1 GENCAB Software
Contents
1. 3 1 Parameters initializing The command Parameters of menu Optimisation allows to display the following dialog box in which the user enters the characteristics of function parameters to optimize PARAMETERS Number of parameters Predefined names To provide table Parameter Type 2 Real va_4 OQ Integer C Binary Min value Max value The scrolling menu at the top right allows to enter the parameters number lt 150 16 The list of parameters appears in a second scrolling menu For any of them the user specifies the type real integer or binary with maximum and minimum limits of variation range Except for the binary case such limits should be imperatively informed The variable name Va_i is default but can be modified directly in the box Equivalence is then defined between the new and old names x Va_1 for example The button allows to select the names of previously defined parameters on the selected sheet using the following dialog box Predefined names Eg Select the pedetined parameters to vary Then press the button below CONTINUE The button allows to get a entry table as indicated below Take into account the parameters The taking into account of the information entered in the table by the user is carried out by an action on the button located on the corresponding sheet Nest The button allows to validate the characteristics of the selected parameter The2. ARRHENIUS temperature Fa exp EalK A T 1 T AF Tp Ta Ea Activation energy K constant Bolzman Tin K RITA R TN Nominal REVERSE POWER voltage load Fa VaN BASQUIN fatigue mechanical load Fa Ca Cy P 7 A TN LOG LINEAR Fa exp b S S Accelerated Eyring temperature other stress Fa exp EalK 1 T 11T 4 Sy afS4y SoafSon NORRIS LANDZBERG thermal cycling Fa exp Ea kK 1 Ty 1 Ta an AT AT py PECK temperature moisture Fa exp Ea K 1 Ty 1 Ta HafHy Cox model Assumption The failure rate is affected by covariates Xi based on values Bi A t A thexp RX R t R t TZ if Xi independent of time Return to previous menu 14 EF DIDACT_6f o B Confidence interval Contains the estimated value of the parameter with the probability B confidence 1 a risk The confidence interval is said exact if based on the distribution of a known probability law Approximate if based on the approximation of a law by another asymptotique if based on asymptotic theorems of convergence 6 is then reached when the sample size goes to infinity with no real control of the convergence speed The Fisher information is used to calculate such intervals after adjustment by the maximum likelihood _ in X 8 amp Inl X 6 _a Ln X8 ag 68 68 86 68 Gin X 6 Inl X6 8 InI X 6 Bin X 8 in X 8 6 In I X 6 26 2b 86 26 88 a In L X ae F
3. ARTICLE 5 PROPERTY RIGHT CAB INNOVATION declares to be holding all the rights provided for by the intellectual property code for GENCAB package software and its documentation As this operating right granting generates no property right transfer the customer abstains from any GENCAB software package reproduction whether it is wholly or partly carried out whatever the form assumed excepting the number of copies authorized in Article 2 any GENCAB software package transcription in any other language than that provided for in this Agreement see Appendix any adaptation to use it in other equipment or with other basic software packages de base than those provided for in this Agreement 42 To ensure this property protection the customer undertakes especially to maintain clearly visible any property and copyright specifications that CAB INNOVATION would have affixed on programs supporting material and documentation assume with respect to his staff and any external person any helpful information and prevention step ARTICLE 6 USING SOURCES Any GENCAB software package modification transcription and as a general rule any operation requiring the use of sources and their documentation are exclusively reserved for CAB INNOVATION The customer holds the right to get the information required for the software package interoperability with other softwares he is using under the conditions provided for in the intellectual proper
4. Graph of function f x y z sin x y sin x z 1 x y 7 according to x 0 4 0 5 0 3 0 4 m 0 2 0 3 m 0 1 0 2 0 0 1 0 0 1 0 0 2 0 1 B 0 3 0 2 Graph of function f x y z sin x y sin x z 1 x y 7 according to x and y The same function with the constraint y 2 x 20 3 4 Processing Command Processing of menu Optimisation generates the display of the following dialog box which helps performing the optimizing of function to be processed Processing Searching C Maximum Cell 0414 Iteration Number 00 Other stopping criteria Value reached Processing Duration hour Initialize the treatment again MW Display successive results Display Final population Algorithm og we oe exploration ae Co operation Constraint CCC CCC Criterion Adjustment of origin Adjustment OK Cancel User specifies whether the search regards the minimum or the maximum and defines a number of processing loops as a criterion to stop the search It may also use two other criteria to stop reaching a better result than an a priori defined value outstripping a certain processing duration in hours The box Cell makes it possible to enter the address of the cell of the sheet which includes the result of the function to optimize automatic entering by the use of the mouse The option Initialize the
5. case NO 50 and Nmax 2000 Demonstration Return pa Decision2 xls Decision making under uncertainty choice between projects Resources Profit Staff Cost Decision Annoit Gee s Bar Action 2 Action 3 289 5 124 0 Action 4 475 3 101 0 Action 5 Action 6 Benefit Action7 619 3 134 O Action8 729 6 461 1 Action 9 __694 7 1 0 Aion ia Soo 2 946 S Ss aaa w 1236 Benefit gt __ SS i Criteria T Constraints lt Probability graph Probability graph Average 16 5 Standard deviation 1 80 Average 152 Standard deviation 3 93 0 25 02 nllllus 0 15 UN 0 05 f 5 0 Rod p a ho we a D AY Ko i g F a Probability graph Probability graph Average 24 5 Standard deviation 3 49 Average 9 30 Standard deviation 1 78 K 32 9 of oF ad oF o PO wt OF AG we 12 2 5 Taking into account of the constraints Ey DIDACT 5 Taking into account the constraints Penalty Addition with the function to be minimized of a penalty which increases with the amplitude of the going beyond of the border delimited by the constraints EAC Method used by GENCAB f x y P EACI Interior point Addition with the function to be minimized of a function barrier which increases very quickly when one approaches the border delimited by the constraints _ Example f x y Log dCi The research of the o
6. 1 6 1 8 The square root of the diagonal elements of the variance covariance matrix is the standard deviation of each parameter Confidence intervals can then be calculated by considering the normal laws Similarly the variance of a function eg quantile is expressed as follows F 8 Ve e y r0 Vg 8 with VeA and Velo q2 T i the gradient and transpose of g and J the inverse of the Fisher matrix 06 Eh DIDACT_6b XLS Adjustment of probabilistic models Models of aging Weibull law Bertholon model S phase model Arrhenius model Basquin model COM model AP process HMHPP process GRP process GAPS process Jack model 1 Jack model 2 GEV law GPO law Acceleration models Maintenance models Probability laws of extreme values Return to previous menu 15 3 Application After the entry of a function by the user on the spreadsheet and the definition of the type and range of parameters to optimize the tool allows assess function according to one or two variables curves 2D or 3D Search the optimum These features described below are illustrated by the following example entered in a spreadsheet cell f x y z sin x y sin x z 1 x y 77 with x y z real comprised between 10 and 10 SIN Varl Var2 SIN Varl Var3 1 Varl1424 Var2 2 4 Var3 2 0 5 The expression NAME is obtained if parameters have not been initialized
