Evolutionary Computation and Convergence to a Pareto Front
نویسندگان
چکیده
Research into solving multiobjective optimization problems (MOP) has as one of its an overall goals that of developing and defining foundations of an Evolutionary Computation (EC)-based MOP theory. In this paper, we introduce relevant MOP concepts, and the notion of Pareto optimality, in particular. Specific notation is defined and theorems are presented ensuring Paretobased Evolutionary Algorithm (EA) implementations are clearly understood. Then, a specific experiment investigating the convergence of an arbitrary EA to a Pareto front is presented. This experiment gives a basis for a theorem showing a specific multiobjective EA statistically converges to the Pareto front. We conclude by using this work to justify further exploration into the theoretical foundations of EC-based MOP solution methods.
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