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Evolutionary Computation

Fall 2002, Vol. 10, No. 3, Pages 263-282
(doi: 10.1162/106365602760234108)
© 2002 Massachusetts Institute of Technology
Combining Convergence and Diversity in Evolutionary Multiobjective Optimization
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Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of ϵ-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of ϵ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.