7. 2 differential evolution f Type 3 mixed Crossbreeding C fone Crossover C Barycentric Selection Sampling of remaining part without replacement Sampling of remaining part with replacement C Deterministic sampling C Lottery wheel i Setting to scale gt gt Truncation f Exponential iw Elitism gt gt Number of individuals p MW Simplex gt gt Mumber of chromosomes For En of iterations Humber of steps After En of iterations Without replacement OK Cancel The user may define the population size and choose among different mutation crossbreeding and selection operators He may also select a setting to scale by choosing between two different techniques Truncation or Exponential an elitism operator by specifying the number of individuals to be maintained for each generation and a link with Simplex algorithm possibly limited to certain loops of calculation in proportion and starting from a certain row If Simplex is selected the user should define a number of chromosomes among the best of the population from which a local optimum will be searched He should also indicate a number of processing steps to be carried out for this research and possibly select the option Without Replacement 30 When such option is requested the chromosome is no longer replaced by the local optimum being found by simplex but its fitness assumes the value of that of the optimum which may increase
8. AN ee 1 Demonstration Return to the menu 39 5 3 Combinatory Problem Eh DIDAC_2c Problem of the sales representative To minimize the distance from the way passing by allthe cities without passing twice to the same city Variable H of ci i Cities Distance Brest Brest Paris Toulouse Nantes BordeauxMarseille Lyon Limoges Strasbourg 123456789 Lyon Brest 12345769 Marseille Paris 1234789 Toulouse Toulouse 134789 Bordeaux Mantes 13789 Limoges Bordeaux 1389 Nantes Marseille 189 Lille Lyon 18 Limoges 2 Strasbourg Lille 5 5 2 3 4 2 3 1 oe ww ae ri on mn Oo The constraint not passing twice to the same city is relieved here by a change of variable Variable position in the list of remaining cities Demonstration Return to the menu 5 4 Linking with SIMCAB Software Such a coupling enables to achieve optimizations from simulation results o Parking strategy Nth free space or first free space after row P f 10 spaces per minute Pg pomere 17757 I nes IPS T MEA A 99H 100 Free space 1 19 Free spaced 496 P E eee Free space 3 N A Free space 4 h A N 5 15 minutes Free spaces ANA Free spaceb ANA P 5b Free space ANA Free spaces ANA space number 46 Free space 4d h A Free space 10 N 4 Time taken to reach the objective 1 36 minutes Mean value 47254 Standard deviation 3 09317466 In this example the two optimal parameters of parking strategy
9. chances to find out new optima on subsequent mutations 9 Simplex with replacement Depending on options selected validation generates the display of different additional dialog boxes 4 2 1 Mutation Three operators of change are proposed to the user e That described on figure 4 3 of the chapter 4 1 1 Type 1 e Differential Evolution Standard 2 e A mixed use of these two operators Type 3 According to the type of operator chosen the following dialog boxes allow to define the mutation probability of each chromosome the decrease in mutation amplitude of a real or integer gene and the mutation probability of a binary gene MUTATION DIFFERENTIAL EVOLUTION Probability of chromosome mutation Probability of chromosome mutation Mutation probability of a gene M Decrease of the amplitude real or integer gene W Decrease of the amplitude real or integer genet Factor of decrease b gt 0 Factor of decrease b gt 0 Number of generations affected T gt 0 Number of generations affected T 0 All T Number of iterations W All iT Number of iterations W Self adapting decrease MW Self adapting decrease Mutation probability of a binary gene 0 3 OK Return bo menu Cancel kK Return bo menu Cancel The mutation amplitude of a real or integer gene can be governed by an adaptive control or the following expression 31 where r is a random number comprised between 0 and 1 and t the number of
10. the processing loop O lt b lt l 0 T 4 2 2 Crossbreeding One of the two crossbreeding operators described in Figure 4 4 Crossover or barycentric may be selected by the user The above described dialog box helps define the crossbreeding probability of each population chromosome with another one randomly chosen in such population CROSSBREEDING EE Crossbreeding probability of a chromosome E OK Return bo menu 4 2 3 Selection In addition to the selection with lottery wheel shown in Figure 4 5 the software proposes three other selection operators Sampling of remaining part without replacement Sampling of remaining part with replacement Deterministic sampling Such operators which cannot be parameterized perform the selection as follows 32 Sampling of remaining part without replacement Assuming a population of n individuals the expected number n of descendants for each individual 1 is computed by the following formula where f designates the adaptation function Each individual 1 is reproduced in new population a number of times equal to the whole part of number n i In order to complete the population and bring it back to its initial size n individuals are successively subject to a random draw by considering the decimal part of number n as probability of success The two other selection operators differ from the previous one only by the processing operated on decimal parts of num
11. treatment again allows not memorizing the best result possibly obtained previously The option Display successive results helps displaying the best result obtained all over the processing The option Display final population allows to display the features of population obtained at end of processing see general presentation of Genetic Algorithms in Chapter 3 1 This population can be changed by the user and serve as an entrance to a new processing by using the button on the sheet The option Adjustment of origin helps finding out the proposed processing algorithm setting configuration when starting up the software 21 This configuration may be totally modified by the user using command Algorithm of menu or partly modified using two 5 position cursors of this dialog box The first one allows working on the algorithm s exploration level and the second one on the operation level multiplication or division by 2 or 4 of size of chromosome population or the number of simplex steps with respect to current state Without using the command Algorithm of the menu a cursor with 8 positions of this same dialog box makes it possible to modify the factor of penalty affecting the results in the event of going beyond of possible constraints The button Adjustment makes it possible to reach directly the command Algorithm without passing by the menu Al over the processing the software specifies in the status bar in screen s lower sect
