Summary
This chapter investigates the convergence behavior of simple evolutionary algorithms with different selection strategies on a continuous multiobjective model problem. Special focus is given to the problem of controlling the mutation strength, since an adaptation of the mutation strength is necessary to converge to the optimum with arbitrary precision, and to achieve linear convergence order. Adaptive parameter control represents a major research topic in the field of evolutionary computation, and several methods have been proposed and applied successfully for single-objective optimization problems. We demonstrate that the convergence properties achieved by a self-adaptation of the mutation strength on single-objective problems do not carry over to the multiobjective case, if a simple dominance-based selection scheme is used. As a solution, a combined strategy is proposed using dominance-based selection in the archive and scalarizing functions in the working population.
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Laumanns, M. (2005). Self-adaptation and Convergence of Multiobjective Evolutionary Algorithms in Continuous Search Spaces. In: Abraham, A., Jain, L., Goldberg, R. (eds) Evolutionary Multiobjective Optimization. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/1-84628-137-7_3
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DOI: https://doi.org/10.1007/1-84628-137-7_3
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