Scored Pareto MEC for Multi-Objective Optimization and Its Convergence

In this paper, a new evolutionary optimization algorithm named Scored Pareto Mind Evolutionary Computation (SP-MEC) is proposed, which embeds the theory of Pareto and information of density into the Mind Evolutionary Computation (MEC) in order to deal with multi-objective optimization problems. Taking advantage of two unique operations, similartaxis and dissimilation, the MEC is an efficient optimization algorithm combining the global search with local search. Thus SP-MEC can further effectively converge to the Pareto front, and achieve the high-quality trade-off front for multi-objective optimization. The features of the proposed SP-MEC are the employments of the relation of Pareto and density information of individuals. Therefore, the optimal solutions acquired by our SP-MEC distribute uniformly on the Pareto front. The feasibility and efficiency of this SP-MEC are demonstrated using numerical examples. The convergence of the sequence of populations generated from the similartaxis operation is also analyzed under certain conditions.

I. Introduction

As we know, numerous optimization problems in scientific research and engineering are multi-objective optimization problems. It has been proved that the Evolutionary Algorithm (EA) is a powerful solution to this kind of problems. The underlying reasons are, firstly, the EA uses chromosome-based populations, and allows the generation of several members of the Pareto optimal set in a single run. Secondly, the EA is less susceptible to the shape or continuity of the Pareto front. Schaffer applied the EA to deal with multi-objective optimization problems in 1984^[1]. During the past decade, a lot of similar methods have also been proposed, and the Multi-Objective Evolutionary Algorithm (MOEA) becomes a typical approach.