Evolution Strategy-Based Many-Objective Evolutionary Algorithm Through Vector Equilibrium

Abstract

In recent years, numerous many-objective evolutionary algorithms (MaOEAs) have been developed to search for well-diversified and well-converged Pareto optimal solutions for high-dimensional many-objective optimization problems (MaOPs). However, existing MaOEAs have to tackle some daunting challenges, including the emergence of dominance resistance solutions, effective diversity preservation scheme, management of a large population size, extremely high computational complexity, sensitivity to the shape of Pareto front (PF), and overly relying on high-quality reference points. In this article, we present an evolution strategy (ES) for solving MaOPs, called MaOES, which can solve these challenges efficiently and effectively. Inspired by the Vector Equilibrium phenomenon in magnetic fields, isotropic magnetic particles would automatically repel from each other, keep the uniform distance from the nearest neighbors, and extend the entire magnetic fields as far as possible, all at the same time. In the proposed algorithm, an efficient self-adaptive Precision-Controllable Mutation operator is designed for individuals to explore and exploit the decision space. In addition, the Maximum Extension Distance strategy, which emulates the isotropic magnetic particle behavior in a magnetic field, is developed to guide individuals to keep uniform distance and extension to approximate the entire PF. As a result, the MaOES can obtain a well-converged and well-diversified PF with much less population size and far lower computational complexity. The larger the number of individuals, the sharper the contour the resulting approximate PF will be. Finally, the proposed algorithm is evaluated by the scalable MaOPs test suites on DTLZ and WFG. The experimental results have been demonstrated to provide a competitive and oftentimes better performance when compared against some chosen state-of-the-art MaOEAs.