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2003 IEEE International Conference on Systems, Man & Cybernetics
Parallel Simulated Annealing with Adaptive
Neighborhood determined by GA
Doshisha University, Kyoto, Japan
Mitsunori MIKI
Tomoyuki HIROYASU
○ Toshihiko FUSHIMI
2003.10.06
Introduction
 Optimization problems become more complicated
and larger.
 Heuristic search
•Simulated Annealing (SA)
based on the simulation of the physical process “annealing”.
•GA, CA, NN etc.
Important matters
1. Parallelization
2. Adaptive parameter tuning
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Algorithm of Simulated Annealing
high
1. Generation
2. Judge
Transition
Energy
Algorithm
low
Design space
3. Cooling
Metropolis probability
good acceptance 1
bad acceptance
-⊿E
)
Temperature
(⊿E = Enext - Enow)
Exp(
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Neighborhood range
The neighborhood range in the continuous Euclid space is the
extent for generating next solution.
Too large neighborhood range
•Can’t search optimum effectively.
•The range has to be small.
Too small neighborhood range
•Often trapped in a local minimum.
•The range has to be large.
Global optimum
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Background
For the control of the neighborhood range, some method are
proposed.
• The adaptive neighborhood mechanism. [Corana 1987]
• The advanced adaptive neighborhood mechanism. [Miki 2002]
These methods control the neighborhood range using
an appropriate acceptance ratio.
This type of adaptive neighborhood method is very effective and useful,
but the target acceptance ratio should be determined experimentally.
Propose a new adaptive neighborhood mechanism
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Purpose
Controlling the neighborhood range adaptively during
the search.
Parallel Simulated Annealing with Adaptive Neighborhood
determined by Genetic Algorithm (PSA/ANGA)
Characteristics
•This method is Parallel model.
•This method parallels neighborhood
ranges on each processes.
•This neighborhood range is controlled
by GA.
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Effect of Neighborhood Ranges
•The neighborhood range has a significant effect on the
accuracy of the solution.
•In order to verify this effect, some numerical experiments
were carried out with various fixed neighborhood ranges.
Fixed neighborhood range
Search space
Neighborhood range
large
Compare the qualities of
the solutions.
Obtain the effect of the
neighborhood ranges.
small
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Test problems
Rastrigin function
Mathematical
test functions
Griewangk function
Rosenbrock function
Rastrigin
Griewangk
Rosenbrock
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Appropriate neighborhood range
The neighborhood range has a significant effect on
the performance of SA.
Rastrigin
Appropriate
neighborhood range
Good solution
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Appropriate neighborhood range
The neighborhood range has a significant effect on
the performance of SA.
Appropriate
neighborhood range
Griewangk
Good solution
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Appropriate neighborhood range
The neighborhood range has a significant effect on
the performance of SA.
Appropriate
neighborhood range
Rosenbrock
Good solution
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Concept of PSA/ANGA
There are the appropriate neighborhood ranges in SA when
solving the continuous optimization problems.
•The appropriate neighborhood ranges depend on problems.
•It is difficult to find the appropriate neighborhood ranges in
advance.
PSA searches the solution with various neighborhood range.
The neighborhood range determined adaptively by GA.
Parallel Simulated Annealing with Adaptive Neighborhood
determined by Genetic Algorithm (PSA/ANGA)
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Algorithms of PSA/ANGA
Multiple SA processes searches the solution with various
1
neighborhood range.
Fitness =
Energy
GA operators are applied on neighborhood ranges.
Neighborhood range
large
small
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Abstract of numerical experiments
PSA/ANGA is compared with a parallel SA with optimum fixed
neighborhood range, PSA/FN.
Comparative method
Optimum fixed neighborhood range
Parallel SA with Fixed Neighborhood (PSA/FN)
Use the optimum fixed neighborhood range
determined by preliminary numerical experiments.
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Parameters used
Functions
Rastrigin
Griewangk
Rosenbrock
Max temperature
10
20
1
Min temperature
0.01
0.001
0.001
Markov length
102400
307200
3072
No. of variable
3
3
3
Cooling rate
0.8
0.7
0.8
Optimum fixed
neighborhood range
1.0
5.5
0.3
No. of processes
32
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Performance of the proposed method
Proposed method
The proposed method, PSA/ANGA, provides better
performance than PSA/FN in all problems.
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
History of Neighborhood range
•History of the neighborhood ranges in 32 SA processes.
•The appropriate neighborhood range varies dynamically during
the search.
Rastrigin
The appropriate neighborhood range is automatically
determined using GA.
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
History of energy (Rastrigin)
•The proposed method, PSA/ANGA, shows fast convergence
of the energy and obtains lower energy than PSA/FN.
•Accuracy of the solution improves because the neighborhood
ranges were changed adaptively.
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
Conclusions
A new Parallel Simulated Annealing method with adaptive
neighborhood range mechanism is proposed.
Parallel SA with Adaptive Neighborhood
determined by Genetic Algorithm (PSA/ANGA)
The appropriate neighborhood range varies according to
the condition of the search.
The proposed method adapts to these appropriate
neighborhood ranges.
PSA/ANGA shows good performance on the some test functions.
The method is effective in SA for continuous optimization
problems.
2003 IEEE International Conference on Systems, Man & Cybernetics
2003.10.06
questions and answers
Thank you for your kind attention.
2003 IEEE International Conference on Systems, Man & Cybernetics