A Diversitycontrolling Adaptive Genetic Algorithm for Vehicle Routing Problem with Time Windows

1
A Diversity-controlling Adaptive Genetic
Algorithm for Vehicle Routing Problem with
Time Windows

• Kenny Q. Zhu
• Dept of Computer Science
• National University of Singapore
• ICTAI 2003
• November 3, 2003

2
Content

• Background Information
• What is VRPTW?
• The GA Primer
• Adaptive Genetic Algorithm
• Chromosome encoding and decoding
• Initial population and tournament selection
• Genetic operators
• Elite recovery and termination

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Content (contd)

• Adaptive Control of Diversity
• Motivation
• Diversity control
• Experiments
• Solomon benchmark characteristics
• Different target diversity
• Adaptive vs. non-adaptive GA
• Conclusion

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Background Information
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What is VRPTW?

• A depot
• A set of customers
• A fleet of vehicles
• Constraints capacity, trip time, time windows
• Minimize the total distance traveled!

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The GA Primer
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The GA Primer

• A population of individuals, a.k.a. chromosomes
• Genes as genetic blueprints
• A selection strategy to pair the chromosomes for
  reproduction
• Crossover and mutation operations
• New generation replaces the old one
• Goes on and on
• till termination criterion is met

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Adaptive Genetic Algorithm
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Chromosome Encoding

• A solution
• Route 1 0 -gt 3 -gt 2 -gt 4 -gt 5 -gt 0
• Route 2 0 -gt 10 -gt 6 -gt 1 -gt 12 -gt 11 -gt 0
• Route 3 0 -gt 9 -gt 8 -gt 7 -gt 0

• encodes to chromosome
• 3 2 4 5 9 8 7 10 6 1 - 12 - 11

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Chromosome Decoding

• Positions (1) (2) (3) (4) (5) (6)
• Genes 3 2 4 5 1 6
• Possible routes are
• 0 3 0, 0 2 0, 0 4 0, 0 5 0,
• 0 1 0, 0 6 0,
• 0 3 2 0, 0 3 2 4 0, 0 2 4
  0,
• 0 2 4 5 1 0, 0 4 5 1 0,
• 0 1 6 0.

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Chromosome Decoding
(K1)-vertex DAG Weights of the edges Wr 1
dr / dmax Bellman-Ford Algo. O(K3) time to
obtain the best solution
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Initial Population and Selection

• Mix of good and bad individuals
• Good solution from PFIH and its neighbors
• Bad Randomized individuals (?)
• Modified tournament selection

• 1, 2, 3, 4 ? 3, 4, 1, 2
• 1 2 3 4 3 1 4 2
• 2 X 4 3 X 4

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Genetic Operators

• Order-based Crossover
• PMX (Goldberg) 1/2 pc
• Order (Goldberg) 1/2 pc
• Mutation
• One-step route reduction 1/3 pm
• One-step cost reduction 1/3 pm
• Gene relocation 1/3 pm

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Recovery and Termination

• Elite recovery replace the worst 100?
  chromosomes by the best 100? from last
  generation
• Terminate the algorithm after fixed number of
  generations or if solution does not improve for
  some time

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Adaptive Control of Diversity
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Definition of Genotype Diversity
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Motivation
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Effects of Crossover on Diversity
pm0, pc 0.3 0.9
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Effect of Mutation on Diversity
pc 0.7, pm 0 0.7
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Adaptive Control by Crossover and Mutation

• Most effective region of control
• Diversity control function

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Experiments
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Solomon VRPTW Benchmarks
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Different Target Diversities
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Different Target Diversities
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Adaptive vs. Non-adaptive
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Conclusion

• A new adaptive GA for VRPTW based on diversity
  control
• An intuitive integer encoding and unique decoding
  scheme
• Diversity control effective in preliminary
  experimental results