User Manual
Contents
1. Constraints Simulation Write Back In Sage adenieeversion or at least bwo A objectives in drege eset ger zi Dr Please enter the range or single cell where objective Functions are stored Objectives must occupy continuous press the Update button and select the type of the objective orange of cells Type in the address of the range e g 41 05 and press the update A 3 button to populate the grid containing IBL Be poate ae Objectives Range e g Al or CAFS Update parameters of objectives Each objective iz described by address of an Excel cell the function that iz applied to tt and its name Objective ini razi function can be either ammmineor Maximize Hint To set the value of 4 whole column click tts heading with right mouse button and choose or type in the desired value Cancel Figure 20 Defining objective functions 8 2 3 Defining the Constraints Constraints are used when it is wanted to penalise certain variables for going out of the bounds For instance in a multiple objective problem if one of the objectives is the cost of a solution and the budget is only 2M then solutions outside of this are useless and should be discouraged Constraints in SolveXL are handled by Excel It is users responsibility to write the formulas To enable use of constraints tick the corresponding checkbox and enter address of an Excel cell which contains penalty cost SO or infeasibility MO of given solution see Figu2. Figure 15 Choosing crossover type and its parameters 8 1 4 Selector Type In the genetic algorithm solutions must be selected for progression into the next generation or for input to the crossover and mutation procedures The method by which the algorithm selects solutions for this purpose then is highly important for the correct operation of the algorithm The type of selector used depends on the problem type There are currently three single objective selection operators Roulette Roulette by Rank and Tournament and one multiple objective operator Crowded Tournament depicted in Figure 16 supported by SolveXL Roulette Each individual is assigned a probability of selection or section of a roulette wheel according to the ratio of its fitness over the total fitnesses of the entire population This roulette wheel is then spun to determine the selected individual The higher the individual s fitness the larger the proportion of the wheel it is assigned and greater the chance that it undertakes mating Goldberg and Deb 1990 Roulette by Rank The population is sorted and each individual is assigned a probability of selection or section of a roulette wheel according to its rank This roulette wheel is then spun to determine the 14 SolveXL User Manual selected individual The higher the individual s rank the larger the proportion of the wheel it is assigned and greater the chance that it undertakes mating Goldberg and Deb 199
3. MO version e About displays information about license expiration date and limitations 7 1 Workbook Requirements The only requirement a workbook compatible with SolveXL must meet is that it contains one worksheet named Problem The worksheet containing configuration is created automatically after pressing the Configuration button This worksheet is by default hidden 8 Configuring SolveXL Configuration wizard is used to configure all required parameters of the application It allows setting up various options of genetic algorithm defining cells containing values of genes objective functions etc To navigate between the tabs in the Configuration wizard one can either use the Next gt and lt Back buttons or directly click the name of the tab located at the top of the window It is recommended to go through all the tabs using the Next gt button at least for the first time in order not to skip any configuration parameters At the end of the set up process the last tab the Next gt button disappears Press the Ok button to save the settings or Cancel to leave Configuration without saving any changes Read the help on the right side of the wizard that contains explanation of the parameters that are configured 8 1 Configuring GA Parameters The first screen of the Configuration wizard see Figure 12 specifies the type of the problem If it is desired to optimize more than one objective func
4. certain parts of the chart by drawing a rectangle If you move your mouse over a point in the chart the values of both objective functions are displayed To update the decision variables in the Problem worksheet please click on the point representing desired solution with left mouse button SolveXL Results Results to be displayed Name eee eee eee cose F Ress En Results oi20 Results ox30 C Resultst0 40 Results ois0 Results Objective 1 Select objectives to be displayed w Objective i yi Objective a Refresh Figure 34 Results Browser 8 7 3 Summary Worksheets When multiple runs are selected then the application generates summary worksheet at the end of the computation The content of the worksheet is different for SO and MO problems Summary worksheet of a single objective problem contains only the best organisms found at the end of each run So the number of organisms on the worksheet is equal to the number of runs In multiple objective version the summary worksheet contains best pareto fronts obtained at the end of each run Each of the pareto fronts can be formed by different number of organisms however the number never exceeds the size of the population Note It is not possible to resume GA from a summary worksheet It is either necessary to abort the execution using the Stop button in this case normal worksheet containing results is created or to enable the automatic saving of
5. complete a run The population size must be an integer value The higher the value of population size is the longer it takes the algorithm to complete its run This is especially problem of the Generational Generational Elitist and NSGA II algorithms It is recommended to enter value lower than 1000 as it might be difficult to stop the algorithm using Stop or Pause buttons on slower machines 11 SolveXL User Manual SolveXL Configuration Wizard Genetic Algarithm Excel Link Options i pusa The genetic algorithm works By Type Population Algorithm Crossover Selector Mutator maintaining a population of solutions chromosomes from which to select Please enter population size mutate and crossover The population size i important az it determines the diversity of the population at the start of the run and algo how long it takes to run GANetL requires an integer number representing the size of the population to be entered Population Size The higher the value of population size is the longer it takes the algorithm ta complete its run This is especially problem of the daacsuiwas zar ata A rand Aea a algorithms Itis recommended to enter value lower than 1000 as it might be difficult to stop the algorithm using Stop or Pause button on slower machines Cancel Figure 13 Defining the size of the population 8 1 2 Algorithm Type In the third tab see Figure 14 the genetic algorithm is selected The appearance
6. eee a 30 8 7 3 SUIMIMArY WOKS NEGIS sistate citata sasa dt data anul aetna au la a aa d 31 9 Opening ING EXAM PleS sist aicea ae s ai Aaaa secu tet dou Ei iai at Aba Et AR sac tot a Aa boat 32 10 Linking SolveXL with Other Simulation Tools eee 32 10 1 Using EPANET to Evaluate Fitness of Organisms ne eee eee 33 11 Writing user defined Penalty multipliers c eee eee eee 34 11 1 Example of a multiplier so asalt a talc lat e adela ele a 34 12 KNOWN NO DIGINS ia seceta arse seats bal iat al aaa iata aaa sapa alma iarta a 34 12 1 Application crashing with access violation error cc eee eee 34 12 2 Microsoft Excel 2007 Worksheet running in compatibility mode 35 12 3 English version of Microsoft Office 2007 and different Windows locale 35 PE ELE IGG Site ara ama angelina ai cec an ucisa aces acento estan ee at ae in a i e n la me ac ai mead 35 SolveXL User Manual 1 Current Version Version number can be determined in the About box accessible from SolveXL s menu To make sure that you are running the latest version visit the website of the application http www solvexl com 2 Reporting bugs and problems To report a bug or problem related to SolveXL please send an email to solvexl Osolvexl com describing the issue and if possible attach an Excel Worksheet which can be used to reproduce the problem 3 Introduction SolveXL is an add in for Mic
