A hypervolume fraction-based adaptive evolutionary algorithm for many-objective optimization and the application to electromagnetic device design

Abstract

Performance of many-objective evolutionary algorithms (MaOEAs) heavily depends on the environmental selection strategy which determines the offspring for next generations. One kind of selection strategy may only suit certain kinds of optimization problems. Moreover, one single strategy might not always work well at different evolutionary stages. To adaptively adjust the environmental selection strategy, this paper proposes a hypervolume fraction-based adaptive evolutionary algorithm (HFAEA). First, a hypervolume fraction-based estimation method is proposed to address the difficulty in detecting the feature of Pareto front. It calculates the ratio of the hypervolume of population coverage to the hypervolume of coordinate axis coverage. With a small or large hypervolume fraction, Pareto front is regarded as irregular or regular respectively and an adaptive switching strategy adaptively selects a proposed vector angle-based strategy or an improved reference vector-based strategy. HFAEA is compared with five state-of-the-art algorithms on 24 problems with a large hypervolume fraction and 24 problems with a small hypervolume fraction. Experimental results show that HFAEA is the most competitive in handling different kinds of problems. It outperforms algorithms that designed for irregular problems as well as algorithms that use uniformly distributed reference vectors in irregular problems. These findings highlight the effectiveness of the proposed hypervolume fraction-based estimation method. The superior performance is also demonstrated in two electromagnetic device optimization problems, including the designs of a compact single-layer butler matrix and a broadband filtering power divider, where better results than original ones are achieved and HFAEA also outperforms state-of-the-art MaOEAs.