Objective Reduction Algorithm Based on Decomposition and Hyperplane Approximation for Evolutionary Many-Objective Optimization

Objective reduction is an important research direction in many-objective optimization. Through proper algorithm design, it can eliminate some redundant objectives to achieve the effect of greatly simplifying an optimization problem. Among the many- objective optimization problems with redundant objectives, the problems with nonlinear Pareto-Front are the most common and most difficult to tackle. In this paper, an algorithm based on Decomposition and Hyperplane Approximation (DHA) is proposed to deal with objective reduction problems with nonlinear Pareto- Front. The proposed algorithm decomposes a population with nonlinear geometric distribution into several subsets with approximate linear distribution in the process of evolution, and uses a hyperplane with sparse coefficients combined with some perturbation terms to fit these subsets, and then it extractes an essential objective set of original problem based on the coefficients of the fitting hyperplane. In order to test the performance of the proposed algorithm, this study compares it with some state-of- the- art algorithms in the benchmark DTLZ5( I, m), WFG3( I, m) and MAOP(I, m). The experimental results show that the proposed algorithm has good performance both in the problems with linear and nonlinear Pareto-Front.