A Bi-Population Based Multi-Objective Evolutionary Algorithm Using Hybrid Identification Method for Finding Knee Points

In the preference-based multi-objective optimization, decision makers may be interested in only a part of the representative solutions and hardly specify their preferences. In this case, knee points are considered as the naturally preferred trade-off solutions. Most research utilizes the trade-off information or certain properties to find knee points. However, little attention has been paid to combine them to further enhance the knee identification. This paper proposes a multi-objective evolutionary algorithm using a hybrid identification method and a bi-population structure to find knee points. The hybrid identification method is based on the localized α-dominance and the distance to the hyperplane. Firstly, two populations are partitioned by a set of predefined reference vectors and apply the localized α-dominance to guide the search towards potential knee regions. Then knee solutions are detected based on the distance to hyperplane constructed by the extreme points. Finally in the environmental selection, a niche-preserving operation is applied to take the knee solutions of all sub-populations into account. The first population is the main part of the search, and affects the offspring generation and environmental selection of the second population. The experiments demonstrate that the proposed method is effective and competitive in identifying knee solutions.