A knee-oriented many-objective differential evolution with bi-strategy and Manhattan distance-domination range

Abstract

Differential evolution multi-objective algorithms effectively address problems with two or three objectives. However, many-objective problems with more than three objectives are challenging because of inadequate selection pressure in environment selection, excessive variation in mutation, and difficulties in representing the Pareto front. This paper introduces a novel approach that combines differential evolution with a knee-oriented strategy to address the mentioned challenges. The approach allows the algorithm to focus on trade-off solutions for representing the surface instead of searching the entire Pareto front. Specifically, the algorithm consists of two stages: knee exploration stage and knee exploitation stage. Each stage utilizes different dominance relationships and mutation operators to enhance selection pressure in high-dimensional spaces. Moreover, a Manhattan distance-domination range is designed to update the reference vector by identifying multiple localized knee points in high-dimensional space. The experimental results demonstrate superior performance to other state-of-the-art algorithms on 50 knee-oriented benchmark problem test sets, including CKP, DO2DK, DEB2DK, DEB3DK, and PMOPs.