12. 1 38000104 154191076 591453191 Censorship interval failure in the interval Beginnings 273 2980707 31 24720534 Ends 1273 29807 1 1031 247205 064655334 597621683 634130463 0 00851492 13262496 625996605 717447451 4 96385475 637561694 306759532 33595416 0 16492699 965902911 641716174 The action on the OK button causes the display of a new dialog box in which the user indicates using the mouse the address of data previously entered in a spreadsheet as in this example above 23 If an acceleration law other than the Cox model was selected the address of the reference values of the covariates must also be entered in the dialog box The data will first be converted to the reference conditions by using an acceleration factor The action on the OK button causes the generation of a worksheet as below and then launches the processing E Feuil4 Adjustment Acceleration COX 4 covariates B tal B ta B ta3 B tad Covariates Vibration 6 4037 12954 1272250294 5 cs 056255 8 09959585 2229971029 1180014947 6 380988244 gogga 4753681276 6 410814 6 800 FEES Rel 49055 3 5525465 3 303296976 8 23046645 F 433848614 Covariates Vibration Covariates Vibration qopar F6 r349109E Covariates Vibration RS RS RS RES FA7447451 asssese74s 8 37561694 3 067595325 3359541796 016492293 3 653029114 6 417181738 Covariates Vibration Fr F4 4883854746 537561694 3 06769
13. 5325 3 364641796 0416492894 9669029114 6 417151738 Heeb TEE 8 466450401 8 43 7108243 4526312203 506250161 F 639530835 B32 783442 8 2209 70962 7503414966 414670173 0399022877 3 46698233 5087770655 1510220244 3 6 r P4be2b6o 6 04 r re361 Maximum Likelihood grits 063561054 T 43093769E 2 002956115 B B41051146 9526341657 3 027 791305 3 293193917 3 62456306 6 H0 S3EE 4 20384142 5953270995 5 673995547 T ogtz42157 gegga ALU 4220064097 BOGOF 73534 B05 7606473 5572756975 9249201632 442036467 Bf be249153 4 04 7516453 QUOTE 8 H0 63534 TOGO STF 9046129923 4317092754 1922710562 45520029H 3905735248 1360001044 0646663342 5979216932 LEHS10777 8 341304629 0002914923 0 95 05008 5914531905 7132824959 254968045 Temperature Temp Humidit Voltage Voltage Acceleration Factor 208 1831328 S14 094107 934 2509651 431882244 irz r 730008 ZBO 5921336 1032211538 FeO Besos 111 4595459 3719835248 512748435 TOO 397 F313 Fes We25F 6044575025 2430975099 417 1552967 Acceleration Factor 15 7 33356 1137 615901 1378236464 1671909902 Acceleration So 52546621 TF S8805516 155 9914204 Acceleration Factor Ea 3023197F era 2o80 70 r 23910752 3124720634 Acceleration factor 153 3023197 1273 298071 1r 23410752 101 24 7206 Probability law WEIBULL 3 parameters B ta Sigma Gamma LN Likelihood _ 110766642 hacen Variable 179 279182
14. 6 122 0542817 135 7 7465 197 4168341 TIE 8181324 2630522503 114 4145417 167 318034 25913718 ZERO 8421858 224 1624933 265 SSB 3312 135 95950471 FE 224351 186 750662 276 2845454 O 004 636967 0 0124 F 4311 00004 Oreo 2 0 002430651 0003216441 O 0i4225639 0 010 722581 00028797S 0 013019629 0 004 664 0025075545 O 00362 7612 0 000455334 0005675814 O01 4866 Foi censored Variable Left censored Variable 213 9904292 2463636076 20 29091629 Lenses Aer t fe ganas Variable Enas Variable LH K uncensored 35 4671135 Ati 1 F ti Densit Ffti 0639649513 03622684 ra Or rouge FE 0 328992601 0932605997 0305922065 0 3616604 O37 SF 68688 0610703985 018979986 0 FANS 00389075T 0457153878 0977945972 0569309172 0121604435 0002966034 0 004 x 00401 0004378352 O 00354001F 000203935 g 002820124 0005144531 OOOO ST O 002363296 0002471124 0 00146016 000035 45 0 0044013 O 000445 735 00032 31F 13 0 007315 106 Lnff ti 5 9205296 5 36010 745 Orage P6436237 613561057 5 604 426 5 2647 4334 B 51949355 6 045554 36 B 00308227 234r 2917 93230296 5 42686534 ALLIE TE rot 30 B 25798225 LN K right censored 2 97252589 Ati 1 Ffti 0 095405926 0 514797147 Ln Rti 2 30854355 0663902344 LH E left censored 11 384628 0698651627 0 49636140 0969170341 0101348373 000263959 0030829604 2 28419146 5 6115697 47927971 LH K
15. 9 2 0 07 0 08 m 0 06 0 07 Na ay 1 0 05 0 06 le Ih ull m 0 04 0 05 il x i 0 0 03 0 04 Constraint x gt 0 3 x y Pi ti ion Hoar S038 OA Function 0 09721014 as 0 0 02 0 03 m 0 01 0 02 1 53645355_ gt m0 0 01 y L1 53645357 LY Demonstration Return to the menu 2 3 Simplex and Genetic Algorithms Eh DIDACT_3 Simplex and Genetic Algorithms The Simplex local research and Genetic Algorith MS total research are complementary methods which can be coupled to accelerate convergence Simplex carried out starting from the best solutions found hy the A G They do not require any knowledge on the functions to be treated except their result for each configuration of the variables The optimality of the solutions obtained cannot be guaranteed Pragmatic approach improvement of a random or imposed initial solution Simplex Genetic algorithms Return to the menu Ej DIDAC_3b Linear si mplex algorithm of Nelder Mead Simplexe Whole of N 1 different solutions N number of variables and B barycentre of the simplex X Y fitness Expension Reflexion or Regeneration tightened simplex Iterative research of the local optimum Demonstration Return EW DIDAC 3c Genetic algorithms Chromosome population Chromosomes Parameter Permanent size LT configuration Parameters Parameter values Lig g z 5 gt e e Progres
16. Cab Innovation 3 rue de la Coquille 31500 Toulouse Tel 33 0 5 61 54 68 08 Fax 33 0 5 61 54 33 32 Mail Contact cabinnovation com Web www cabinnovation com GENCAB version 13 using Microsoft EXCEL il l i i Hat si LA Optimizing With Genetic Algorithms amp Simplex User s Manual FOREWORD The software GENCAB BASIC version 4 includes some of the GENCAB version 13 features It is not the subject of a specific user manual The copyright law and international conventions protect the GENCAB software and its User s Manual Their reproduction or distribution either wholly or partly through any means whatsoever is strictly prohibited Any person who does not comply with such provisions is committing an offence of forgery and is liable to prosecution and can be sentenced under the provisions prescribed by the law The Programming Protection Agency A P P references GENCAB at the I D D N Inter Deposit Digital Number index with the following reference IDDN FR 001 070019 00 R P 2000 000 20600 CONTENTS 1 GENCAB Software 1 1 General Presentation 1 2 Installing GENCAB on hard disk 1 3 Starting GENCAB 2 Teachware 2 1 Principle of optimization 2 2 Types of problems and methods of resolution 2 3 Simplex and Genetic Algorithms 2 4 Coupling with method of evaluation or simulation 2 5 Taking into account of the constraints 2 6 Adjustment of probabilistic models 3 Application 3 1 Parameters initia
17. Nth free parking lot and row P from which the first free parking lot will be systematically taken are being searched by GENCAB by minimizing the average of times taken to reach the objective assessed by SIMCAB 40 5 5 Linking with SUPERCAB Software GENCAB may be linked with other Excel operating softwares especially with the RAMS Reliability Availability Maintenability and Safety SUPERCAB software also issued by CAB INNOVATION Linking with this software may thereby be used for optimizing system architecture aa Exemple_9 XLS Optimization of an architecture reception station of satellites Jperational Lost fhour av ilabilit Euros Rae R Mos Le cl Markovian fle ae 15104 26 1000 30206 Treatments 1 au iE 500 SUPERCAB tool Configuration of 24 real or integers parameters in blue Availability gt Objective 0 99 Demonstration Return to the menu 4 OPERATING LICENCE AGREEMENT OF GENCAB SOFTWARE PACKAGE ARTICLE 1 SUBJECT The purpose of this Agreement is to define the conditions in which the CAB INNOVATION Company grants the customer with a non transferable non exclusive and personal right to use the software package referred to as GENCAB and whose features are specified in user s manual ARTICLE 2 SCOPE OF THE OPERATING RIGHT The customer may use the software package on one single computer and on a second one provided that the second computer does not operat
