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Optimization Problem with Simple Genetic Algorithms. 2000. 9. 27 Cho, Dong-Yeon (dycho@scai.snu.ac.kr). Function Optimization Problem. Example. Representation – Binary String. Code length. Mapping from a binary string to real number. Framework of Simple GA. Generate Initial Population.
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Optimization Problem with Simple Genetic Algorithms 2000. 9. 27 Cho, Dong-Yeon (dycho@scai.snu.ac.kr)
Function Optimization Problem • Example
Representation – Binary String • Code length
Framework of Simple GA Generate Initial Population Fitness Function Evaluate Fitness Termination Condition? Yes Best Individual No Select Parents Crossover, Mutation Generate New Offspring
Initial Population • Initial population is randomly generated.
Fitness Evaluation • Procedure: Evaluation • Convert the chromosome’s genotype to its phenotype. • This means converting binary string into relative real values. • Evaluate the objective function. • Convert the value of objective function into fitness. • For the maximization problem, the fitness is simply equal to the value of objective function. • For the minimization problem, the fitness is the reciprocal of the value of objective function.
Selection • Fitness proportional (roulette wheel) selection • The roulette wheel can be constructed as follows. • Calculate the total fitness for the population. • Calculate selection probability pk for each chromosome vk. • Calculate cumulative probability qk for each chromosome vk.
Procedure: Selection • Generate a random number r from the range [0,1]. • If r q1, then select the first chromosome v1; else, select the kth chromosome vk (2 k pop_size) such that qk-1< r qk.
Genetic Operations • Crossover • One point crossover • Crossover rate pc • Procedure: Crossover • Select two parents. • Generate a random number rc from the range [0,1]. • If rc< pc then perform undergo crossover. • Mutation • Mutation alters one or more genes with a probability equal to the mutation rate pm.
Experiments • Various experimental setup • Termination condition: maximum_generation • 2 pop_size (large, small) 5 parameter settings 10 runs • Parameter setting (pc, pm) • Elitism • The best chromosome of the previous population is just copied. • At least two test functions • Example function given here (*) - maximization • Rastrigin’s function –minimization • Ackley’s function – minimization • Schwefel’s (sine root) function – minimization
Test Functions • Rastrigin’s function
Ackley’s function • Schwefel’s (sine root) function
Results • For each test function • Result table for the best solution and your analysis • fopt, (xopt, yopt), chromosomeopt among whole runs • Fitness curve for the run where the best solution was found.
References • Source Codes • Simple GA code • GA libraries • Web sites • Books • Genetic Algorithms and Engineering Design, Mitsuo Gen and Runwei Cheng, pp. 1-15, John Wiley & Sons, 1997.
제출 • 제출 마감 (10월 25일, 수): 두 가지 모두 제출 • 제출물 • Source code, 실행 file • Source에 적절한 comment 작성 • File들은 e-mail이나 diskette에 제출 • 보고서: 반드시 인쇄물로 제출 • 여러 가지 실험 설정에 대한 결과 • 실험 결과를 다양한 형식으로 표현하여 분석하고 그 결과를 기술한다. • 실행 환경 명시