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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 80
PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 101
Multiobjective Optimization Algorithms using Evolution Strategy T.Y. Chen and Y.S. Hsu
Department of Mechanical Engineering, National Chung Hsing University, Taichung, Taiwan Full Bibliographic Reference for this paper
T.Y. Chen, Y.S. Hsu, "Multiobjective Optimization Algorithms using Evolution Strategy", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Fourth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 101, 2004. doi:10.4203/ccp.80.101
Keywords: multiobjective optimization, evolution strategy, rank-niche fitness function.
Summary
Many evolution-based algorithms have been developed to solve optimization
problems in recent years. Most of these algorithms were based on genetic
algorithms(GA). Owing to the nature of simultaneous searches from many points in
the design space, the evolution-based solvers are deemed to be better than
mathematical programming methods to locate the global optimum solution. Since the
evolution algorithms search the design space from many different points, they have
another advantage to find Pareto-optimal solutions for multiobjective optimization
problems in a single run. The efficiency of these evolution-based methods in finding
Pareto-optimal solutions is in general better than mathematical programming
methods. Fonseca and Fleming [1] gave an overview of evolutionary algorithms in
multiobjective optimization and classified those approaches into three categories:
the plain aggregating approach, the population-based non-Pareto approach and the Pareto based
approach. In general the last category generates the best results.
The evolution strategy(ES) which was developed by Rechenberg [2] in 1973 is another important evolutionary algorithm other than the GA. Three evolutionary steps are included in ES. The first one is recombination which blends genetic materials from two randomly chosen individuals from the parent generation. The second step is mutation which causes self change of genetic materials based on the random number of a normal distribution. The last step is selection which chooses the best individuals resulted from previous two evolution steps to survive. The key step to generate many converged and evenly distributed Pareto-optimal solutions is in the selection step. This paper proposes the following fitness function to be used as the selection basis.
where ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() Preliminary results show this approach indeed generates many evenly distributed Pareto-optimal solutions on the Pareto front for several test problems. References References
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