7. of the tab varies according to the problem type settings In MO version there is only one algorithm available NSGA II however in SO there are three algorithms to choose from Generational The generational genetic algorithm is the most widely used At each iteration an entire new population is created from the old by using the selection crossover and mutation operators This means that a new population must be evaluated for each new population Therefore the generational GA can be more effective but also more time consuming Generational Elitist Similar to the generational algorithm but in this version the top one or two solutions are copied without alteration into the next population The remainder of the population is filled with the products of crossover and mutation This ensures that the best solution s are retained from one population to the next When this algorithm is selected a text box enabling to define the level of elitism appears The level of elitism corresponds to the number of best organisms that are directly copied to next generation Steady State The steady state algorithm generates only a handful of new individuals in each generation These new solutions generated by the selection crossover and mutation operators are added to the current population by replacing weaker solutions in the population To use steady state an extra operator a Replacer is needed to determine which weaker solutions to replace When Steady st
8. order to use this functionality simulation software must expose its API in form of DLL library e g EPANET or any other way that allows invoking its functions from Visual Basic for Applications To enable cooperation with other tools it is necessary to enable this feature in the Configuration This can be done in the Excel Link Simulation tab sheet Tick the Enable Support for simulation tools checkbox and fill in the name of the Macro which is then called in the evaluate fitness method Note The name of the macro must also contain the name of its module For example Module1 Macro_name To determine the name of the module in Excel press Alt F11 to get to VBA Editor Expand the folders in the right panel see Figure 35 to find out the name of the module where the macro is stored Project BAProject x Microsoft Excel Objects List ev_HiddenInfo A List Problem fe Thisworkbook Module 2 EEE BA VBAPrOJE exiti 2 Microsoft Excel Objects A List Problem Figure 35 A panel in VBA showing the name of the module 32 SolveXL User Manual 10 1 Using EPANET to Evaluate Fitness of Organisms The easiest way how to run simulations with EPANET is to modify one of the examples shipped with SolveXL The example code in VB comprises of two modules EPANetDLL and EPANetInterface e EPANetDLL is module which was imported into the project The original file epanet2 bas is part of th
9. recover the computation into external tle In case that the addin crashes and Excel ts closed the computation can be restored later Note Backup negatively affects the B l performance of the algorithm Filename C backup bin amp however the impact i not az significant as when auto saving i used The backup interval should be chosen wisely with respect to the character of the problem ard assumed duration time Recovery after a crash To recover the information saved Using backup function Just press the Runt button IF any backup was created itis ingpected and in case Cancel Figure 27 Backup of population into an external file Recovery after a crash To recover the information saved using the backup function Just press the Run button If any backup was created it is inspected and in case that it contains any information a new worksheet is created containing the whole population from the last backup before a crash occurred Confirm P Backup file From previous run was Found Ss Do you want to recover the results Figure 28 A message box displayed when restoring population from a backup file 8 3 5 Miscellaneous This is the last tab of the configuration wizard It allows user to define several options but also to enter new serial number in order to extend the expiry date of the application Please contact the author if your version of SolveXL has expired and you would like to continue using it Flo
10. 0 Tournament Tournament selection involves the random selection of a designated number of individuals from the population who compete in a tournament for inclusion into the mating pool Tournament selection in its simplest form consists of a binary tournament involving the direct competition of two individuals for survival by the comparison of their fitness function with the fitter of the two surviving The tournament size can be increased thereby increasing the selection pressure in the GA This ranking of the population allows for a constant selection pressure as in rank based fitness allocation Use of tournament selection has shown better performance than the roulette wheel selection Goldberg and Deb 1990 Crowded Tournament Similar to the standard Tournament Selection two solutions are chosen at random from the population and compared The solution with better lower rank wins If both solutions have the same rank then the solution with larger crowding distance wins In case that both solutions have the same rank and also crowding distance then winner is chosen randomly SolveXL Configuration Wizard E E ie Multi Objective Selector Genetic Algorithm Excel Link Options PEE The multi objective algonthm can require Type Population Algorithm Crossover Selector Mutator specialist selection operators G amp Net lt L curently supports only one MO specitic Choose selector selector Selector Crowded Tournament a a Simil
11. 1 Resuming Computation Comprising of Multiple Runs When resuming the results that were obtained from multiple runs then the algorithm normally completes current run and continues on consequent runs This behaviour might not be wanted in certain situations One might use multiple runs to see the effect of different initial populations and then just continue the computation with the best results obtained so far In order to do this it is necessary to change the configuration of the GA and also to modify the worksheet containing the results In the configuration the number of runs must be set back to 0 and the number of generations increased to a desired value Then the worksheet with results has to be changed Find the value indicating the Run highlighted in Figure 33 and ensure that it is set to 0 2 RESULTS 29 11 200 16 38 15 Fopulation zji 4 Run Generation zji E Random Seed 1 Randomize Count 15470 Figure 33 Resetting the number of a run to 0 8 7 The Results After completing a run either reaching the given number of generations or terminating it using the Stop button the obtained results are saved to the worksheet which was selected prior to starting the GA 8 7 1 Single Objective Results After SO algorithm finishes it updates the Problem worksheet with gene values of the best organism found and generates a worksheet containing the whole population and the global best organism stored at the end The globa
