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Optimization Problem with Simple Genetic Algorithms 2000. 9. 27 Cho, Dong-Yeon

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Presentation on theme: "Optimization Problem with Simple Genetic Algorithms 2000. 9. 27 Cho, Dong-Yeon"— Presentation transcript:

1 Optimization Problem with Simple Genetic Algorithms Cho, Dong-Yeon

2 Function Optimization Problem Example

3 Representation – Binary String Code length

4 Mapping from a binary string to real number

5 Framework of Simple GA Generate Initial Population Evaluate Fitness Select Parents Generate New Offspring Termination Condition? Yes No Fitness Function Crossover, Mutation Best Individual

6 Initial Population Initial population is randomly generated.

7 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.

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9 Selection Fitness proportional (roulette wheel) selection  The roulette wheel can be constructed as follows.  Calculate the total fitness for the population.  Calculate selection probability p k for each chromosome v k.  Calculate cumulative probability q k for each chromosome v k.

10 Procedure: Selection  Generate a random number r from the range [0,1].  If r  q 1, then select the first chromosome v 1 ; else, select the kth chromosome v k (2  k  pop_size) such that q k-1 < r  q k.

11 pkpk qkqk

12 Genetic Operations Crossover  One point crossover  Crossover rate p c Procedure: Crossover  Select two parents.  Generate a random number r c from the range [0,1].  If r c < p c then perform undergo crossover. Mutation  Mutation alters one or more genes with a probability equal to the mutation rate p m.

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14 Experiments Various experimental setup  Termination condition: maximum_generation  2 pop_size (large, small)  5 parameter settings  10 runs  Parameter setting (p c, p m )  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

15 Test Functions Rastrigin’s function

16 Ackley’s function Schwefel’s (sine root) function

17 Results For each test function  Result table for the best solution and your analysis  f opt, (x opt, y opt ), chromosome opt among whole runs  Fitness curve for the run where the best solution was found. Large (pop_size)Small (pop_size) Average  SD BestWorst Average  SD BestWorst Setting 1 Setting 2 Setting 3 Setting 4 Setting 5

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19 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.

20 제출 제출 마감 (10 월 25 일, 수 ): 두 가지 모두 제출 제출물  Source code, 실행 file  Source 에 적절한 comment 작성  File 들은 이나 diskette 에 제출  보고서 : 반드시 인쇄물로 제출  여러 가지 실험 설정에 대한 결과  실험 결과를 다양한 형식으로 표현하여 분석하고 그 결과 를 기술한다.  실행 환경 명시


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