A New Parallel Distributed Genetic Algorithm Applied to Traveling Salesman Problems

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A New Parallel Distributed Genetic Algorithm
Applied to Traveling Salesman Problems

• Mitsunori MIKI
• Tomoyuki HIROYASU
• Takanori MIZUTA

Doshisha University
Kyoto, Japan
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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
Migrant
Migration Scheme
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Background and Purpose
The performance of DGA compared withSPGA(Single
population GA)
High performance Higher performance, but
difficult to obtain the optimum
For Continuous Optimization Problems For
Combinational Optimization Problems
TSP (eil51)
Rastrigin
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New Method
Problem in DGA for combinational optimization
problems
Difficult to escape from local optima
? The crossover does not work? 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 CrossoverCMX
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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
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Concept (Continued)
Multiple crossovers without selection is the key
of the method
1. Creation of the smallelements 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
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Flowchart of the Proposed Method
Initialize
Creation of the initial population by the 2-opt
method
Successive CMX
The elitists of all sub-populations are
transferred to the crossover island
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
(isolated DGA)
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Detail of the Proposed Method
?
?
?
?
Crossover Island
? Gather the elitists
? Increase population size by crossover?
Successive crossovers without selection
? Divide the population for original DGA
population
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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
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Performance of the Proposed Method
DGA vs. CMX
The repeated number of CMX
The number ofthe sub-populations
Pop. size
400
Sub-pop
16
1 ? worse then DGA
The larger number
EXX
Crossover
Cross Rate
2, 5 ? better then DGA
0.8
The higher performance
2-change
Mutation
Mutation rate
1/ L
The performance can be maximized by the parameter
tuning
10 Gens.
Migration interval
0.5
Mig. rate
100 city
Problem
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Crossover Methods in CMX
ch150
EXX
EAX
The performance of CMX is increasedby using a
better crossover method
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Conclusion and Future Works
Conclusion
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