12. EXETER ADVANCED ANALYTICS LLP SolveXL User Manual SolveXL User Manual Table of Contents De GRO RIE NCSI O ard sage teeta na iat a aerate ict aise meee ete eh n ta apa ta 3 2 Reporting bugs and ProbleMs ccccccccsecccscccseccceecccueeceucecseeceueecueeseeecsuseseuesseeessusensess 3 3 lit 079 0 1c cetera noi ta Aaa 0 a 0 sado ene ene aia 0 digi ee ee 3 A MSTA AMON ea seat ot aci bait ac Et Palat Eat c Put Cd Ea Pe Dl Ca ba Dl B but Dl B pda 3 5 Wporades ana UNINSIAIMO css erezia tao atatia done cari Aaaa ic la d nat 8 6 Constrainis and LimitaliOns n ceace orei da doo dia ia Aa dia ta Aa baiat a Aa aci e a ue 9 6 1 MIGKOSOM OMICS 2007 reri seii penn cleo alea acul E E else aluat ei 9 7 Working with SOIVEXLm ss sei a sett scons Setare a aa DD situ Gta Sta a va Gt Sti Daia ra Sta St Cal 10 7 1 VVOFKDOOK FMECUIFEIMEMIS sercis an E 10 8 GORPIGUPIAG SONGA Laie ane hho ea atata d at alti o atatia at 10 8 1 Configuring GA P rametlers sis scai cca sea ata ezita Da la ia Da ala a Da a St 10 8 1 1 PODUIAUON SIZE uenn e EE ohare i ceapa ali ee Gaiei i Dias eta 11 8 1 2 PAO O ILIA ENE i oa a n tr na a n a le n a la o Ea 12 8 1 3 CIOSSOVEL T yD E cit trai caca inot ee zoana nec alias Lua ea za miau Sa 13 8 1 4 5510 10 p I IRI BERI ERE ENE SRSC MIR RN NR CI TE EI SRR RT EA CI RR NNE Ne RRC Se 14 8 1 5 MUNO TSD iad oa iaca aia Da a Dia abc val 15 8 1 6 Roplacer TYPO stari ai eit dstia iran Suiaasia a
13. Using cache to improve the performance 8 3 3 Automatic Saving This feature displayed in Figure 26 allows saving of intermediate populations in user specified interval This might be useful when performing optimization containing multiple runs to save the population at the end of each run Without using this option only the best organism SO or pareto front MO is saved to summary result sheet which does not allow to resume the computation at later time Hint To save the population at the end of each run set the interval to the number of generations comprising single run Note Automatic saving of population negatively affects the performance of the algorithm and might produce enormous number of worksheets It might be desired to use the backup function which is faster and does not create any worksheets refer to section 8 3 4 Overwrite This specifies whether new result sheets which are created either manually or automatically are overwritten This variable is also controlled by the Save Results dialog displayed in Figure 31 24 SolveXL User Manual SolveXL Configuration Wizard F Autosayin GeneticAlgorithm Excel Link Options 3 This feature allows saving of Running Cache Auto Saving Backup Miscellaneous Intermediate populations ini user specitied interval This might be peer Pon Ree na useful when performing optimization containing multiple ring to sawe the Autosave Population to a Worksheet population at the end
14. al Simple Multi Point Multi point crossover acts in the same way as single point but multiple points are selected along the chromosome This leads to a better distribution of genes across the offspring Uniform Random Uniform crossover is essentially the ultimate case of multi point crossover in that it selects each gene at random to be part of either child A or child B This makes the distribution of genetic material independent of the position of the gene in the chromosome SolveXL Configuration Wizard Crossover A Genetic Algorithm Becel Link Options The crossover operator i designed Type Population Algorithm Crossover Selector Mutator ee ene Individuals to create entirely new Choose crossover type and enter probability of crossover solutions which have some of the attributes of their parents similar to Crossover the way in which sexual reproduction occurs In nature Normally taro offspring are created by crossing over two parents and they are often better solutions that either of their parents but also occasionally worse Uniform Random The choice of crossover operator can Influence the effectiveness of the genetic algonthm There are Crossover Rate O05 2 oo operators tn Crossover occurs by splicing the chromosome at a particular point s on each chromosome and then recombining one section of chromosome A with the opposite section of chromosome E ba Simple Gne Point Simple Multi Point Cancel
15. ar to the standard Jivaraacasea See bea solutions are chosen at random from the population and compared The solution with better flower rank wings IE both solutions hawe the same rank then the solution with larger crowding distance wins In case that both solutions have the same rank and also crowding distance then winner is chosen randomly Figure 16 Choosing GA selector 8 1 5 Mutator Type The mutation operator is designed to provide new genetic material during an optimisation Without the mutation operator the algorithm could find locally optimal solutions without searching for better globally optimal solutions The mutation operator works by selecting a gene at random in a chromosome and changing it to a random value within the bounds of the gene This is performed within a certain probability soecified by the user There are two mutators available in SolveXL see Figure 17 Simple 15 SolveXL User Manual Mutation is performed on a gene when a random value is bigger than the user selected mutation rate This gene will be given a random value within its range Simple by Gene An integer value is calculated by multiplying the mutation probability times the chromosome length MutationRate Chormosome Length When this value is smaller then a random value mutation is performed The value of the probability of mutation needs to be carefully thought out If the probability of mutation is less than 1 chromosome len
16. aspx 3 EPANet Project http Awww epa qgov nrmrl wswrd epanet html 4 Deb K S Agrawal et al 2000 A Fast Elitist Non Dominated Sorting Genetic Algorithm for Multi Objective Optimization NSGA II Kanpur India Indian Institute of Technology Kanpur Genetic Algorithms Laboratory Microsoft Excel Office XP Vista and Windows are either registered trademarks or trademarks of Microsoft Corporation in the United States and or other countries 35
17. at Precision The value of this variable controls the precision of Real Bounded Genes if they are utilised The default value is 4 however the precision can be increased up to 8 Chart Update Interval 26 SolveXL User Manual This variable specifies the update interval of the chart and grid displaying the progress of GA during a run Please Display Progress Chart The state of this variable indicates whether progress chart will be displayed during the computation In case that the application is crashing unexpectedly try to disable the progress chart Note Updating the chart is a time consuming operation which can significantly decrease the performance of the application It is recommended to disable updating of a chart and grid when working with population sizes greater than 1000 SolveXL Configuration Wizard Float Precizion Genetic Algorithm Excel Link Options The value of this Yarnable controls Running Cache Auto Saving Backup Miscellaneous the precision of Real Bounded Genes it they are utilised The default value i 4 digits however the Float Precision precision can be increased up to S digits Chart Update Interval 10 generations Chart Update Interval Display progress chart This variable species the update interval of chart and grid displaying the progress of GA during a run Please note that updating the chart ts time consuming operation which cari significant decrease the performance of the a
18. ate algorithm is used an extra tab appears see Figure 18 Choosing replacer used in SO Steady StateFigure 18 to allow user specify the type of a replacer 12 SolveXL User Manual NSGA Il NSGA II 4 is multi objective optimization algorithm based on non dominated sorting At first offspring population is created by using the parent population The two populations are combined together to form population of size 2N Then a non dominated sorting is used to classify the entire population After that the new population is filled by solutions of different fronts one at a time The filling starts with the best non dominated front and continues with solutions form other fronts until the population size of N is reached SolveXL Configuration Wizard E ARE i HSGA Il Genetic Algorithm Excel Link Options Mall is multi objective optimization Type Population Algorithm Crossover Selector Mutator algorithm Based on non dorinated sorting At first offspring population i Please choose algorithm to be used For GA Information about created by using the parent population available algorithms are displayed in the right panel The two populations are combined together to form population of size 2M Algorithm Then a nonidominated sorting iz used to Pa II classify the entire population After that the new population iz filled by solutions of different fronts one at a time The filing starts with the best nor dominated front and continues w