18. arent nonconformity with respect to the order The customer is liable for any loss or any damage caused to supplies as from the delivery ARTICLE 4 TESTING AND GUARANTEE Guarantee is effective as from the mail delivery date set forth in Article 3 and has a three month validity During the guarantee validity if the customer experiences a software package operation trouble he should inform CAB INNOVATION about it so as to receive any helpful explanations with the purpose of remedying such trouble If the trouble is continuing the customer will return the C D ROM to CAB INNOVATION at CAB INNOVATION s Head Office at his own expense and with registered mail with acknowledgement of receipt by specifying exactly the troubles encountered Within the three months of reception of consignment set forth in preceding paragraph CAB INNOVATION will deliver at its Own expense a new product version to the customer This new version will be benefiting of the same guarantee as benefited the first version The customer looses the benefit of the guarantee if he does not comply with the instructions manual recommendations if he performs modifications of configuration set forth in Article 2 above without obtaining a prior written consent from CAB INNOVATION or if he performs modifications additions corrections etc on software package even with the support from a specialized service company without obtaining a prior written consent from CAB INNOVATION
19. ariates DATA reference cell ranges Name loptional Uncensored B 5 B42 Bts Right censoring B23 64 7s Left censoring tB 27 464 5 Interval event during the censorship Beginning censorship B 33 4B s End censorship B 37 64 Si B Variables Uncensored 179 2791626 132 0542617 139 77468 197 4168641 1166151354 263 0522503 1144149417 167 318034 259 6113718 260 8421658 224 1624933 265 5863312 139 995047 1 56 12214851 186 750662 276 8048494 Data Vibration 6 40371295 1 37225828 5 33805629 8 09989555 2 280987103 1 18001895 6 38098824 5 60553312 4 75381278 574310232 6 80047632 821779903 9 8826465 9 30389698 8 33096545 7 933804861 Temperature 5 22567292 8 9684504 8 43710525 4 5263122 5 06350116 7 63933023 9 31278344 8 22097096 7 55341497 414670173 0 39902288 3 45599234 5 08777068 1 51022024 3 87746267 6 04787236 063561055 4309377 200298611 5 57675668 664105115 624920163 952733156 7 44203647 30277913 3 76224915 929319392 404751645 3 62456306 0 53033128 6 41068366 6 41086383 2 5364142 7 50601538 6 953271 9 04612992 6 6 099555 4 31709275 64242158 1 92271056 29644941 455208294 7 11551121 3 90573525 Right censored 1197 615901 5 68790855 1 90940971 8 22257495 0941141354 1671 909902 1 11544159 0 66606671 662016793 0 65515268 Left censored 213 9904292 29 63636076 26 29091689 385433877 6734911 0 95703071
20. ation number And parameters S SO PI P2 and a are defined by the following dialog box SETTING TO EXPONENTIAL SCALE 4 2 5 Taking into account of the constraints The taking into account of the constraints is carried out by the addition of a term of penalty to the result of the function to optimize This one with the following form in which fp can be adjusted by the user Tp fp dci with dci Max 0 B A if A gt B B A 1f A B or A INT A if A Integer TAKING INTO ACCOUNT OF THE CONSTRAINTS Ei ES 35 This adjustment is in particular necessary in the case of constraints of the equality type or Integer value not to block the algorithm in its research by a too strong penalty to increase the penalty gradually 4 2 6 Optimization starting from results of simulation The following dialog box makes it possible to the user to activate the optimized strategy of coupling between optimization and Monte Carlo simulation described in paragraph 4 1 4 and to define the minimum number No of simulations carried out for the coarse evaluation as well as maximum number N necessary to the necessary precision OPTIMIZATION FROM RESULTS OF SIMULATION EE MW Optimized coupling Max number of simulations by evaluation Min number of simulations by evaluation Evolution Factor of the number of simulations O Max lt 1 Fast 1 linear gt 1 slow OK Return to menu According to the entered value of a coeffi
21. bers nj Sampling of remaining part with replacement To complete the population decimal parts of numbers n are used to form a lottery wheel Deterministic sampling Decimal parts of n are arranged in decreasing order and chromosomes corresponding to first elements of list complete population The method of selection with lottery wheel offers a great variance and often conducts to results far from those expected especially disappearance of best elements But no one could really demonstrate to date the superiority of one of the other selection methods being proposed 4 2 4 Setting to Scale Two different techniques of setting to scale are offered to user Setting to scale by truncation in sigma The preliminary transformation of fitness of each chromosome is performed as follows f f f co 33 with f the average of fitness for all chromosomes and o the typical deviation Transformation may be represented as follows if o gt PA Fitness tightening in relative value if o Ly Unchanged if o lt Va Fitness deviation in relative value f fitness cancelled for the weakest ones User using dialog box below defines scale factor c SETTING TO SCALE BY TRUNCATION IN SIGMA ix Setting to exponential scale Preliminary fitness transformation of each chromosome is carried out as follows End Beginning f 34 where k is the current generation N the number of generations being wished iter
22. censorship interval 0 94536977 ti 1 F ti O S36366968 R t 1 F tj OF S246531 F tjj F ti 0470614016 0823120437 LnfF tj F ti 0 537 02 0194665275 Processing can be restarted by the user as many times as necessary The latter can also change the minimum and maximum limits proposed by the tool for each parameter At the end of processing a dialog box proposes to estimate confidence intervals on the parameters or quantile values by inverting the Fischer matrix It also proposes to show the results in the form of various graphs distribution function and Kaplan Meier curve quantile quantile diagram Weibull paper etc 24 4 Algorithms 3 1 General Presentation 4 1 1 Genetic Algorithms Developed by John Holland et al at the University of Michigan genetic algorithms are optimizing algorithms based on natural selection and genetics mechanisms The first of such mechanisms deals with principles of survival of best adapted species based on Darwin postulate The second one relies on diversity of individuals in a population of a same species that evolves over the time by crossbreeds and mutations The analogy between biology and genetic algorithms is shown in Figure 4 1 Genetic algorithms Chromosomes Parameter gt configuration Genes Parameters Allele Parameter values gt lt Y 9 23 5 1 0 0 8 Figure 4 1 Analogy between bio
23. cient K this required precision can be fixed or progress during the treatment according to the following formula parallel to the progressive improvement of the population of solutions 1000 900 800 700 600 500 400 300 200 100 k 0 k 0 5 ke k 2 N MIN Nmin INT Nmax Nmin N of iteration Number of iterations k Nmax 36 4 3 Initial Population Command Initial Population of menu Optimisation generates the display of a dialog box which helps define the initial population randomly drawn by default Initial population f Eg Population size so Creating a data acquisition sheet C Considering population entry on sheet supplement randomly drawn f Random population generation C Displaying initial population f Assessing initial population Cell ati MW Maintain only the best individual at each new processing OK Cancel This box allows to define population size generate a chromosome data acquisition sheet to be considered in initial population consider obviously such chromosomes in initial population generate randomly initial population display initial population assess such population according to the result of the cell of the sheet whose address is in the box Cell An option allows maintaining only the best individual on each new processing and generating randomly the remainder of population If such op
