Many-Objective Optimization Using Adaptive Differential Evolution with a New Ranking Method

Pareto dominance is an important concept and is usually used in multiobjective evolutionary algorithms (MOEAs) to determine the nondominated solutions. However, for many-objective problems, using Pareto dominance to rank the solutions even in the early generation, most obtained solutions are often the nondominated solutions, which results in a little selection pressure of MOEAs toward the optimal solutions. In this paper, a new ranking method is proposed for many-objective optimization problems to verify a relatively smaller number of representative nondominated solutions with a uniform and wide distribution and improve the selection pressure of MOEAs. After that, a many-objective differential evolution with the new ranking method (MODER) for handling many-objective optimization problems is designed. At last, the experiments are conducted and the proposed algorithm is compared with several well-known algorithms. The experimental results show that the proposed algorithm can guide the search to converge to the true PF and maintain the diversity of solutions for many-objective problems.