Global Multiobjective Optimization with Evolutionary Algorithms: Selection Mechanisms and Mutation Control

In this paper we discuss some questions of applying evolutionary algorithms to multiobjective optimization problems with continuous variables. A main question of transforming evolutionary algorithms for scalar optimization into those for multiobjective optimization concerns the modification of the selection step. In an earlier article we have analyzed special properties of selection rules called efficiency preservation and negative efficiency preservation. Here, we discuss the use of these properties by applying an accordingly modified selection rule to some test problems. The number of efficient alternatives of a population for different test problems provides a better understanding of the change of data during the evolutionary process. Also effects of the number of objective functions are treated. We also analyze the influence of the number of objectives and the relevance of these results in the context of the 1/5 rule, a mutation control concept for scalar evolutionary algorithms which cannot easily be transformed into the multiobjective case.

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