24. dialog box then displays the characteristics of the parameter following in the list if they were beforehand defined or preserves those of the precedent in order to facilitate the initialisation 17 of parameters having the same characteristics A parameter can be also selected directly in the list by using the scroll box On completion of this initialization phase the names of parameters Va_1 Va_2 Va_n and their possible equivalence are automatically defined in spreadsheet and their value is drawn randomly in the corresponding range Names of limits max_vari and min_vari are also defined in sheet 3 2 Entering the constraints Command Constraints of menu Optimisation allows to display the following dialog box used to enter constraints between parameters or cells of the sheet CONSTRAINTS The constraints considered are of type A gt B A B A lt B or A Integer in which A and B are cells references or combinations of parameters Three scrolling menus facilitate the definition of the constraints The name of parameters beforehand defined in the worksheet can be immediately entered and in position REF simple a clic of the mouse allows to enter the reference of the selected cell Button oe and make it possible to record the constraint in progress or to delete a beforehand definite constraint selected in the corresponding list Delete 18 3 3 Assessment Command Assessment of menu Optimisatio
25. e at the same time as the first one The customer can only have one software package copy maintained in a safe place as a backup copy If this license is regarding a performance on site the customer may install the package software on a server while scrupulously complying with purchase conditions stated on specific conditions especially defining the maximum number of users authorized to use the software package from their terminal and the maximum number of users authorized to use it simultaneously The customer is therefore authorized to perform a number of software package documentation copies equal to the maximum number of users allowed to use it CAB INNOVATION will be in a position to perform inspections either itself or through a specialized entity purposefully authorized by CAB INNOVATION at customer premises to verify if customer has met its requirements number of software package copies used location of such copies etc Parties will agree as regards the practical modalities of performance of such inspections so as to disturb minimally customer s activity ARTICLE 3 DELIVERY INSTALLATION AND RECEPTION The software package and attached supplies will be delivered to the customer on mail reception date The customer installs at its own costs the software package using relevant manual delivered by CAB INNOVATION The customer performs the inventory and shall inform CAB INNOVATION within three working days of the delivery of any app
26. e treated by various methods amp tools Data input Evaluation of the system performanc Evaluation of the system Performance calculation or simulation amp Data of cost Cost of the services E i Parameters Criteria amp constraints a OPTIMIZATION r ja D aL Cote 5 3 00 pi poe atte pilin The evaluation duration leads the treatment duration in particular in the case of Monte Carlo simulation Simulation Return to the menu ai Exemple_9 XLS mB Optimization of an architecture reception station of satellites Operational Lost availability Euros Pa SU 1 2 al ide fl Markovian sive 1 2 EE Seer 11 2 i Treatments er Passive 141 3 des ser P eea SUPERCAB tool ae biel Pas f Pepe 3S Configuration of 24 real or integers parameters in blue ma pea ER ae ee Availability gt Objective 099 e Demonstration Return to the menu 11 Eh DIDAC 4b Coupling with the Monte Carlo simulation Coupling very penalizing T treatment nb evaluations x nb simulations x T simulation Original technique pre evaluation of each candidate and possible continuation of this one according to its rest Population of chromosomes Optimization GENCAB Differential Evaluation evolution pm mm in No then N simulations according to result Simulation No N Nmax SIMCAB aa Sa Reduction of the computing times in a ratio approximately 30
27. fines the function to be optimized on a spreadsheet folio from different parameters The function may be directly entered in spreadsheet cells may use macro functions or be implemented using a link between sheet and existing softwares Constraints between parameters or cells of the sheet can be also defined Then the software automatically searches the optimal parameter configuration which maximizes or minimizes the function result this result being likely to be located in any sheet cell GENCAB requires no especial knowledge in mathematics and may be used in any engineering field It 1s delivered in a setting configuration of its algorithms which enables to efficiently process highly different functions However the user may modify at his discretion the different setting parameters to consider more efficiently specificities of functions to be processed The understanding of algorithms being used is therefore required and such algorithms are described in Chapter 3 GENCAB allows to adjust probabilistic models by using maximum likelihood method using uncensored or censored data right left or interval It considers acceleration factors Arrhenius Basquin Cox etc to process heterogeneous data from different environments and conditions of use 1 2 Installing GENCAB on Hard Disk Please follow instructions shown in manual 1 3 Starting GENCAB In EXCEL open GENCAB XLA file Software s functionalities are then accessible using
28. g material CD ROM even free of charge available to a person not expressly set forth in second paragraph of Article 2 ARTICLE 12 ADDITIONAL SERVICES Any additional services will be subject to an amendment of these provisions possibly through an exchange of letters so as to specify the contents modalities of achievement and the price ARTICLE 13 CORRECTIVE AND PREVENTIVE MAINTENANCE 43 The corrective and preventive maintenance may be subject upon customer s request to a separate Agreement attached to these provisions ARTICLE 14 ENTIRETY OF THE AGREEMENT The user s manual defining the GENCAB software package features is appended to these provisions The provisions of this Agreement and his Appendix express the entirety of the Agreement entered into between the parties They are prevailing among any proposition exchange of letters preceding its signing up together with any other provision stated in documents exchanged between the parties and relating to the Agreement s subject matter If any whatsoever clause of this Agreement is null and void with respect to a rule of Law or a Law in force it will considered as not being written though not involving the Agreement s nullity ARTICLE 15 ADVERTISING CAB INNOVATION could mention the customer in its business references as a GENCAB software package user ARTICLE 16 CONFIDENTIALITY Each party undertakes not to disclose any kind of documents or information about the other pa
