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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

Optimization Problem with Simple Genetic Algorithms

2000. 9. 27

Cho, Dong-Yeon

(dycho@scai.snu.ac.kr)

slide5

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
  • Initial population is randomly generated.
fitness evaluation
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
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.
slide10
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
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
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
Test Functions
  • Rastrigin’s function
slide16
Ackley’s function
  • Schwefel’s (sine root) function
results
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
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.
slide20
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