Coping With a Severely Changing Number of Objectives in Dynamic Multi-Objective Optimization

In dynamic multi-objective optimization problems (DMOPs) where the number of objectives changes, the Pareto-optimal set (PS) manifold may expand or contract over time. Knowledge transfer has been utilized to solve DMOPs because it can transfer valuable information from one problem-solving instance (i.e., source) to solving another related problem instance. However, existing transfer approaches suffer from poor diversity and convergence after a severe increase and decrease in the number of objectives, respectively. The reason is that most transfer approaches simply transfer knowledge from the solutions before the change, which causes degeneration in quality of transferred solutions due to dissimilarity between the problem instances before and after the severe change. In this paper, we propose a simple-yet-effective transfer approach, called similarity transfer approach (STA) to tackling a severely changing number of objectives. It selects the historically most similar environment to the current one as the source problem instance and transfers knowledge from that environment. Furthermore, a novel strategy of randomization enhancing transfer diversity is proposed in STA if the transfer from the most similar environment still lacks sufficient diversity when increasing the number of objectives. Comprehensive studies using 13 DMOP benchmarks with a severely changing number of objectives demonstrate that our proposed STA is effective in improving solution quality not only immediately after changes but also after optimization, in comparison to state-of-the-art algorithms.