29. ion the number of processing loop in progress the duration of a loop the number of function assessments performed during each loop and the duration of an assessment higher than second As the optimum is not necessarily reached at end of processing the user may repeat the latter while maintaining the best result obtained so far 1 2 The maximum of function f x y z sin x y sin x z 1 x y z assumed as an example is thereby obtained following a few processing loops Varl 0 920822364 Var2 0 46041 1148 Var3 0 460411163 Result 0 453288276 Remark The stochastically optimizing methods such Genetic Algorithms allow searching the global optimum of a function without guaranty to find it 3 5 Adjustment of probabilistic models The Adjustment command of the optimization menu involves the display of the next dialog box that lets you adjust probabilistic models by using maximum likelihood method The action on the button direct access to the relevant pages of the tutorial 22 ADJUSTMENT OF PROBABILITY LAWS DISCRETE LIFETIME A parameters EIBULL 3 parameters COX 4 covariates ACCELERATION LEFT CENSORED BY INTERVAL Using scrolling menus the user chooses a probability distribution associated with a possible acceleration law It also indicates whether the data are censored ADJUSTMENT OF PROBABILITY LAWS Lov WETBULL 3 parameters ACCELERATION COM 4 cov
30. lizing 3 2 Entering the constraints 3 3 Assessment 3 4 Processing 3 5 Adjustment of probabilistic models 4 Algorithms 4 1 General Presentation 4 1 1 Genetic Algorithms 4 1 2 Differential Evolution 4 1 3 Nonlinear Simplex 4 1 4 Coupling between optimization and Monte Carlo simulation 4 2 Algorithms Selection and Setting 4 2 1 Mutation 4 2 2 Crossbreeding 4 2 3 Selection 4 2 4 Setting to Scale 4 2 5 Taking into account of the constraints 4 2 6 Optimization starting from results of simulation 4 3 Initial Population 5 Examples of Applications 5 1 Mathematical Functions 5 2 Polynomial Adjustment 5 3 Combinatory Problem 4 4 Linking with SIMCAB Software 5 5 Linking with SUPERCAB Software OPERATING LICENCE AGREEMENT 1 GENCAB Software 1 1 General Presentation GENCAB is a generic optimizing software implementing developments which are among the latest in operational research and artificial intelligence Based on a hybrid optimizing method with Genetic Algorithms and non linear Simplex it enables to optimize real integer or binary parameters of any function with possible constraints without stopping at the first local optimum found Its general principle is described in diagram below Set of parameters GENCAB binary integer real Function defined by user on a spreadsheet folio Genetic algorithms Differential Evolution amp Simplex Selections and settings Assessment result The user de
31. logy and genetic algorithms Each parameter configuration corresponds to a chromosome whose genes are parameters of different types binary integer real Such chromosomes are affected within a population mutation crossbreeding and selection operations considering respective performance of each single one Figure 4 2 Chromosome population Permanent size CI ion c Col Crossbreeding J Selection Figure 4 2 Basic principle of genetic algorithms 29 For every generation a new identical size population is created consisting partly of best elements of previous generation and new elements generated by mutation or crossbreeding Such operations are conducted in accordance with two objectives reaching local optima and exploring variable space to search all optima in order in this way to find out the global optimum Mutation consists in introducing a noise in the gene value of a chromosome 1 e a random deviation around such value In this respect mutation is an exploration operation of the searching space Figure 4 3 shows an example of mutation to be applied to different types of parameters Disturbance introduced in the parameter value eure 1101101101 gt 1101001101 Integer and real x Xk X X X Xin X Amplitude Or X X Xnax X Amplitude a ne Xmin Xk Xmax Ra
32. menu Optimisation spreadsheet functionalities remaining always available 41 E i A fa EA a Accueil Insertion Mise en page Formules Donn es Revision Affichage Optimisation E Help Teachware Parameters E Assessment cla Adjustment ir Other menus a Constraints gi Initial Population cs Processing es Algorithm Option General Optimisation Supplement Statistics F k Tx Banner on Excel versions after 2007 E GENCAB V 11 Classeur JE Fichier Edition Affichage Insertion Format Outils Donn es Fen tre Optimisation S SO 47 Ad Er cf ER CESE Help Teachware Other menus fe PB D E parameters A r Constraints Assessment Algorithm Option Initial Population Adjustenent Processing Menu on Excel versions prior to 2007 A help and a teachware are proposed in the menu 2 Teachware The teachware presents optimization by means of various boards and many demonstrations 2 1 Principle of optimization DIDACT_1 Principle of optimization Seek of an extremum maximum or minimum of a function criterion whose variables can be submited to constraints Required optimum Total maximum f x y A Local maximum Field prohibited by x y EC the constraint There is no method allowing to find a total extremum whatever the type of function Example Return to the menu Eh DIDAC_1b Agricultural plantations Criteri
33. n initiates the display of the following dialog box helping assess the function typed on spreadsheet folio for a given configuration of parameters or draw variation graphs according to one or two parameters ASSESSMENT Cell far fl far fl Parameter nn a Type Real Min Max 10 Value Abscissal 20 30 Graph Abscissa 1 Nb values Min Max Wo Abscissa 2 Mb values Minv Max Continue Cancel The box Cell allows to enter the address of the cell of the sheet which includes the result of the function to evaluate automatic entering by the use of the mouse Any parameter can be selected in the same way as in the dialog box Type of parameter so as to give it an especial value comprised between its limits This value will be immediately considered in spreadsheet folio following validation Options Abscissa 1 and Abscissa 2 allow opting for one or two parameters to be considered as variables in a graph with two or three dimensions that will be automatically generated by the software following validation The user may then define a number of values equidistant from the selected parameter 11 by default located in a subassembly of the variation range entire range by default to be subject to an assessment The function being previously taken as an example thereby reaches the graphs thereafter at one dimension according to x or two dimensions according to x and y 19 Var1
34. ndom amplitude decreasing over the time Figure 4 3 Example of mutation In this example mutation of a chromosome randomly drawn in population is carried out through modification of one of its randomly selected genes Such gene simply changes state if binary or performs a decreasing amplitude leap over the time if real or integer so as to progressively limit the exploration as research goes on Crossbreeding is performed by pairing two population chromosomes which exchange information each other to give birth to two descendants Just as for mutation crossbreeding is an exploration operation of the research space of which two examples are given in Figure 4 4 Exchanging information between chromosomes 000111011000111 01001101100011 Crossover a gt 010011010010101 0001 11010010101 9 oda EE deaf Barycentric x 0X1 1 0 x2 de LT del l 0 lt a lt l X QAX2 1 0 X1 Figure 4 4 Examples of crossbreeding 26 In these examples crossbreeding of two parent chromosomes randomly drawn in population is carried out either by gene exchange crossover each gene being reproduced in either descendants or by averaging values integer or real of parent genes barycentric Selection is a process whereby each chromosome 1s duplicated a number of times in the new population according to value or fitness of function to be optimized also called adaptation function Chromosomes the adaptation function value
35. of which is high have a strong probability to contribute to the next generation by creating one or more descendants identical to them Such operator an example of which is proposed in Figure 4 5 is of course an artificial version of the biological selection In the nature adapting a species is determined by its ability to survive to predators diseases and obstacles to get over to reach adulthood and reproduction period whereas in our artificial environment the function to be optimized is the final arbitrator of life or death of any chromosome In this respect selection operation is a development operation of research space Duplicating best adapted chromosomes Example Chromosomest 1 2 3 4 5 6 7 8 9 10 Population Fitness fi 10 98 1 30 0 82 0 50 0 65 1 06 0 13 0 65 0 04 0 10 Pi 10 16 0 21 0 13 0 08 0 10 0 17 0 02 0 10 0 01 0 02 n f Draw by D f Lottery wheel i a Rag Population a 2 2 2 2 d 6 6 Figure 4 5 Example of selection In this example selection probability pi of each chromosome computed from the relative weight of the result of its assessment corresponds to a lottery wheel section whereby N draws are carried out to obtain the new population N being the constant population size In addition to the specified examples mutation crossbreeding and selection operations may be performed in different ways proving to be more or less efficient depending on problems to be dealt with Moreove
36. on to maximize the income profits costs Profits G Gx X Gy Gz Z Sweet com Costs X Manure Ce Cex X Cey Cez Z Insecticides Ci Cix X Ciy Ciz Z Constraints Surface S X 7 lt 100 ha Watering A Ax X Ay Az Z lt 1000 m Profit cost and volume of water per hectare Se x p Bas Eaux Income 911 07 Z 2251 Jha So Surface 100 D Sunflower Watering Demonstration Return to the menu 2 2 Types of problems and methods of resolution Sh DIDACT 2 PEK Types of problems and methods of resolution EXAMPLES Types Linear the criterion and the constraints are linear functions Dimensioning Linear in integer some of the variables have discrete values Sales representative Nonlinear general case Mathematical function Stochastic the criterion and the constraints depend on random variables Stock of replacement Methods Polynomial Algorithms Dynamic Programming resolution using a formula of recurrence Stochastic Methods Linear and nonlinear Programming gradient simplex Arborescent Methods branch and bound Heuristic and metaheuristic genetic algorithms simulated annealing tabout colonies of ants The methods best adapted to the resolution of the problems depend on their type Return to the menu Eh DIDAC_2d Mathematical function m0 09 0 1 Function MAX 0 02 sinx x siny 100 x2 x y AN 12 0 080 0
37. pon that the total amount of compensation to be paid by CAB INNOVATION all cases taken together could not in any way exceed the initial royalty price reduced by 25 per period of twelve months elapsed as from the mailing delivery date ARTICLE 8 DURATION This Agreement is entered into for an undetermined period of time as of the date set forth in Article 3 ARTICLE 9 TERMINATION Each party may terminate this Agreement by registered mail with acknowledgement of receipt forwarded to the other party for any breach by such party of its obligations despite a notice remaining unresponsive for 15 days and this occurring with no prejudice to damages it could claim and provided that the last paragraph of Article 7 above be enforced At end of this Agreement or in case of termination for whatsoever reason the customer will have to stop using GENCAB software package pay all sums remaining due on date of termination and return all elements composing the software package computer programs documentation etc without maintaining any copy of it ARTICLE 10 ROYALTY As a payment for the operating right concession the customer pays CAB INNOVATION an initial royalty the amount of which is determined in specific conditions ARTICLE 11 PROHIBITED TRANFER The customer refrains from transferring the software package operating right granted personally to him by these provisions The customer also abstains from making documentation and supportin
38. ptimum remains inside the whole of the realizable solutions It is sometimes interesting to facilitate research to relieve temporarily certain constraints or to decrease the penalty FM Return to the menu 2 6 Adjustment of probabilistic models Eh DIDACT_6 XLS Adjustment of probabilistic models search parameters of a probability law in order to match the best experimental data Maximum likelihood method Parameters 0 giving the maximum probability density for all experimental data Maximizing the product Max I1 f ti 8 If the data are many it s better to maximize the sum of logarithms of probability densities to avoid numerical problems values surrounding zero Data is censored if itis not the result of observation of the entire phenomenon considered The latter can be accelerated by various factors environmental usage etc specific to each data Censored data Acceleration Demonstration Examples Return to the menu 13 Eh DIDACT_6c XLS Censored data The observation does not cover the entire phenomenon considered Likelihood Uncensored data II f ti 0 Right censoring TIn 1 F tj 6 Left censoring IL 1 F tk 6 Interval Censoring TI F tm 6 F tl 6 ff Density of probability Fil Distribution funchon Return to previous menu Eh DIDACT 6d XLS Acceleration Acceleration factors AF Assumption Stress changes only the scale of the reliability curve
39. r the optimum research may be improved by linking with such basic operations more classical techniques of setting to scale elitism or optimizing method of climber Setting to scale is transformation acting on the adaptation function value whose purpose is creating a zoom effect on results as research goes on At first steps of research deviations between fitness are wished to be reduced so as to prevent good chromosomes from becoming too predominating Then deviations are amplified to accelerate convergence Elitism consists in preserving for each generation a number of best population chromosomes which might disappear due to mutation crossbreeding or selection operations A climber method such as non linear simplex may be related with the genetic algorithm to form together a hybrid method with a best ability to develop research of local optima 21 4 1 2 Differential Evolution Proposed in 1995 per K Price and R Storn the Differential Evolution consists in generating a new chromosome by adding to genes of a member of the population the difference between genes of two other chromosomes Similar to the mutation and the crossbreeding of the Genetic Algorithms this operator explores the space of the solutions by simultaneously modifying the totality of genes of each chromosome It requires a permanent diversity of each gene in the population to avoid a premature convergence Also a hybrid use associating Genetic Algorithms Differen
40. rty that it would have been informed of on the Agreement s performance and undertakes to have such obligation fulfilled by the persons it is liable for ARTICLE 17 AGREEMENT S LANGUAGE This Agreement is entered into and drawn up in the French language In the event where it is translated into one or more foreign languages only the French text will be deemed authentic in case of any dispute between the parties ARTICLE 18 APPLICABLE LAW DISPUTES The French Law governs this Agreement In the event of any disagreement over the interpretation and performance of any whatsoever provision of this Agreement and if parties fail to reach an agreement under an arbitration procedure only Toulouse s Courts will be competent to settle the dispute despite the plurality of defendants or the appeal for guarantee 44
41. ry evaluation limited to No simulations Ni Nj M m o G0 M mjo oo M current optimum The guiding principle of this technique consists in giving to each solution the same probability of inappropriate rejection which results in a condition between respective values Nj and N of the number of simulations realized to evaluate two candidates I and J This condition results directly from the application of the central limit theorem In order to significantly decrease the total duration of the treatments from 1 to 30 according to the problems to be solved and the adjustment of the algorithms the user can thus activate this strategy by defining the No number of simulations carried out for the coarse evaluation as well as number N necessary to the necessary precision He can also make grow the precision requested during the treatment parallel to the progressive improvement of the population of solutions Note Contrary to the ordinary coupling between simulation and optimization optimization should not relate to results of simulation in the form of a combination between average value and or standard deviation when this technique of improvement of the coupling is activated 29 4 2 Algorithms Selection and Setting Command Algorithm of menu Optimisation generates the display of following dialog box which helps set the optimizing parameters ALGORITHM Population size Mutation Type 1 gene by gene Type
42. sive improvement of a population of solutions chromosomes by analogy with the alive world Examples of operators of Mutation Crossover Selection Eh DIDAC_3d Algorithm Genetics Operators of mutation Disturbance introduced in the parameter value Binary 1101101101 1101001101 Integer and real x E Ja LT Xa Xu X Xan Amplitude or X X X X Amplitude Re Xmin Xk Xmax Random amplitude decreasing over the time The differential evolution is a mutation which simultaneously exploits the totality of genes of the chromosome It consists in adding with genes of a chromosome the difference between genes of two other chromosomes taken randomly Return Eh DIDAC_ 3e Algorithm Genetics Operators of crossing Exchanging information between chromosomes Crossover 010011010010101 000111010010101 da dall Barycentric x 0x1H 1 0 x3 dei CREER 0 lt a lt 1 X 2 OX 1 1 xy 000111011000111 01001101100011 Return El DIDAC_3f Algorithm Genetics Operator of selection Duplicating best adapted chromosomes Example Chromosomes 1 2 3 4 5 6 7 8 9 Population Fitness fi 0 98 1 30 0 82 0 50 0 65 1 06 0 13 0 65 0 04 0 10 Pi 0 16 0 21 0 13 0 08 0 10 0 17 0 02 0 10 0 01 0 02 Draw by Lottery wheel paonon onomu 10 2 4 Coupling with method of evaluation or simulation Coupling with method of evaluation or simulation The function of evaluation can b
43. tial Evolution and nonlinear Simplex is particularly robust to solve various problems 4 1 3 Nonlinear simplex The local method of the nonlinear simplex illustrated below can be associated the genetic algorithms and the differential evolution to constitute together a hybrid method having a better capacity of exploitation research of the local optima Fitness Cont action AE EZ SZ Expension NS Reflexion X Simplex of n 1 points in R 28 4 1 4 Coupling between optimization and Monte Carlo simulation The function to be optimized cannot be always expressed in an analytical way and its evaluation can result from a Monte Carlo simulation see an example of coupling with the simulation software SIMCAB in chapter 4 4 However the coupling between optimization and stochastic simulation which consists in search of an optimal configuration of parameters starting from the results of a function of evaluation treated by Monte Carlo simulation is very penalizing in term of duration of treatment At first approximation the number of simulations to be realized is equal to the number of evaluations necessary to optimization multiplied by number N of simulations required by the required precision This 1s why GENCAB implements an original strategy consisting in varying during the treatment the number of simulations N of each evaluation by exploiting the average and the variance of the results obtained starting from a prelimina
44. tion is not selected population obtained at end of previous processing is entirely preserved as new initial population 37 5 Examples of Applications Examples shown here are provided for demonstration in online help 5 1 Mathematical Functions bp A YY Le SPRAY ANS PLAN TTN x 1140 160 E 120 140 E 100 120 E 80 100 cu g QE E 0 20 DANNA f x y 200 x y with x y real comprised between 10 and 10 This convex function may be optimized only by simplex iteration number 1 population size 1 f x y Integer Part of 10 24 x y 25 with x y real comprised between 10 and 10 This function shows only stages making simplex inoperative 38 0 09 0 1 0 08 0 09 0 0 07 0 08 0 06 0 07 m 0 05 0 06 MK Wh th HL ance M M i Hi 1 0 02 0 03 aa E 0 0 01 S x y Maximum 0 02 sin x sin y 1 00 x ty r 2 with x y real comprised between 10 and 10 This function shows multiple local optima and its optimizing is made especially efficient by linking Genetic Algoritmes and Simplex 5 2 Polynomial Adjustment ai Exemple_4 xls Method of least squares Adjustment of a function to a polynomial Pix va vb x ve x 2 vd x7 Error 0 9162 12 2166 10 5476 20 5693 5 7 00h 25 0093 1 0167 26 6646 p979 25 6055 heae5 ec 3334 Cite 175288 02203 11 5476 12 5070 4 0001 aadi z aoa S a wN Mm
45. ty code In each case an amendment of these provisions will set out the price time limits and general terms of performance thereof ARTICLE 7 LIABILITY The customer is liable for choosing GENCAB software package its adequacy with his requirements precautions to be assumed and back up files to be made for his operation his staff qualification as he received from CAB INNOVATION recommendations and information required upon its operating conditions and limits of its performances set forth in user s manual the use made for results he obtains CAB INNOVATION is liable for the software package conformity with his documentation The customer shall prove any possible non conformity CAB INNOVATION does not assume any whatsoever guarantee whether explicit or implicit relating to the software package manuals attached documentation or any supporting item or material provided and especially any guarantee for marketing of any products relating to software package or for using software package for a determined use any guarantee for absence of forgery etc Under no circumstances CAB INNOVATION could be held responsible for any whatsoever damage especially loss in performance data loss or any other financial loss resulting from the use or impossibility to use the GENCAB software package even if CAB INNOVATION was told about the possibility of such damage In the event where CAB INNOVATION liability is retained it is expressly agreed u
Download Pdf Manuals
Related Search