Hongfeng Wang Pusan, Korea

 Introduction  General framwork of GA  An example of GA programming 2

 GA is a population-based, iterative stochastic optimization method.  Population-based: GA employs a population of chromosomes to search for the optimum in the solution space in parallel. Each chromosome corresponds to a solution.  Iterative: GA is running during a iterative course. The algorithm result can be obtained by the best chromosome in the population at the last iteration (generation) until this iteration is terminated.  Stochastic: All GA operators (crossover, mutation and selection) are designed in a probability mechanism. 3

 Then, GA is called as a meta-heuristic method  GA cannot ensure the optimal solution is achieved. It just can achieve a high quality solution within an acceptive compute time.  GA uses a non-determinate way when its chromosome are searching for optimum. 4

5 begin parameterize(popsize, pc, pm); t = 0; initializePopulation(P(0)); evaluatePopulation(P(0)); repeat P’(t) = selectForReproduction(P(t)); P’’(t) = crossover(P’(t)); mutate(P’’(t)); evaluatePopulation(P’’(t)); P(t+1) = selectForProceed(P(t)+P’’(t)); t = t+1; until a stop condition is met end

 Test function  One-Max function: It is a 100-bit binary function, which aims to maximize the number of ones in a binary string.  Algorithm design  Binary encoding scheme  Tournament selection method where the tournament size is set to 2  One-point crossover where the probability pc is set to 0.8  Bit-wise mutation where the probability pm is set to

 Chromosome  Define a class to express a chromosome  Attributes: code and fitness  Methods: initialize(), evaluate(), clone() and mutate(); 7

Class Chromosome{ int[] code; int fitness; public Chromosome(int length){ code=new int[length]; fitness=0; // this is a constructive method for class Chromosome, which aims to initialize the // values of two attributes (code and fitness) in Chromosome } void initialize(){ … } void evaluate(){ … } void clone(Chromosome chr){ … } void mutate(double pm){ … } void toprint(){ … } } 8

Class Chromosome{ … void initialize(){ for(int i=0;i<code.length;i++){ if(Math.random()<0.5){ code[i]=0; } else{ code[i]=1; } } void evaluate(){ fitness=0; for(int i=0;i<code.length;i++) {fitness+=code[i]; } } … } 9

Class Chromosome{ … void clone(Chromosome chr){ for(int i=0;i<code.length;i++){ code[i]=chr.code[i]; } fitness=chr.fitness } void mutate(double pm){ for(int i=0;i<code.length;i++) { if(Math.random()<pm){ code[i]=1-code[i]; } } void toprint(){ … } } 10

 GA  a main class to execute GA  Attributes: length, popsize, max_gen, elite_num, pc, pm, old_pop, new_pop, pool_pop, good_chr, best_chr  Methods: initializePop(), selectChr(), crossover(), sort() and run(); 11

Class GA{ int length=100,popsize=100,max_gen=200,elite_num=0; double pc=0.8, pm=0.01; Chromosome[] old_pop,new_pop,pool_pop; Chromosome good_chr,best_chr; public GA(){ … // this is a constructive method for a class (GA), which aims to initialize the values of // all attributes (code and fitness) in GA } void initializePop(){ … } void run(){ … } void sort(Chromosome[] pop){ … } int selectChr(Chromosome[] pop){ … } void crossover(Chromosome chr1, Chromosome chr2){ … } } 12

Class GA{ … public GA(){ old_pop=new Chromosome[popsize]; new_pop=new Chromosome[popsize]; for(int i=0;i<popsize;i++){ old_pop[i]=new Chromosome(length); new_pop[i]=new Chromosome(length); } pool_pop=new Chromosome[popsize+elite_num]; for(int i=0;i<pool_pop.length;i++){ pool_pop [i]=new Chromosome(length); } good_chr=new Chromosome(length); best_chr=new Chromosome(length); } … } 13

Class GA{ … void initializePop(){ for(int i=0;i<popsize;i++){ old_pop[i].initialize(); old_pop[i].evaluate(); } … } 14

Class GA{ … void run(){ initializePop(); sort(old_pop); good_chr.clone(old_pop[0]); best_chr.clone(good_chr); for(int gen=1;gen<max_gen;gen++){ for(int i=0;i<popsize;i++){ new_pop[i].clone(old_pop[selectChr(old_pop)]); } for(int i=0;i<popsize/2;i++){ if(Math.random()<pc){ crossover(new_pop[2*i], new_pop[2*i+1]); } } for(int i=0;i<popsize;i++){ new_pop[i].mutate(pm); } for(int i=0;i<popsize;i++){ new_pop[i].evaluate(); } for(int i=0;i<popsize;i++){ pool_pop[i].clone(new_pop[i]); } for(int i=0;i<elite_num;i++){ pool_pop[popsize+i].clone(old_pop[i]); } sort(pool_pop); for(int i=0;i<popsize;i++){ old_pop[i].clone(pool_pop[i]); } good_chr.clone(old_pop[0]); if(good_chr.fitness>best_chr.fitness){ best_chr.clone(good_chr); } } best_chr.toprint(); } … } 15

Class GA{ … void sort(Chromosome[] pop){ … // this method is used to sort a set of chromosomes in descending order } int selectChr(Chromosome[] pop){ int n1=(int)(popsize*Math.random()),n2; do{ n2 =(int)(popsize*Math.random()); }while(n1==n2); if(pop[n1].fitness>pop[n2].fitness){ return n1; } else{ return n2; } } … } 16

Class GA{ … void crossover(Chromosome chr1, Chromosome chr2){ Chromosome chi1=new Chromosome(length), chi2=new Chromosome(length); int n=(int)(length*Math.random()); for(int i=0;i<n;i++){ chi1.code[i]=chr1.code[i]; chi2.code[i]=chr2.code[i]; } for(int i=n;i<length;i++){ chi1.code[i]=chr2.code[i]; chi2.code[i]=chr1.code[i]; } chr1.clone(chi1); chr2.clone(chi2); } … } 17

Class GA{ … public void static main(String[] args){ GA ga=new GA(); ga.run(); } … } 18

Production System Analysis Lab. Pusan National University, Busan, Korea