An R2 Indicator and Decomposition Based Steady-State Evolutionary Algorithm for Many-Objective Optimization

An R 2 indicator based selection method is a major ingredient in the formulation of indicator based evolutionary multiobjective optimization algorithms. The existing classical indicator based selection methodologies have demonstrated an excellent performance to solve low-dimensional optimization problems. However, the R 2 indicator based evolutionary multiobjective optimization algorithms encounter enormous challenges in high-dimensional objective space. Our main purpose is to explore how to extend the R 2 indicator to handle many-objective optimization problems. After analyzing the R 2 indicator, the objective space partition strategy, and the decomposition method, we propose a steady-state evolutionary algorithm based on the R 2 indicator and the decomposition method, named, R 2 -MOEA/D, to obtain well-converged and well-distributed Pareto front. The main contribution of this paper contains two aspects. (1) The convergence and diversity for the R 2 indicator based selection are analyzed. Two improper selection situations will be properly solved via applying the decomposition method. (2) According to the position of a new individual in the steady-state evolutionary algorithm, two different objective space partition strategies and the corresponding selection methods are proposed. Extensive experiments are conducted on a variety of benchmark test problems, and the experimental results demonstrate that the proposed algorithm has competitive performance in comparison with several tailored algorithms for many-objective optimization.