A Multiobjective Evolutionary Algorithm for Finding Knee Regions Using Two Localized Dominance Relationships

In preference-based optimization, knee points are considered the naturally preferred tradeoff solutions, especially when the decision maker has little a priori knowledge about the problem to be solved. However, identifying all convex knee regions of a Pareto front remains extremely challenging, in particular in a high-dimensional objective space. This article presents a new evolutionary multiobjective algorithm for locating knee regions using two localized dominance relationships. In the environmental selection, the $\alpha $ -dominance is applied to each subpopulation partitioned by a set of predefined reference vectors, thereby guiding the search toward different potential knee regions while removing possible dominance resistant solutions. A knee-oriented-dominance measure making use of the extreme points is then proposed to detect knee solutions in convex knee regions and discard solutions in concave knee regions. Our experimental results demonstrate that the proposed algorithm outperforms the state-of-the-art knee identification algorithms on a majority of multiobjective optimization test problems having up to eight objectives and a hybrid electric vehicle controller design problem with seven objectives.