title: Combining convergence and diversity in evolutionary multiobjective optimization.
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 epsilon-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 epsilon-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.
authors.affiliation: Department of Information Technology and Electrical Engineering, Swiss Federal Institute of Technology Zurich, 8092 Zurich, Switzerland. laumanns@tik.ee.ethz.ch
authors.forename: Marco
authors.initials: M
authors.lastname: Laumanns
authors.forename: Lothar
authors.initials: L
authors.lastname: Thiele
authors.forename: Kalyanmoy
authors.initials: K
authors.lastname: Deb
authors.forename: Eckart
authors.initials: E
authors.lastname: Zitzler
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D003198:Computer Simulation; D014644:Genetic Variation; D008954:Models, Biological