Convergence of multi-objective evolutionary algorithms to a uniformly distributed representation of the Pareto front

  • Authors:

  • Yu Chen;Xiufen Zou;Weicheng Xie

  • Affiliations:

  • School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent.