Angle-Based Crowding Degree Estimation for Many-Objective Optimization

Many-objective optimization, which deals with an optimization problem with more than three objectives, poses a big challenge to various search techniques, including evolutionary algorithms. Recently, a meta-objective optimization approach (called bi-goal evolution, BiGE) which maps solutions from the original high-dimensional objective space into a bi-goal space of proximity and crowding degree has received increasing attention in the area. However, it has been found that BiGE tends to struggle on a class of many-objective problems where the search process involves dominance resistant solutions, namely, those solutions with an extremely poor value in at least one of the objectives but with (near) optimal values in some of the others. It is difficult for BiGE to get rid of dominance resistant solutions as they are Pareto nondominated and far away from the main population, thus always having a good crowding degree. In this paper, we propose an angle-based crowding degree estimation method for BiGE (denoted as aBiGE) to replace distance-based crowding degree estimation in BiGE. Experimental studies show the effectiveness of this replacement.