19. e epanet toolkit EN2toolkit zip which can be downloaded from EPANet website 3 To insert this module into an existing workbook press Alt F11 to get to the VBA editor right click the Modules folder and choose Import file e EPANetInterface is a set of functions exploiting the EPANet interface created to simplify calling of original methods The key functions are openNetwork opens the EPANET input file and initializes hydraulic solver closeNetwork shuts down the EPANET and closes all files solve runs the hydraulic simulation of the network simulation main function which writes new pipe diameters to EPANET runs hydraulic simulation and then reads node heads from EPANET and stores them in the Excel worksheet O O 0 0 Public Sub openNetwork ERROR ENOpen Input Tiie rnp y report TAG Lepa T ERROR ENopenH Ena Sul Public Sub closeNetwork ERROR ENclose End Sub Public Sub solve Dim t As Long Dim tstep As Long ENR 1 EI LOY Do ENrunH t ENnextH tstep Loop While tstep gt 0 End Sub Sub simulation Dim i As Long ActiveSheet Calculate For i 1 To selectedLinkCount Call EPANetInterface setLinkDiameter linkIndexAddr Cells i i diamAddr Cells i 1 value Next 1 33 SolveXL User Manual EPANetInterface solve For j 1 To nodeCount nodeAddr Cells j 1 value EPANetInterface getNodeHead Next J ActiveSheet Calculate End Sub 11 Writi
20. er version and everything should be done automatically for you Please make sure that Microsoft Excel is not running while upgrading or uninstalling SolveXL can be uninstalled by removing it using Add or Remove Programs from Control Panel or by clicking the Uninstall icon which is located in SolveXL s folder under Start All Programs Please note that removing SolveXL does not remove any of your documents unless they are stored in the folder where the add in was installed by default C Program Files SolveXL SolveXL User Manual SolveXL Uninstall lees s Uninstall SolveXL Remove Sole From your computer Solves will be uninstalled From the Following Folder Click Uninstall ta start the uninstallation Uninstalling From C Program Files Sole Uninstall Cancel Figure 10 Removing SolveXL 6 Constraints and Limitations When formulating a problem and deciding whether to use SolveXL it must be kept in mind that there are certain restrictions imposed by Microsoft Excel applies to Microsoft Excel 2003 Maximum number of rows 65 536 Maximum number of columns 256 Number precision 15 digits Length of formula contents 1 024 characters Sheets in a workbook limited by available memory The maximum number of columns is the biggest issue One might think that about putting genes into rows instead of columns but when the results are saved every organism occupies one row and thus the maximum number
21. ext picture in order to copy the identifier to clipboard SolrexL O Vi Version 1 0 3 0 Invalid serial number Identifier Enter New Serial Number Copyright Diapason Consulting Ltd 2009 All rights reserved Figure 7 About box unregistered Once you are provided with a serial number 32 alphanumeric characters click the Enter new serial number button and paste the number as displayed on the following picture SolveXL Serial Number Your Identifier iz E C47 83C Please enter new senal number Figure 8 About box entering a Serial Number SolveXL should now display information about your license including expiration date and all limitations of your copy SolveXL User Manual SolrexL O Vi Version 1 0 3 0 Valid serial number Days remaining 315 Expiration Date 17 01 2010 Limitations Genes 256 Objectives 256 Population 2147463647 Generations 21446364 Identifier as Enter New Serial Number Copyright Diapason Consulting Ltd 2009 All rights reserved Figure 9 About box registered Note Never try to copy already installed application from one computer to another During the installation process important information is stored in system registry Without these registry entries the application will not work properly 5 Upgrades and Uninstalling Before upgrading SolveXL it is not necessary to uninstall the previous version Simply run the installation of the new
22. gth then no mutation will occur If 1 chromosome length lt MutationRate lt 2 chromosome length then one mutation can be expected per chromosome In effect the choice of mutation rate implies how many bits will undergo mutation The Ammended Morley GA Library Adaptive Mutation This is an experimental feature The algorithm records a history of mutations and tracks mutations that lead to improvement of the fitness of the organism Use of adaptive mutation can increase the performance of GA however the learning time is rather long and should be thousands of generations SolveXL Configuration Wizard zi E ERE Mutator A Genetic Algarithm Excel Link Options The mutation operator is designed to Type Population Algorithm Crossover Selector Mutator provide new genetic material during an optimisation Without the matatior Choose mutator type and enter probabilky of mutation operator the algorithm could find locally optimal solutions without Mutator searching for better globally optimal solutions The mutation operator works by selecting a gene at random in a chromosome and changing itto a random value within the bounds of the gene This iz performed within a D Simple Simple By Gene Mutation Rate 0 05 2 certain probability specified by the user There are two mutatarz available in pet Use Adaptive mutation Simple Mutation is performed on a gene when a random value is bigger than the user
23. iA Nas a 16 8 2 Defining Link to Excel Worksheei eee aaa 17 8 2 1 Defining the Chromosome eee ea aaa 17 8 2 2 Dening the Objeclives cico iata diac pa ta 0 li da aa 18 8 2 3 Denning the Conste se sec ez 30 aici eet tii azot Eat atata abil 19 8 2 4 Simul lioti SUD DOM pecs sect tiesto anul ete a la a ad 20 8 2 5 Writing Values Back to Excel eee eee eee eee 21 8 3 setting Up Program Options nisa eee oaza amana conac de caiac anis de aie ad inu pala 22 8 3 1 RUANIN tata it 8 aa tu ua ta a aa ta hewn au ta ea a ta ta a ta ta a la a 22 8 3 2 a OPINE epee oii iei pediatra tat dr aia dr e eet cre ara 23 8 3 3 ANILOR NIG VIC os tii aa aa tt ai tnt he la aut ala 24 8 3 4 AG KU Sci e aa adi aa udata d a tata d a uta aut acuta 25 8 3 5 MiS coloane OU G aneis e RRDP SORRENTO a SORINA e 26 8 4 Advanced CONIigUrati OI ct ie o o i e i tt i a a a ca e 27 8 5 Pendoring a RUN ea RE RR POE RRC ee PRR PREA 27 8 5 1 SVE BSUS sees crea ai et nee ce ee com ee tata 28 8 5 2 Displaying the Progress Of a RUN ccccseccseccseecneeeseeeneeeneeseeeneeeseeeseeeneeenes 28 8 6 Resuming Suspended RUN scai ceia ee eee ees ad ada d ca 29 8 6 1 Resuming Computation Comprising of Multiple RUNS cccccceeceeeeeeeee 30 8 The RESUS concessa Ba re atatea Eat arata aut Bata e tal all at ar at ete 30 8 7 1 Single ODIECIVE TOSUMNS sence eles aaa o to td rele aa ee wea eine le 30 8 7 2 Multiple Objective RESUNSia ic oi c i oa dit
