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

Abstract

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.