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One of the main difficulties in solving many-objective optimization is the lack of selection pressure. For an optimization problem, its main purpose is to obtain a nondominated solution set with better convergence and diversity. In this paper, two estimation methods are proposed to convert a many-objective optimization problem into a simple bi-objective optimization problem, that is, the convergence and diversity estimation methods, so as to greatly improve the probability of certain dominance relation between solutions, and then increase the selection pressure. Based on the proposed estimation methods, a new many-objective evolutionary algorithm, termed ABOEA, is proposed. In the convergence estimation method, we use a modified ASF function to solve the performance degradation of the traditional norm distance on the irregular Pareto front. In the diversity estimation method, we innovatively propose a diversity estimation method based on the angle between solutions. Empirical experimental results demonstrate that the proposed algorithm shows its competitiveness against the state-of-art algorithms in solving many-objective optimization problems. Two estimation methods proposed in this paper can greatly improve the performance of algorithms in solving many-objective optimization problems.

An Angle-Based Bi-Objective Evolutionary Algorithm for Many-Objective Optimization