RODE: Ranking-Dominance-Based Algorithm for Many-Objective Optimization with Opposition-Based Differential Evolution

During the period of 1990s and early 2000s, the Pareto-dominance (PD) relation was successfully applied for solving multiobjective optimization problems (MOPs) with small number of objectives (typically not exceeding four objectives). However, the performance of these PD-based multiobjective evolutionary algorithms (MOEAs) becomes hopeless when it comes to solving problems with larger number of objectives. Many alternative dominance relations have been proposed in the last few years to improve the search ability of EMO algorithms. In this paper, we present the RODE algorithm as a novel scalable approach for many-objective problems which adopts the ranking-dominance relation for evaluating the fitness of solutions that provides improved convergence. The evolutionary search mechanism employed in our algorithm is the conventional differential evolution (DE) approach. However, for attaining the improved diversity of solutions, we have incorporated the weight vectors and opposition-based differential evolution (ODE) in a unique way. In order to validate our RODE approach, we have compared it with other state-of-the-art MOEAs, namely GDE3, NSGAII and two versions of MOEA/D, namely MOEA/D-TCH and MOEA/D-PBI. All the MOEAs have been executed on the standard benchmark problems DTLZ1-DTLZ4 with 5-, 8-, 10-, 15-, and 20-D objective spaces and MaF03, MaF05 and MaF06 with 8-, 10- and 15-D objective spaces. In almost all the simulation experiments (especially with higher than 5-objectives), our approach has achieved promising results in terms of convergence and diversity of solutions.