Title: A Diversitycontrolling Adaptive Genetic Algorithm for Vehicle Routing Problem with Time Windows
1A 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
2Content
- 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
3Content (contd)
- Adaptive Control of Diversity
- Motivation
- Diversity control
- Experiments
- Solomon benchmark characteristics
- Different target diversity
- Adaptive vs. non-adaptive GA
- Conclusion
4Background Information
5What is VRPTW?
- A depot
- A set of customers
- A fleet of vehicles
- Constraints capacity, trip time, time windows
- Minimize the total distance traveled!
6The GA Primer
7The 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
8Adaptive Genetic Algorithm
9Chromosome 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
10Chromosome 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.
11Chromosome Decoding
(K1)-vertex DAG Weights of the edges Wr 1
dr / dmax Bellman-Ford Algo. O(K3) time to
obtain the best solution
12Initial 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
13Genetic 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
14Recovery 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
15Adaptive Control of Diversity
16Definition of Genotype Diversity
17Motivation
18Effects of Crossover on Diversity
pm0, pc 0.3 0.9
19Effect of Mutation on Diversity
pc 0.7, pm 0 0.7
20Adaptive Control by Crossover and Mutation
- Most effective region of control
- Diversity control function
21Experiments
22Solomon VRPTW Benchmarks
23Different Target Diversities
24Different Target Diversities
25Adaptive vs. Non-adaptive
26Conclusion
- 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