An Effective and Efficient Evolutionary Algorithm for Many-Objective Optimization

TL;DR

This paper introduces E3A, a new evolutionary algorithm designed for many-objective optimization that improves solution quality and computational efficiency over existing methods, especially for problems with irregular Pareto fronts.

Contribution

The paper proposes a novel population maintenance method inspired by SDE, enhancing selection pressure and efficiency in many-objective evolutionary algorithms.

Findings

E3A outperforms 11 state-of-the-art algorithms in convergence and diversity.

E3A maintains computational efficiency with increasing objectives.

E3A effectively handles irregular Pareto fronts.

Abstract

In evolutionary multiobjective optimization, effectiveness refers to how an evolutionary algorithm performs in terms of converging its solutions into the Pareto front and also diversifying them over the front. This is not an easy job, particularly for optimization problems with more than three objectives, dubbed many-objective optimization problems. In such problems, classic Pareto-based algorithms fail to provide sufficient selection pressure towards the Pareto front, whilst recently developed algorithms, such as decomposition-based ones, may struggle to maintain a set of well-distributed solutions on certain problems (e.g., those with irregular Pareto fronts). Another issue in some many-objective optimizers is rapidly increasing computational requirement with the number of objectives, such as hypervolume-based algorithms and shift-based density estimation (SDE) methods. In this paper, we aim to address this problem and develop an effective and efficient evolutionary algorithm (E3A) that can handle various many-objective problems. In E3A, inspired by SDE, a novel population maintenance method is proposed to select high-quality solutions in the environmental selection procedure. We conduct extensive experiments and show that E3A performs better than 11 state-of-the-art many-objective evolutionary algorithms in quickly finding a set of well-converged and well-diversified solutions.