A Novel Nonlinear Expanded Dominance Relation Based Evolutionary Algorithm for Many-Objective Optimization Problems

Abstract

Multi-objective optimization problems exist widely in scientific research and engineering applications. With the number of objectives increasing, the proportion of non-dominated individuals in the population of many-objective optimization problems increases sharply, resulting in a reduction of convergence pressure of the traditional multi-objective optimization algorithms. In some cases, the optimal solutions may be located in the special regions, such as many discrete regions and the regions with very few feasible solutions. In this case, the existing nonlinear expanded evolutionary algorithm can not find the true Pareto fronts. To address the limitation, a novel nonlinear expanded dominance relation based manyobjective evolutionary algorithm is proposed to handle many-objective optimization problems. Experimental results show that compared with the state of art algorithms, the proposed algorithm is effective for DTLZs, in terms of IGD, PD and GD metrics.

Evolutionary Many‐objective Optimization: Difficulties, Approaches, and Discussions

“…A controlled SDR (CSDR) [25] complies with Pareto dominance, uses generalized convergence criteria with a parameter, and adjusts this parameter and the niche angle during the search. A similar niche angle was also employed in nonlinear expanded dominance (NED) [26]. If the two solutions are compared inside the niche angle, they are compared according to their nonlinearly expanded dominance areas.…”