Abstract
In preference based optimization, knee points are considered the naturally preferred trade-off 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 paper presents a new evolutionary multi-objective algorithm for locating knee regions using two localized dominance relationships. In the environmental selection, the -dominance is applied to each subpopulation partitioned by a set of predefined reference vectors, thereby guiding the search towards 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 multi-objective optimization test problems having up to eight objectives and a hybrid electric vehicle controller design problem with seven objectives.