24. ide you through the installation of SolvexL It is recommended that wou close all other applications before starting Setup This will make it possible to update relevant system Files without having to reboot your computer Click het ta continue Cancel Figure 1 Installation welcome screen It is recommended to install the application with typical options This installs all the available features including all examples SolveXL Setup Choose Components Choose which Features of Sole you want to install Check the components vou want ta install and uncheck the components you don t want to install Click Next ta continue Select the type of install bud Or select the optional Solve L Core Files ae ee ditai Documentation aya Ele aur Examples see its description EPANET Demo Description Space required 10 1MB Nullsoft Install System v2 31 Figure 2 Selecting Setup type SolveXL User Manual SolveXL can be installed into any folder on your computer However it should be installed on your hard drive and not on any removal devices SolveXL Setup SER gt Choose Install Location i Choose the Folder in which to install SolveL Setup will install Solve L in the Following Folder Ta install in a different Folder click Browse and select another Folder Click Next to continue Destination Folder Browse Space required 10 1MB Space available 319 5MB Figure 3 Choosing the target fo
25. ing the constraints or infeasibility 8 2 4 Simulation Support Simulation allows linking SolveXL with other simulation packages used to evaluate fitness of solutions To enable this feature tick the appropriate checkbox on this tab and enter the name of VB macro to be called to evaluate fitness of an organism see Figure 22 For more details refer to chapter 10 page 32 Please note that automatic re calculation of the worksheet is disabled while GA computation is running It is the responsibility of user defined macro to ensure that worksheet is recalculated at the end of the evaluation if this is necessary 20 SolveXL User Manual SolveXL Configuration Wizard E Simulation Genetic Algorithm Excel Link Options simulation allows inking Sole with Chromosome Objectives Constraints Simulation Write Back other simulation packages used to evaluate fitness of solutions Ta enable Following tab allows to enable SolvexL ta use capabilities of various simulation this feature tick the appropriate tools e g EPANET checkbox on this tab and enter the name of YB macro ta be called to evaluate fitness of an organism Enable support For simulation tools Ta ensure that the name of the macro Simulation tool parametes has been entered corectly please press the West button to tru to execute the Please enter the name of Excel macro that should be called instead of ee asking Excel to recalculate the worksheet Please note that automatic
26. ith solutions Form other fronts until the population size of N Is reached Cancel Figure 14 Choosing a genetic algorithm MO problem type 8 1 3 Crossover Type The crossover operator is designed to share information between individuals to create entirely new solutions which have some of the attributes of their parents similar to the way in which sexual reproduction occurs in nature Normally two offspring are created by crossing over two parents and they are often better solutions that either of their parents but also occasionally worse The choice of crossover operator can influence the effectiveness of the genetic algorithm SolveXL currently supports three crossover types see Figure 15 Simple One Point Simple Multi Point and Uniform Random After selecting the desired crossover it is also necessary to enter the crossover rate which corresponds to the probability of a crossover to be performed Crossover occurs by splicing the chromosome at a particular point s on each chromosome and then recombining one section of chromosome A with the opposite section of chromosome B Simple One Point A single location in the chromosome is chosen The first child consists of all the genes located before this crossover point of the chromosome A and the genes after this crossover point of chromosome B Similarly the second child consists of the first portion of chromosome B and the second portion of chromosome B 13 SolveXL User Manu
27. l best organism is used by the GA library to store the best organism from multiple runs and necessarily does not have to be the best organism The organisms are sorted according to fitness function thus the best organism can always be found on the top of the table Note When using Generational algorithm the organism which is written into the Problem sheet does not need to exist in the results worksheet containing the population This is due to the character of Generational algorithm which unlike the Elitist version of this algorithm does not guarantee that any of the fittest organisms propagates to the next generation 8 7 2 Multiple Objective Results Results in MO version are represented by the Pareto Front and are stored in the Results sheet of the Workbook Please note that the whole population is stored in the worksheet and that the best pareto front is formed only by organisms with rank equal to 0 The true pareto front can be easily obtained using Excel s automatic filter which can be found under Data gt Filter gt Automatic Filter To display the results in a form of a chart similar to the one that 30 SolveXL User Manual was displayed during the computation process activate the sheet that contains the desired values and click the Results icon located in the SolveXL s toolbar When the results are displayed it is possible to change the objective functions that are displayed in the chart and also to zoom to
28. lder to install SolveXL In the following step please choose a folder where the Start menu shortcuts are going to be placed SolveXL User Manual SolveXL Setup A Choose Start Henu Folder Choose a Start Menu Folder Far the Solel shortcuts Select the Start Menu Folder in which you would like bo create the program s shortcuts You can also enter a name to create a new Folder Accessories Acersystem ActivePerl 5 5 8 Build 619 Administrative Tools Adobe Advanced Office Password Recovery AMF Font viewer Apache HTTP Server 2 0 Aquators Hv Free 6 0 AZUreUS VUZE F Do nat create shorkcuks Nullsoft Install System v2 31 Figure 4 Choosing Start menu folder name The installation will commence after pressing the Install button and should finish shortly SolveXL Setup DiR Completing the SolvexL Setup Wizard Solvexl has been installed on your computer Click Finish ta close this wizard Figure 5 Installation completed successfully SolveXL User Manual Please launch Microsoft Excel after the installation completes If the installation was successful a toolbar similar to the one depicted on Figure 6 should appear in Microsoft Excel Click the About button on SolveXL s toolbar It is necessary to send a hardware identifier e g 5E2EE818 to solvexi solvexl com so that a unique serial number can be generated for you based on this information Click the button as displayed on the n
29. ng user defined Penalty multipliers Penalty multipliers can be used to modify the penalty function according to the progress of the GA To use penalty multipliers it is necessary to get the current generation and run from the GA This can be achieved by enabling the write back feature in Excel Link Write Back tab see the section 8 2 5 on page 21 711 7 Example of a multiplier This example demonstrates creation of a simple penalty multiplier which changes its value every run after 100 generations Let us assume that value of generation is written into cell B2 and current run is stored in cell B1 The penalty function which is defines the constraint is stored in cell B7 and contains following formula some function B5 The actual value of the penalty multiplier is stored in cell B5 A screenshot of the worksheet is in Figure 36 Current unl 4 a values filled in by GA Penalty implied by violation Current generation l of some constraints e g F IF H10 50 1 0 Penalty multiplier modifier POVWVER 1 1 B1 Penalty multiplier lF B4 gt 100 641 First penalty a second penalty 7 Penalty function G8 B5 Third penalty EEE Fourth penalty Total penalty Fi Figure 36 Example of creation of user defined penalty multiplier 12 Known problems This chapter highlights some of the known problems related to SolveXL and provides the user with possible solutions where applicable 12 1 Application c
