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Genetic Algorithms: Evolutionary Approach to Optimization, Lecture notes of Data Mining

Arab Academy for Banking and Financial SciencesData Mining

Genetic algorithms (gas) are a powerful optimization technique inspired by the process of natural selection. An introduction to gas, explaining their origins in darwin's theory of evolution and holland's application of these principles to optimization problems. The basics of a simple ga, including chromosome representation, reproduction operators, selection, and the evolution process. Additionally, the document discusses the advantages of gas over conventional optimization techniques and lists various applications in fields such as robotics, machine learning, and scheduling.

Typology: Lecture notes

2019/2020

Uploaded on 10/16/2020

saleh-alshabwani
saleh-alshabwani 🇾🇪

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GeneticAlgorithms
1.Introduction
CharlesDarwinstatedthetheoryofnaturalevolutionintheoriginofspecies.Over
severalgenerations,biologicalorganismsevolvebasedontheprincipleofnatural
selection“survivalofthefittest”toreachcertainremarkabletasks.
In nature,an individualin population competeswith each otherforvirtual
resourceslikefood,shelterand so on.Also inthesamespecies,individuals
competetoattractmatesforreproduction.
Duetothisselection,poorlyperformingindividualshavelesschancetosurvive,
andthemostadaptedor“fit”individualsproducearelativelylargenumberof
offspring’s.Itcanalsobenotedthatduringreproduction,arecombinationofthe
goodcharacteristicsofeachancestorcanproduce“bestfit”offspring whose
fitnessisgreaterthanthatofaparent.Afterafew generations,speciesevolve
spontaneouslytobecomemoreandmoreadaptedtotheirenvironment.
In1975,Holland developed thisideainhisbook“Adaptation innaturaland
artificialsystems”.Hedescribedhowtoapplytheprinciplesofnaturalevolutionto
optimizationproblemsandbuiltthefirstGeneticAlgorithms.Holland’stheoryhas
beenfurtherdevelopedandnowGeneticAlgorithms(GAs)standupasapowerful
toolforsolvingsearchandoptimizationproblems.Geneticalgorithmsarebased
ontheprincipleofgeneticsandevolution.
Thepowerofmathematicsliesintechnologytransfer:thereexistcertainmodels
andmethods,whichdescribemanydifferentphenomenaandsolvewidevarietyof
problems.GAsareanexampleofmathematicaltechnologytransfer:bysimulating
evolutiononecansolveoptimizationproblemsfrom avarietyofsources.Today,
GAsareusedtoresolvecomplicatedoptimizationproblems,like,timetabling,job
shopscheduling,gamesplaying.
2.ASimpleGeneticAlgorithm
Analgorithm isaseriesofstepsforsolvingaproblem.Ageneticalgorithm isa
problem solvingmethodthatusesgeneticsasitsmodelofproblem solving.It’sa
search technique to find approximate solutions to optimization and search
problems.
Basically,anoptimizationproblemlooksreallysimple.
GA handles a population ofpossiblesolutions.Each solution isrepresented
throughachromosome,whichisjustanabstractrepresentation.Codingallthe
possiblesolutionsintoachromosomeisthefirstpart,butcertainlynotthemost
straightforwardoneofaGeneticAlgorithm.Asetofreproductionoperatorshasto
be determined,too. Reproduction operators are applied directly on the
chromosomes,and are used to perform mutations and recombination over
solutionsoftheproblem.Appropriaterepresentationandreproductionoperators
are really something determinant,as the behaviorofthe GA is extremely
dependantonit.Frequently,itcanbeextremelydifficulttofindarepresentation,
pf3
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GeneticAlgorithms

1 .Introduction CharlesDarwinstatedthetheoryofnaturalevolutionintheoriginofspecies.Over severalgenerations,biologicalorganismsevolvebasedontheprincipleofnatural selection“survivalofthefittest”toreachcertainremarkabletasks. In nature,an individualin population competes with each otherforvirtual resourceslikefood,shelterand so on.Also in thesamespecies,individuals competetoattractmatesforreproduction. Duetothisselection,poorlyperformingindividualshavelesschancetosurvive, andthemostadaptedor“fit”individualsproducearelativelylargenumberof offspring’s.Itcanalsobenotedthatduringreproduction,arecombinationofthe good characteristicsofeach ancestorcan produce“bestfit”offspring whose fitnessisgreaterthanthatofaparent.Afterafew generations,speciesevolve spontaneouslytobecomemoreandmoreadaptedtotheirenvironment. In 1 975 ,Holland developed thisideain hisbook“Adaptation in naturaland artificialsystems”.Hedescribedhowtoapplytheprinciplesofnaturalevolutionto optimizationproblemsandbuiltthefirstGeneticAlgorithms.Holland’stheoryhas beenfurtherdevelopedandnowGeneticAlgorithms(GAs)standupasapowerful toolforsolvingsearchandoptimizationproblems.Geneticalgorithmsarebased ontheprincipleofgeneticsandevolution. Thepowerofmathematicsliesintechnologytransfer:thereexistcertainmodels andmethods,whichdescribemanydifferentphenomenaandsolvewidevarietyof problems.GAsareanexampleofmathematicaltechnologytransfer:bysimulating evolutiononecansolveoptimizationproblemsfrom avarietyofsources.Today, GAsareusedtoresolvecomplicatedoptimizationproblems,like,timetabling,job shopscheduling,gamesplaying. 2 .ASimpleGeneticAlgorithm Analgorithm isaseriesofstepsforsolvingaproblem.Ageneticalgorithm isa problem solvingmethodthatusesgeneticsasitsmodelofproblem solving.It’sa search technique to find approximate solutions to optimization and search problems. Basically,anoptimizationproblem looksreallysimple. GA handlesa population ofpossible solutions.Each solution isrepresented throughachromosome,whichisjustanabstractrepresentation.Codingallthe possiblesolutionsintoachromosomeisthefirstpart,butcertainlynotthemost straightforwardoneofaGeneticAlgorithm.Asetofreproductionoperatorshasto be determined, too. Reproduction operators are applied directly on the chromosomes,and are used to perform mutations and recombination over solutionsoftheproblem.Appropriaterepresentationandreproductionoperators are really something determinant,as the behaviorofthe GA is extremely dependantonit.Frequently,itcanbeextremelydifficulttofindarepresentation,

