalized adjoint cor responding to the source number iscr will be drawn key word used to specify that the distribution of the implicit generalized adjoint cor responding to the source number iscr will be drawn identifier for the source number corresponding to generalized adjoint to be drawn key word used to specify that the distribution of the flux corresponding to the harmonic numbe
63. tlgrd ASCII MAT MATLAB FLUX TRACK INDEX GEOM descmatlflu where ASCII MAT character 12 name of the ASCII file executable by MATLAB OPTIM character 12 name of the OPTIMISATION linked list or XSM file containing the gra diants and the stored perturbated values of the functions Such file is obtained using the module GPTVRF descmatlgrd structure containing the data input to module MATLAB for gradiants ploting FLUX character 12 name of the FLUX linked list or xsM file containing the flux or adjoint or generalized adjoints or harmonics to be mapped TRACK character 12 name of the TRACK linked list or XSM file containing the tracking datas TRIVAA is the only type of tracking compatible INDEX character 12 name of the INDEX linked list or XSM file containing the index datas GEOM character 12 name of the GEOM linked list or XSM file containing the geometry de scription descmatlflu structure containing the data input to module MATLAB for flux distribution s mapping 2 2 1 Data input for module MATLAB Table 1 28 Structure descmatlgrd EDIT iprint OPT GRAD VRF where EDIT key word used to set iprint IGE 314 iprint OPT GRAD VRF EDIT iprint 35 index used to control the printing in module XSFUEL 0 for no print default value 1 for minimum printing larger values produce increasing amounts of output key word used to select the gradiants verification and ploting op
64. to evaluate the perturbated cross section k k dx X X X Xj AA 1 15 dXF xk E 118 IGE 314 EPS epsilon PREVIOUS NEW VAL UPDT PERTURB VAR Varl RESTORE BKP MACRO P twar2 MAT FLUX AxPHI BxPHI APxPHI BP PHI twar3 LA PNLT INITIAL F EVAL COEF UPDATE CONV TEST conv ALMOST FSBLE feas 15 where X o is the perturbated decision variable key word used to define XF by X7 1 4 value of e k k 1 key word used to define X7 by X7 gt key word used to update the new decision variables key word used to perturbate a decision variable number of the decision variable to perturbate key word used to restore the unperturbated decision variables key word used to store the perturbated macroscopic cross section By default all cross section are stored To store only some of them see PQLUTL DEFINITION BKP MCR P XS number of the decision variable for which the cross section are perturbated and will be stored key word used to precalulate the system matrice times the flux key word used to precalulate the 4 0 ivar3 0 is implicit key word used to precalulate the B ivarz 0 is implicit key word used to precalulate the A key word used to precalulate the B 9 number of the step directory where the A and B will be stored 4 43 represents the decision variable for which the system matrice were perturbated and will be multiplied by the flux for optimiza
65. ulated for all decision variables IGE 314 eval data INDIRECT EXPLICIT IMPLICIT FOBJ CONSTRAINT ifeni fen2 25 see explainations in the module FOBJCT key word EVAL OBJ CST Some prede fined function are described too key word used to specify that the indirect part of the gradient will be calculated key word used to obtain the solution of an direct fixed source eigenvalue problem key word used to obtain the solution of an adjoint fixed source eigenvalue problem If neither EXPLICIT nor IMPLICIT are provided the default value will be chosen as a function of Nyar and nest 1 key word used to specify that the gradient of the objective function will be defined key word used to specify that the gradient of conctraints will be defined first constraint for which the gradient will be defined last constraint for which the gradient will be defined IGE 314 26 1 6 The TABU module The TABU module is used to define options and data storage for the tabu search optimization algorithm The calling specifications are Table 1 20 Structure TABU TABUSH OPTIM TABU TABUSH OPTIM desctabu where TABUSH character 12 name of the extended TABU linked list file OPTIM character 12 name of the extended OPTIMIZE linked list file If OPTIM appears on the LHS decision variables or their limits for exemple may be changed for further evaluation of the objective function and constraint desc
66. used to specify that the several constraint weights will be identical key word used to set a limit for a burnup type decision varaible key word used to set a limit for a enrichment type decision varaible weight for the decision variable key word used to limit the outer step of the optimization problem key word used to set the maximum of inner iteration of the optimization problem key word used to set the maximum of outer iteration of the optimization problem maximum number of iterations key word used to set the tolerence of inner iteration convergence criterium of the optimization problem tolerence for convergence of inner iterations real key word used to set the tolerence of outer iteration convergence criterium of the optimization problem tolerence for convergence of external iterations real key word used to define the method of the reduction of the outer step IGE 314 HALF PARABOLIC CST QUAD LIM epsilon4 BKP MCR P XS ADD NEW XS name F C VOLUME FOBJ CONSTRAINT testi dest2 REACTOR CORE ZONE CST WGT MFAC a CST VIOL EPS Ecst MIN PCMX 2N m 18 key word used to specify that the step will be reduced by a factor 2 key word used to specify that the step will be reduced with the parabolic method key word to set the parameter epsilon4 for the guadratic limit of the step parameter 4 key word used to specify which of the perturbated macroscopic cross section will be
67. will be substracted keyword to specify that the same numerical operation will performed on flux and adjoint flux keyword to specify that the numerical operation will be performed on the adjoint flux only keyword to specify that the two objects contain one part of the result flux An addition will be performed to calculate the complete object This option can not be done with other options except EDIT in the same call of the module keyword to specify that the flux will be used or the result of the addition keyword to specify that the adjoint flux will be used or the result of the addition keyword to specify that the explicit generalized adjoint will be used or the result of the addition keyword to specify that the implicit generalized adjoint will be used or the result of the addition number of the first generalized adjoint if applicable number of the second generalized adjoint if applicable keyword to specify that the type of flux for the result of the addition number of the third generalized adjoint if applicable IGE 314 34 2 2 The MATLAB module The MATLAB module is used to create an ASCII file executable by MATLAB Two options are available First one is used to create a file to draw the gradiants of functions calulated in a optimisation problem Second option allows to draw maps of the flux distribution The calling specifications are Table 1 27 Structure MATLAB ASCIEMAT MATLAB OPTIM descma

A USER GUIDE FOR OPTEX VERSION4 R. Chambon

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