A multiplicative maximin-based evaluation approach for evolutionary many-objective optimization

• Published in: Applied soft computing Vol. 121; p. 108760
• Main Authors: Ma, Jia, Yang, Shujun, Shi, Gang, Ma, Lianbo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2022
• Subjects: M2F-p; Many-objective optimization; Maximin; Multi-objective optimization; M2F-p; Multi-objective optimization; Many-objective optimization; Maximin
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2022.108760

This paper presents a new fitness evaluation approach based on aggregated pairwise comparisons (APC), i.e., a multiplicative maximin fitness ranking indicator with norm-p (M2F-p), for solving multi/many-objective problems. The M2F-p uses an adjustable aggregation of pairwise comparisons induced by p to alleviate the incomparability of solutions in terms of Pareto dominance when the number of objectives increases. We analyze the search ability of M2F-p under different p values. It is shown that the p values can control the shape of contour lines (i.e., a set of equal M2F-p values), which can affect the convergence and uniformity of solutions. Then, we illustrate that the M2F-p offers a set of promising properties that can enhance the discriminability of solutions. Further, we develop an efficient algorithm based on M2F-p by using an adaptive p-selection strategy and a diversity-maintenance mechanism. We conduct experiments on a suit of test problems with up to 10 objectives. The experimental results validate the effectiveness of the proposed algorithm on both multi-objective problems and many-objective problems. •We propose M2F-p with adjustable contour lines and analyze its properties. The p value can adjust the shape of the contour lines (i.e., a set of equal M2F-p values).•Based on M2F-p, an efficient algorithm called M2FMOEA is designed. In detail, an adaptive strategy is devised to select p during the search and a new diversity-based method is used in environmental selection.•The effectiveness and efficiency of M2F-p are verified experimentally. Extensive comparisons and discussions are conducted to show that the algorithm obtains a better performance than compared algorithms.