1. Mitsunori MIKI Tomoyuki HIROYASU Takanori MIZUTA
A New Parallel Distributed Genetic Algorithm Applied to Traveling Salesman Problems
Mitsunori MIKI
Tomoyuki HIROYASU
Takanori MIZUTA
Doshisha University
Kyoto, Japan

2. Distributed Genetic Algorithms
Genetic Algorithms(GA)
High computation cost due to many individuals(solutions) and many generations
Parallel processing is required
- Distributed GA with multiple sub-populations(DGA)
A single population is divided into multiple sub-populations
Genetic operation in each sub-populations
Migration of some individuals
Individual
Sub-Population
Migration Scheme
Migrant

3. Background and Purpose
The performance of DGA compared with SPGA(Single population GA)
: High performance
: Higher performance, but difficult to obtain the optimum
For Continuous Optimization Problems
For Combinational Optimization Problems
Rastrigin
TSP (eil51)

4. New Method
Problem in DGA for combinational optimization problems
Difficult to escape from local optima
① The crossover does not work ② The mutation does not yield better solutions
Reasons:
Solution: To construct global optimum solution based on the local optima
The combination of the smallest elements of the local optima is very important
SUCCESSIVE CROSSOVERS WITHOUT SELECTION maximize the diversity of the solution
Centralized Multiple Crossover:CMX

5. Concept of the Proposed Method
Best tour routes(Elitist) in the sub-populations in DGA
Red lines show the optimum elements
The combination of these elements becomes the global solution
Very small partial solutions exist in each elitist solution

6. The elements of the global optimum can be seen in these elitists
Concept (Continued)
　Multiple crossovers without selection is the key of the method
1. Creation of the small elements of the global solution
Conventional DGA or other method(e.g. 2-opt)
2. Combination of the small elements
Eight elitists are superimposed
Perform multiple crossovers without selection in order to maintain the solutions which are to become good solutions
The elements of the global optimum can be seen in these elitists

7. Flowchart of the Proposed Method
Creation of the initial population by the 2-opt method
Initialize
CMX
The elitists of all sub-populations are transferred to the “crossover island”
Successive CMX
Gather the elitists
Repeat the crossover until the size of the population becomes the total population size
Increase the population size
Successive multiple crossover without selection
Centralized Multiple Crossover
Divide the population
Divide the population for DGA
DGA without migration
After final CMX
DGA
iDGA
(isolated DGA)

8. Detail of the Proposed Method
Global Population
Global Population ① ② ④ ③
Crossover Island
① Gather the elitists
② Increase population size by crossover ③ Successive crossovers without selection
④ Divide the population for original DGA population

9. Successive Crossovers without Selection
Crossover operations are repeated
without selection and mutation
Crossover Island
Crossover Island ・
The selection is not performed to maintain the solutions which are to become good solutions afterwards
solution
Local optimum

10. Performance of the Proposed Method
DGA vs. CMX
The repeated number of CMX
The number of the sub-populations
Pop. size
400
Sub-pop 16
1 ‥ worse then DGA
The larger number
Crossover
EXX
Cross Rate
0.8
2, 5 ‥ better then DGA
The higher performance
Mutation
2-change
Mutation rate
1/ L
The performance can be maximized by the parameter tuning
Migration interval
10 Gens.
Mig. rate
0.5
Problem
100 city

11. Crossover Methods in CMX
・ Partially Mapped Crossover ・ Cycle Crossover ・ Subtour Exchange Crossover ・ Edge Exchange Crossover ・ Edge Asembly Crossover
(PMX) (CX) (SXX) (EXX) (EAX)
[Goldberg 85] [Oliver 87] [Yamamura 92] [Maekawa 95] [Nagata 97]
ch150
EXX
EAX
The performance of CMX is increased by using a better crossover method

12. Conclusion and Future Works
Proposed Method(CMX) shows higher performance then conventional DGA
Future works
・ To Examine the parallel model of the proposed method
・ To Apply the proposed method to the other combinational problems