Genetic Algorithms (GA).ppt

icAlgorithms(GA)“survivaloffittest”.GAoriginallydevelopedbyJohnHolland(1975)GA–generalconceptsIterativeprocedure(iterativeimprovement)Producesaseriesof“generationsofpopulations”oneperiterationEachmemberofapopulationrepresentsafeasiblesolution,(mating)p1123KmevolutionChromosome-afeasiblesolutionSelectioncrossovermutationPkP3ThepopulationduringiterationofGAisdenotedbythe“bag”Pi={X1i,X2i,……..,Xni}.;isabag,notaset,hencecancontainrepeatedsolutions,,maybecreatedrandomlyorbyadeterministic(constructive)(x)(x)>=(x)=1/1+cost(x),thusVx,0<=fitness(x)<=-fitness(Pi)=Σfitness(xji)Best-fitness(Pi)=max{fitness(xji)}GoingfromP1toP2toP3…..iscalled“evolution”.Goal:ensurethatitishighlylikelythataverage-fitness(Pi)>average-fitness(Pj)fori>+:“highlyfit“(imaginary)=>37%-----------%D2%10%F20%E33%B14%C1)Whenwheelisturnedandeventuallystops,probabilityofstoppingatAis2)Thefunctionselect-roulette(f)spinsroulettewheelbyarandomdegree(uniformbetween0and2)andreturnsachromosome–theone(chromosome)SayXaandXbusingselect-roulette().Divideparentsintotwoparts;Xa<Xa1,Xa2>Xb<Xb1,Xb2>Exchangetoget<Xa1,Xb2><Xb1,Xa2>:;100011;1110ya;100011;1010Xb;101010;1010yb;101010;1110