M Mutation() 16888 E077 (no ) too little mutation leads to an impoverished genetic pool with increasing number of generations dilemma Too much mutation decreases convergence rate and undermines fitness-based selection bias What is mutation?. a genetic operator Modifies chromosomes to restore diversity Permit random changes in a member of a population Examples with probability 1 20 randomly flip a single bit of a solution from o to 1 or 1 to o probability of mutation often called"mutation rate expressing the probability Pm that a bit is changed C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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M Example with Mutation 16888 ESD.77 Improved population fitness with 1% mutation rate Original gen 5th gen 10th gen 10011 11011 11111 01000 10111 11111 00001 11111 11011 00000 01110 11111 11011 11111 Avg Fitness Avg Fitness Avg. Fitness 2.6 4.8 49 C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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M Example without Mutation 16888 E077 Stagnant population with 0% mutation rate Original gen 5th gen 10th gen No“1 1001 11011 11011 01000 10011 11011 00001 11011 11011 Cal 00000 01010 1101 Never 110h1 11011 1 Achieve 11111 Avg Fitness Avg Fitness Avg. Fitness 2.6 3.2 4.0 C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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Mutation( 16888 ESD.77 EXample: eneration: 20 Before mutation 010111000 After mutation 010101000 Mutation rate can be variable usually gradually decreasing with increasing number of generations) 21 Mutation rate is an important tuning knob"for a GA Generation C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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GA Convergence 16888 E077 global ypIcal Results optimum Average (unknown) Fitness Converged too fast(mutation rate too small? generation Average performance of individuals in a population is expected to increase, as good individuals are preserved and bred and less fit individuals die out C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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