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
• Random immigrants to further diversify the
  population

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. GA-4. Do random immigrants if
required. GA-5. If stop criterion is met, stop
else go to GA-2.
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Diversity Measures (1)

• Phenotypes (ptype)
• Genotypes (gtype)

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Diversity Measures (2)

• Standard Deviation (stddev)
• Ancestral id (uid)
• Number of unique ids in the population P.

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Diversity-Fitness Correlations
Ptype rankings vs. fitness rankings
Gtype rankings vs. fitness rankings
Uid rankings vs. fitness rankings
Stddev rankings vs. fitness rankings
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Controlling Diversity with Crossover (PMX)
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Controlling Diversity with Mutation
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Controlling Diversity with Random Immigrants
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Adaptive Control of Diversity

• Adaptive control function
• Oscillation in the feedback control

Mean fitness at various target diversities
Oscillation at different sensitivities ?