whichrespectsthestructureofthesearchspaceandreproductionoperators, whicharecoherentandrelevantaccordingtothepropertiesoftheproblems. Selectionissupposedtobeabletocompareeachindividualinthepopulation. Selectionisdonebyusingafitnessfunction.Eachchromosomehasanassociated valuecorrespondingtothefitnessofthesolutionitrepresents.Thefitnessshould correspondtoanevaluationofhow goodthecandidatesolutionis.Theoptimal solutionistheone,whichmaximizesthefitnessfunction.GeneticAlgorithmsdeal withtheproblemsthatmaximizethefitnessfunction.But,iftheproblem consists inminimizingacostfunction,theadaptationisquiteeasy.Eitherthecostfunction canbetransformedintoafitnessfunction,forexamplebyinvertingit;orthe selection can beadapted in such waythattheyconsiderindividualswith low evaluation functionsasbetter.Oncethereproductionandthefitnessfunctionhavebeen properlydefined,aGeneticAlgorithm isevolvedaccordingtothesamebasic structure.Itstartsbygeneratinganinitialpopulationofchromosomes.Thisfirst populationmustoffer awidediversityofgeneticmaterials.Thegenepoolshouldbeaslargeaspossible sothatanysolutionofthesearchspacecanbeengendered.Generally,theinitial population isgenerated randomly.Then,thegeneticalgorithm loopsoveran iterationprocesstomakethepopulationevolve. Eachiterationconsistsofthefollowingsteps:

  • SELECTION:Thefirststepconsistsinselectingindividualsfor reproduction.Thisselectionisdonerandomlywithaprobability dependingontherelativefitnessoftheindividualssothatbest onesareoftenchosenforreproductionthanpoorones.
  • REPRODUCTION:Inthesecondstep,offspringarebredbythe selectedindividuals.Forgeneratingnewchromosomes,the algorithm canusebothrecombinationandmutation.
  • EVALUATION:Thenthefitnessofthenewchromosomesis evaluated.
  • REPLACEMENT:Duringthelaststep,individualsfrom theold populationarekilledandreplacedbythenewones. Thealgorithm isstoppedwhenthepopulationconvergestoward theoptimalsolution. Thebasicgeneticalgorithm isasfollows:
  • [start]Geneticrandom populationofnchromosomes(suitable solutionsfortheproblem)
  • [Fitness]Evaluatethefitnessf(x)ofeachchromosomexinthe

canbeappliedtoanykindofcontinuousordiscreteoptimizationproblem.Thekey pointto beperformed hereisto identifyand specifyameaningfuldecoding function. 4 .GAs use probabilistic transition operates while conventionalmethods for continuousoptimizationapplydeterministictransitionoperatesi.e.,GAsdoesnot usedeterministicrules. 4 .ApplicationsofGeneticAlgorithm AfewapplicationsofGAareasfollows:

  • Nonlineardynamicalsystems–predicting,dataanalysis
  • Robottrajectoryplanning
  • EvolvingLISPprograms(geneticprogramming)
  • Strategyplanning
  • Findingshapeofproteinmolecules
  • TSPandsequencescheduling
  • Functionsforcreatingimages
  • Control–gaspipeline,polebalancing,missileevasion,pursuit
  • Design–semiconductorlayout,aircraftdesign,keyboard configuration,communicationnetworks
  • Scheduling–manufacturing,facilityscheduling,resource allocation
  • MachineLearning–Designingneuralnetworks,botharchitecture andweights,improvingclassificationalgorithms,classifier systems
  • SignalProcessing–filterdesign
  • CombinatorialOptimization–setcovering,travelingsalesman (TSP),Sequencescheduling,routing,binpacking,graph coloringandpartitioning