30. nk Options j When Using a Siaa miae genetic Algorithm Crossover Selector Mutator Replacer gt algorithm the new solutions created are added to the current population Choose replacer rather than creating a whole new population To maintain the Replacer population size therefore some solutions must be replaced Deciding which solutions to replace i the job of the Semans There are number of criteria for deciding which solutions O First Weaker are replaced in G4NetsL 1 weakest unconditional O By Rank Weakest The new individual i added to the 1 Uniform Random population which iz then sorted according to fitness The solution With the worst fitness is then deleted note that this could be the new solution Weakest unconditional The population iz sorted according to fitness before new individual iz added Cancel Figure 18 Choosing replacer used in SO Steady State 8 2 Defining Link to Excel Worksheet This section describes all the options that can be set under the Excel Link tab 8 2 1 Defining the Chromosome Each of the decision variables for a problem constitutes a gene in the genetic algorithm All of the genes are appended together to form a chromosome Therefore the choice of genes determines what variables the genetic algorithm uses to discover optimal solutions Microsoft Excel cells corresponding to the genes must occupy continuous area range Type in the range address e g A1 C5 and press
31. of decision variables genes is limited to around 250 Full list of other limits can be found in 1 6 1 Microsoft Office 2007 Microsoft Office 2007 is supported by the latest version of SolveXL and significantly extends the limits applied to worksheets e Maximum number of rows 1 048 576 e Maximum number of columns 16 384 e Length of formula contents 8 192 characters For further information about new features of Microsoft Excel 2007 see 2 SolveXL User Manual 7 Working with SolveXL After successful installation SolveXL integrates within Microsoft Excel and creates a toolbar containing 5 control buttons Configuration Run Resume Results and About displayed in Figure 11 ast Configuration Run Resume 4d Results a About Figure 11 SolveXL Toolbar Each of the buttons controls one of the key components of SolveXL This new version introduces the Resume function which significantly distinguishes it from the previous version To create an empty Excel workbook it is recommended to use the Empty Project template which is located in SolveXL s folder in Start menu This template creates an initial workbook e Configuration used to configure the application e Run starts the optimization or attempts to recover crashed computation from a backup file if automatic backup is enabled e Resume resumes suspended optimization the active worksheet is resumed e Results displays the pareto front in
32. of each run Without using this option only the best organism S50 ar pareto front MO iz saved to summary result Saving Interval sog generation sheet which does not allow to resume the computation at later time Automatic Results Saving To save the population at the end of each run set the interval to the number of generations comprising single run Hate Automatic saving of population negatively affects the performance of the algorithm and might produce enormous number of worksheets It might be desired to use the backup function which iz faster and does not Cancel Figure 26 Automatic saving of the population 8 3 4 Backups This function allows storing population and other information that can be used to recover the computation into external file In case that the addin crashes and Excel is closed the computation can be restored later from the file Note Backup negatively affects the performance of the algorithm however the impact is not as significant as when auto saving is used The backup interval should be chosen wisely with respect to the character of the problem and assumed duration time 25 SolveXL User Manual SolveXL Configuration Wizard Genetic Algorithm Excel Link Options Running Cache Auto Saving Backup Miscellaneous Backup Population to External File Backup Saving Interval 1000 generation Backup This function allows storing population and other information that can be used to
33. population and save population at the end of 31 SolveXL User Manual each run The use of automatic saving of population at the end of each run is recommended because it gives the possibility to resume the GA later refer to section 8 3 3 on page 24 9 Opening the Examples The application is shipped with 2 Multiple Objective examples and 1 Single Objective example All the examples are easily accessible from the All Programs gt SolveXL gt Examples folder located in the Start menu The first MO example and the single objective example represent the Advertising selection The task is to select the most effective advertising campaign within your budget to reach the largest audience while meeting necessary restrictions The second MO example represents the Purchasing with Quantity Discounts The task is to buy at least 155 litres of solvent while keeping the cost as low as possible These easy to understand examples should help the user to learn how to setup SolveXL and use it to solve various tasks using the flexibility of Excel s functions The single objective example is only a modification of the first MO example This can be useful for comparison of solutions that are found by both versions Note All the examples are based on the samples shipped with the Evolver package 10 Linking SolveXL with Other Simulation Tools SolveXL can use other simulation tools and packages to evaluate fitness of organisms In
34. pplication It is recommended to disable updating of a chart and grid when working with population sizes greater than 1000 Display Progress Chart The state of this variable indicates Cancel Figure 29 Miscellaneous options 8 4 Advanced Configuration The previous version of SolveXL was exposing a worksheet called Settings which contained all the configuration parameters In the current version this worksheet is hidden by default however it is possible to unhide it To do so open your workbook and go to Format gt Sheet gt Unhide and select the Settings sheet Note Please be careful when editing the settings directly because the values read from this sheet are not validated against any errors 8 5 Performing a Run After configuring all the parameters the algorithm can be executed by pressing the Run button in application s toolbar SEP Configuration Cp Run gt Resume amp d Results Q About 2 SolveXL User Manual Figure 30 Starting the optimization 8 5 1 Saving the Results Before the computation process starts a pop up window appears requiring to enter a name of worksheet into which results will be saved at the end of computation Note Bear in mind that maximum length of the name of a worksheet is limited to 30 characters Save Results Please choose or enter the name of worksheet where obtained solutions will be stored and press OK button Press Cancel button to not to execute cu
35. ram Options This section describes all the parameters that can be set under the Options tab 8 3 1 Running This tab displayed in Figure 24 specifies parameters of a run The most important variable is the number of generations in every run It is also possible to create a batch consisting of multiple runs Each of the runs then lasts N generations Multiple runs can be used to find out the influence of different initial populations on the performance of GA If multiple runs are used results are then stored in a summary worksheet In order to be able to resume the calculation of one of the runs it is necessary to use the auto saving feature and save the population at the end of each run Random Seed This number modifies the starting point of the random number generator Changing this value causes GA to start the computation with different initial population 22 SolveXL User Manual SolveXL Configuration Wizard E Runnin Genetic Algorithm Excel Link Options z Thiz tab pechies parameters of Running Cache Auto Saving Backup Miscellaneous nun The most important variable ts the number of gansa Eve Setup parameters of a run ruin It iz also possible to create a batch consisting of multiple exs Iterations Each of the runs then lasts M TE enact Multiple runs can be bi used to find out the influence of different initial populations on the Number of Generations 100 performance of GA IF multiple runs are used results a
36. rashing with access violation error This problem is related to the TChart component which is used to display the progress chart during the run The only known workaround is to hide the progress chart to prevent it from updating and thus crashing 34 SolveXL User Manual 12 2 Microsoft Excel 2007 Worksheet running in compatibility mode Please note that when Microsoft Excel 2007 opens a workbook created using an older version the workbook is opened in compatibility mode This implies that the limits of ranges in Excel remain the same as in the previous version and might cause problems when working with larger worksheets over 255 columns or over 65535 rows In order to resolve this problem please save the worksheet in new format 12 3English version of Microsoft Office 2007 and different Windows locale Microsoft Excel 2007 contains a bug which causes SolveXL not to be able to operate if the language version of Microsoft Office does not match the locale used in Microsoft Windows The only workaround at the moment is to change the locale in Windows to match the language version of Microsoft Office or maybe to download Multilanguage pack for Microsoft Office Further information about this bug can be found at http support microsoft com kb 320369 References 1 Microsoft Excel 2003 Limits http office microsoft com en qb excel HP051992911033 aspx 2 Microsoft Excel 2007 Limits http ologs msdn com excel archive 2005 09 26 474258
37. re then stored ini a summary Worksheet In order to be able to resume the calculation of one of the runs it is Random Seed value 1B Generate necessary to use the auto sawing feature and save the population at the end of each run Number of Runs Random Number Generator Random Seed This number modifies the starting paint of the random number we Cancel Figure 24 Specifying parameters of runs 8 3 2 Caching Caching is an experimental feature which maintains certain number of organisms and stores their fitness This is done to reduce the time normally needed to re evaluate fitness of existing solutions which might be an issue when complex formulas or external simulation packages are used The benefits of caching are still under intensive research and therefore it is not recommended to use this feature 23 SolveXL User Manual SolveXL Configuration Wizard GeneticAlgorithm Excel Link Options Pane Caching i an experirnental feature which Running Cache Auto Sawing Backup Miscellaneous maintains certain number of organisms and stores their fitness This iz done to reduce the time normally needed ta re evaluate fitness of existing solutions which might be an sue when comples formulas or external simulation packages Initial Cache Size 40 are used The benefits of caching are shill under intensive research and therefore it iz not recommended to use Maximum Cache Size 4000 bsi salir Cancel Figure 25
38. re 21 Example of a Constraint The value of objective function must not exceed 50 Let us assume that the objective function is stored in cell C5 The value of the penalty cell might look similar to this F 400307 C5 90 1000 0 The above formula penalises all solutions violating given constraint 19 SolveXL User Manual SolveXL Configuration Wizard E Constraints Genetic Algorithm Excel Link Options Constraints are used when it Is Chromosome Objectives Constraints Simulation Write Back wanted to penalise certain variables for going out of the bounds For This tabsheet allows specification of constraints IF the use constraints is wanted instance in a multiple objective then tick the Use Constraints checkbox and enter address of cell which problem if one of the objectives is contains penalty of given solution in 32 case or infeasibility of the solution in MO the cost of a solution and the budget Is only E2M then solutions outside of Lise Constraints this are useless and should be discouraged Infeasibility Constraints in SolvesL are defined by Infeasibility Cell Excel formulas To enable use of constraints tick the corresponding checkbos and enter address of an Excel cell which contains enti ey SO or secat MO of giver solution a Example of a Constraint The value of objective function must not exceed 50 Let us assume that the objective function iz stored in cell Cancel Figure 21 Defin
39. re calculation Please note that the name of the macro must be in Following Format nf ui lea ei aul sabiei sai esta Au a Module Macro e g Module simulate computation is running It is the responsibility of user defined macro to Macro name Module1 Simulation Test ensure that worksheet is recalculated at the end of the evaluation if this ts necessary Cancel Figure 22 Setting up SolveXL to work with other simulation packages To verify that a macro of the specified name can be executed by SolveXL please press the Test button to attempt to execute it 8 2 5 Writing Values Back to Excel This feature displayed in Figure 23 allows writing current generation and run back into specified Excel cells This might be used to implement user defined penalty multipliers that take into account progress of the algorithm 21 SolveXL User Manual SolveXL Configuration Wizard E Exposing GA Yariables to Excel Genetic Algorithm Excel Link Options i a This feature allows writing curent Chromosome Objectives Constraints Simulation Write Back generation and run back into specified Excel cells This might be used to implement User defined penalty multiplers that take into account progress of the algorithrn Write Current Run and Generation back bo Excel write values Back to Excel Run Cell Address Generation Cell Address Cancel Figure 23 Writing values of run amp generation into Excel 8 3 Setting Up Prog
40. rosoft Excel that adds the possibility to use genetic algorithms to solve various optimization problems To be able to work with this add in user is required to have only basic knowledge of Microsoft Excel to enter appropriate formulas that represent given problem Some basic knowledge of genetic algorithms is also essential in order to configure the algorithm properly to obtain best results The new version of the add in uses Mark Morley s GA library which should perform much faster in comparison to the original library written in Pascal 4 Installation Before installing SolveXL please make sure that your system meets following configuration requirements Operating system Microsoft Windows 2000 XP and Vista Microsoft Excel Microsoft Excel 2000 XP 2003 and 2007 To install and use SolveXL the user performing this operation must have sufficient privileges Currently it is not possible to install or run this application under the limited account in Microsoft Windows XP Home Please ensure that Microsoft Excel isn t running before Starting the installation To install the application it is necessary to download installation package from following address http www solvexl com After downloading the installation package run the installer SolveXL exe and follow the instructions SolveXL is always installed under current user SolveXL User Manual SolveXL Setup Welcome to the SolyexL Setup Wizard This wizard will gu
