A fuzzy-guided adaptive algorithm with hierarchy mechanism for solving dynamic multi-objective optimization problems

Abstract

Dynamic multi-objective optimization problems (DMOPs) require an algorithm to track the true Pareto-optimal front (POF) or Pareto-optimal set (POS) quickly and accurately when the environment suffers changes. However, many existing prediction-based methods ignore the association of individual movement directions, resulting in biased predictions and misleading the subsequent search process. To address this problem, a fuzzy-guided adaptive algorithm with hierarchy mechanism for solving DMOPs (FGAHM) is proposed, where a membership function is used to map movement vectors of the center point and individuals to the fuzzy sets for measuring the association. Thus, entire population is adaptively divided into three hierarchies, high, medium, and low based on the fuzzy relative entropy (FRE). Highly associated subpopulation is committed to leading the movement direction of the population through the linear prediction model. Medially associated subpopulation is dedicated to correcting the movement direction of the population and estimating changes in POS and POF by the multiview prediction. Lowly associated subpopulation is discarded, replaced by the t-test sampling to promote the population convergence and diversity. Although three subpopulations carry out different optimization purposes, they also synergistically contribute to the evolution of the entire population. Systematic experiments demonstrate that the performance of the proposed FGAHM outperforms seven state-of-the-art algorithms on 27 benchmark problems with 10 decision variables and 2 or 3 objectives, as evaluated by inverted generational distance (IGD), mean inverted generational distance (MIGD), DMIGD, mean hypervolume (MHV), and mean Schott's spacing (MSP).