A Dimension Convergence-Based Evolutionary Algorithm for Many-Objective Optimization Problems

Abstract

Recently, multi-objective evolutionary algorithms have become the most popular and efficient approach for multi-objective optimization problems involving two and three objectives. However, as the number of objectives increases, the performance of multi-objective evolutionary algorithms tends to deteriorate. This can be mainly attributed to the loss of sufficient selection pressure towards the Pareto front. To address this issue, this paper proposes a dimension convergence-based many-objective evolutionary algorithm to solve many-objective optimization problems (MaOPs). To be specific, a convergence indicator, named dimension convergence, is presented to enhance the selection pressure toward the Pareto front. When the Pareto dominance-based indicator loses the discrimination, the new indicator can further measure the convergence performance of the candidates. Moreover, a new selection strategy is designed to balance the convergence and diversity of the evolutionary process. The mating selection is applied to strengthen the selection pressure, while the environmental selection is developed to comprehensive evaluate the candidates. The proposed algorithm is tested on 36 instances of 12 many-objective benchmarks and compared with five state-of-the-art algorithms. 3 real-world problems are also used to evaluate the performance of the comparison algorithms. Experimental results show that DC-MaOEA is competitive concerning the peer algorithms.