Combining convergence and diversity in evolutionary multiobjective optimization

  • Authors:

  • Marco Laumanns;Lothar Thiele;Kalyanmoy Deb;Eckart Zitzler

  • Affiliations:

  • Department of Information Technology and Electrical Engineering, Swiss Federal Institute of Technology Zurich, 8092 Zurich, Switzerland;Department of Information Technology and Electrical Engineering, Swiss Federal Institute of Technology Zurich, 8092 Zurich, Switzerland;Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, PIN 208 016, India;Department of Information Technology and Electrical Engineering, Swiss Federal Institute of Technology Zurich, 8092 Zurich, Switzerland

  • Venue:
  • Evolutionary Computation
  • Year:
  • 2002

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Abstract

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.