Generational Distance Indicator-Based Evolutionary Algorithm With an Improved Niching Method for Many-Objective Optimization Problems

Abstract

With the number of objectives increasing, the traditional multi-objective evolutionary algorithms (MOEAs) will lead to a reduction of convergence pressure. Specifically, the number of non-dominated solutions in many-objective optimization problems (MaOPs) accounts for the majority of the population. Generational distance (GD) is originally designed to calculate the sum of adjacent distances of solution sets obtained by different algorithms and thus GD is a credible indicator to measure the convergence of many-objective evolutionary algorithms (MaOEAs). In this paper, a GD indicator-based evolutionary algorithm is proposed to solve many-objective optimization problems. First, for the same rank of non-dominated solutions, their adjacent distances are introduced to be the indicator for the selection of the potentially appropriate individuals. Second, in order to maintain good diversity at the same time, an improved niching method based on the angles of candidate solutions is proposed. One solution can only compare the adjacent distance with the solutions in its niche. Solutions are assigned new ranks according to the niching method. Third, in order to eliminate the influence of the order of comparison and assign a higher rank to the solutions with good diversity, a new comparison method is proposed to solve the problem. Finally, the simulation results show that compared with the state of the art algorithms, the proposed algorithm is effective.