Empirical Study of Population Diversity in Permutationbased Genetic Algorithm

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Empirical Study of Population Diversity in
Permutation-based Genetic Algorithm

• Kenny Q. Zhu and Ziwei Liu
• Department of Computer Science
• National University of Singapore
• kzhu_at_comp.nus.edu.sg
• lziwei_at_hotmail.com

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Introduction (1)

• Traditional GA are bit-encoded, and crossover are
  based on cutting and swapping
• 0010010 100010 0010010
  001100
• 1001001 001100 1001001
  100010
• Permutation-based GA are integer encoded and the
  crossover and mutation give a permutation of the
  original encoding (e.g. PMX)
• 0 3 5 4 2 8 1 7 6 0 0 3 5 4 2 1 7 6 8 0
• 0 1 2 4 7 6 3 8 5 0 0 1 2 4 7 8 6 3 5 0
• Examples of Permutation-based GA GA for
  Traveling Salesman Problem (TSP) and GA for
  Vehicle Routing Problem (VRP VRPTW)

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Introduction (2)

• Diversity Measures
• Variance of fitness
• Uncertainty
• Evolution history
• Distance
• Epistasis
• Phenotype/genotype space
• Maintenance of Diversity
• Crowding and preselection
• Self-adapting mutation rates
• And others.

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Canonical GA for TSP/VRP

• String of integers of length K as a chromosome.
• A problem-specific decoding algorithm
• Tournament selection
• Crossover Order (OX), Partially-matched (PMX)
  and Cycle (CX)
• Mutation sequence insertion

GA-1. Initialize population GA-2. Decode
population in fitnesses. Set crossover rate pc
and mutation rate pm GA-3. Select parents,
crossover and mutate, and replace the old
generation