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A Study of Mutation Methods for Evolutionary Algorithms

A Study of Mutation Methods for Evolutionary Algorithms. Andreas Koenig December 6, 2002 CS 447- Advanced Topics in Artificial Intelligence. Objective. Find a mutation operator to quickly converge to local minimum (maximum)

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A Study of Mutation Methods for Evolutionary Algorithms

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  1. A Study of Mutation Methods for Evolutionary Algorithms Andreas Koenig December 6, 2002 CS 447- Advanced Topics in Artificial Intelligence

  2. Objective • Find a mutation operator to quickly converge to local minimum (maximum) • Introduce and compare the effectiveness of various types of mutation operators for evolutionary algorithms • Apply one of these mutation operators to maximize the output current of an automotive alternator

  3. Evolutionary Algorithms 1. Create Population 2. Evaluate Fitness 4. Recombine Parents (Optional) 3. Select Parents 5. Mutate Offspring 6. Evaluate Offspring 7. Select New Population

  4. 5. Mutate Offspring • Combination of Evolutionary Strategies (ES) & Evolutionary Programming (EP) • Fundamental Equations: • where: • n = number of x’s in member • D = random number • N(0,1) = Gaussian random number with mean = 0, variance = 1

  5. Mutation Operators • Random Distributions: • Gaussian • Classical Evolutionary Programming (CEP) • Cauchy • Fast Evolutionary Programming (FEP) • Xin Yao and Yong Liu • Combined Gaussian-Cauchy • Mean Mutation Operator (MMO) • Adaptive Mean Mutation Operator (AMMO) • Kumar Chellapilla • Adaptive Lévy • Chang-Yong Lee and Xin Yao

  6. Mutation Operator: Gaussian (CEP) • Gaussian Probability Density Function:

  7. Mutation Operator: Cauchy (FEP) • Cauchy Probability Density Function:

  8. Mutation Operator: Combined Gaussian & Cauchy (MMO,AMMO) • Mean Mutation Operator (MMO) Mutation Procedure: • Adaptive Mean Mutation Operator (AMMO) Mutation Procedure:

  9. Mutation Operator: Adaptive Lévy • Lévy Probability Density Function: • Mutation Procedure Changes: • 4 offspring created from each parent using α = 1.0, 1.3, 1.7 and 2.0 • Most fit offspring is chosen for competition • ¼ Population is used to help match computational time of other methods

  10. Mutation Operator: Adaptive Lévy • Lévy Probability Density Function:

  11. Experimental Parameters • Same initial population was used for each run of a given function

  12. Results

  13. Results

  14. Results • FEP, MMO and AMMO are generally fastest

  15. Rotor Tip Height Rotor Tip Width Machine Optimization • Claw Pole Alternator: • Maximize DC Output Current • Machine Parameters

  16. Machine Optimization Results • FEP Parameters

  17. Machine Optimization Results

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