Optimization Problem with Simple Genetic Algorithms

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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)

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