41. rrent run Result Sheet Name Results Cancel Figure 31 The Save Results Form It is possible to choose a name of existing worksheet with results by clicking the down arrow on the right side of the edit box Please note that the Overwrite data checkbox must be ticked when entering the name of an existing worksheet The algorithm can be started by pressing the OK button or the run can be aborted using the Cancel button 8 5 2 Displaying the Progress of a Run When the algorithm is running it displays some variables reflecting its progress see Figure 32 The overall progress of the algorithm is displayed on the progress bar According to the value of the Chart Update Interva which can be set on the Options gt Miscellaneous tab see Figure 29 The algorithm displays the obtained solutions in form of a grid containing values of genes objective functions penalty infeasibility and other statistical indicators To visualise the progress a chart is used to display the best pareto front in MO or just the fitness of the best organism in SO 28 SolveXL User Manual SolveXL Running Computation Statistics Chart Options Su 2 xi Objective 1 Generation Gt Progress MEH 2696 li Objective 2 E Progress Chart CA IL E u FF ID eae IE 3 18 8 Objective 1 Figure 32 Form showing the progress of the algorithm The chart can be disabled or enabled by clicking at the minimi
42. se arrow as depicted on Figure 32 Disabling the chart might be especially useful when the application crashes regularly at the same phase of computation Note Setting too low value of chart update interval negatively affects the performance of the algorithm because chart and grid updating is a time consuming operation In case of MO run it is possible to select the objectives that are displayed on the chart This can be done using the combo boxes corresponding to the X amp Y axes in the Chart Options panel the chart is not updated immediately after changing these values 8 6 Resuming Suspended Run To resume a run which was stopped using the Stop button or any save point created using the auto save feature It is necessary to select appropriate worksheet containing the population and press the Resume button In order to be able to resume the GA the population size number of genes and objectives must not be changed Other parameters such as number of runs generations or GA settings can be modified Please bear in mind that changing GA settings might lead to unwanted effects 29 SolveXL User Manual Note If the computation has reached the maximum number of generations then the application displays an error and does not allow resuming of the run There are several ways how to bypass this The easiest way is to increase the number of generations in the Configuration wizard refer to section 8 3 1 on page 22 8 6
43. selected mutation rate This gene will be given a random value within its range Cancel Figure 17 Choosing Mutator and defining its parameters 8 1 6 Replacer Type When using a Steady State genetic algorithm the new solutions created are added to the current population rather than creating a whole new population To maintain the population size therefore some solutions must be replaced Deciding which solutions to replace is the job of the Replacer There are number of criteria for deciding which solutions are replaced in SolveXL see Figure 18 Weakest 16 SolveXL User Manual The new individual is added to the population which is then sorted according to fitness The solution with the worst fitness is then deleted note that this could be the new solution Weakest unconditional The population is sorted according to fitness before new individual is added and the solution with the worst fitness is then deleted note that unlike in the case of Weakest replacer the new individual is added every time First Weaker This starts with the best individual and works its way down the population The first solution it encounters with worse fitness than the new solution is replaced By Rank This is similar to the First Weaker method but uses rank values instead of raw fitness values Uniform Random The solution which is replaced is selected randomly SolveXL Configuration Wizard Heplacer Genetic Algorithm Excel Li
44. the Update button to populate the grid containing 17 SolveXL User Manual parameters of genes Please note that the after the pressing the Update button the values of existing cells are preserved and new cells are filled in with default values Hint To set the value of a whole column click on its heading with right mouse button and choose or type in the desired value SolveXL Configuration Wizard Chromosome A Genetic Algorithm Excel Link Options Each of the decision variables for a Chromosome Objectives Constraints Simulation Write Back problem constitutes a gene in the genetic algorithm All of the genes Please enter the range containing genes inta the text box bellow press the are appended together to form a Update button to and specify parameters of the genes chromosome Therefore the choice of genes determines what variables the genetic algonthm uses to a aS ate Benes Pande 2 9 ALCS Hearts discover optimal solutions Excel cells corresponding genes must occupy Gene Type Lower Bound Upper Bound continuous area range Type in the J range address e g A1 C5 and press Integer Bounded 0 the update button to populate the Real Bounded 0 8 grid containing parameters of genes Gray Integer Bounded Hint Ta set the value of a whole column click tte heading with right mouse button and choose or type in Integer Bounded the desired value Integer Bounded Hybrid Integer Bounded Gene Gray Real Bo
45. tion select Multiple Objective MO otherwise select Single Objective SO Depending on problem type chosen different options will be provided in the following steps 10 SolveXL User Manual SolveXL Configuration Wizard Welcome ps Genetic Algarithm Excel Link Options To set up all required parameters fill Type Population Algorithm Crossover Selector Mutator in all the values you re required on E 2 A each tab and press the faza biuttar Welcome to SolvweXL Add In Configuration Wizard This wizard helps you After reaching the final tab in the ta set up all required parameters configuration wizard save the changes by pressing the f button It iz only necessary to go through all of the tabs in the wizard for the first time After becoming familiar with the way how to configure the parameters it iz sufficient to change values in specitic tabs and sawe the changes Wing the Ae button Problem Type Single Objective To leave the wizard without saving ari changes that hawe been made press the AC aeaceybutton Problem type 4s a starting point the problem type must be chosen Choose Sarge Aye iret there s only 1 cell in Cancel Figure 12 Selecting the problem type 8 1 1 Population Size The second tab see Figure 13 allows defining the size of the population GA works with The population size is important as it determines the diversity of the population at the start of the run and also how long it takes to
46. unded The gene iz an integer number i e 1 23 456 and its value is within the Cancel Figure 19 Defining the chromosome Hybrid Integer Bounded Gene The gene is an integer number e g 1 23 456 and its value is within the range upper bound lower bound Hybrid Real Bounded Gene The gene is a real number e g 1 2 3 45 and its value is within the range upper bound lower bound The precision of real gene is defined in Options Miscellaneous tab Hybrid Gray Integer Real Bounded Gene and These are special cases of the two previously stated gene types used especially in optimization of water networks These gene types should be used with pipe sizing problems 8 2 2 Defining the Objectives Exactly one objective must be specified in Single objective version or at least two objectives in multiple objective version Objectives must occupy continuous range of cells Type in the address of the range e g A1 C5 and press the Update button to populate the grid containing parameters of objectives Each objective is described by address of an Excel cell the function that is applied to it and its name Objective function can be either minimize or maximize Hint To set the value of a whole column click on its heading with right mouse button and choose or type in the desired value 18 SolveXL User Manual SolveXL Configuration Wizard i Objectives Excel Link Exactly one objective must be specihed Objectives
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