A New Decomposition-Based Many-Objective Algorithm Based on Adaptive Reference Vectors and Fractional Dominance Relation

Decomposition-based evolutionary multi-objective algorithms (MOEAs) and many-objective algorithms (MaOEAs) divide a multi-objective problem (MOP) or a many-objective problem (MaOP) into several subproblems by using a set of predefined uniformly distributed reference vectors and can achieve good overall performance especially in maintaining population diversity. However, they encounter huge difficulties in addressing problems with irregular Pareto Fronts (PFs) since many reference vectors do not work during the searching process. To cope with this problem, this paper aims to improve an existing decomposition-based algorithm called reference vector guided evolutionary algorithm (RVEA) by designing an adaptive reference vectors adjustment strategy and strengthening the poor selection pressure. By adding the adaptive strategy, the predefined reference vectors will be dynamically adjusted according to the distribution of promising solutions with good overall performance and the subspaces where the PF lies may be further divided so as to contribute more to the searching process. Besides, the selection pressure with respect to convergence performance posed by RVEA is mainly from the length of normalized objective vectors and the metric is poor in evaluating the convergence performance of a solution with the increasing of objective size. Motivated by that, an improved angle-penalized distance (APD) method based on a newly proposed fractional dominance relation is developed to better distinguish solutions with sound convergence performance in each subspace. To investigate the performance of the proposed algorithm, extensive experiments are conducted to compare it with 5 state-of-the-art decomposition-based algorithms on 3-, 5-, 8-, 10- objective MaF1-MaF9. The results demonstrate that the proposed algorithm obtains the best overall performance.