Learning to Expand/Contract Pareto Sets in Dynamic Multi-Objective Optimization With a Changing Number of Objectives

Dynamic multiobjective optimization problems (DMOPs) with a changing number of objectives (NObjs) may have Pareto-optimal set (PS) manifold expanding or contracting over time. Knowledge transfer has been used for solving DMOPs, since it can transfer useful information from solving one problem instance to solve another related problem instance. However, we show that the state-of-the-art transfer approach based on heuristic lacks diversity on problem with extremely strong bias and loses convergence on problems with multimodality and variable correlation, after the NObjs increases and decreases, respectively. Therefore, we propose a novel transfer strategy based on learning, called learning to expand and contract PS (denoted as LEC) for enhancing diversity and convergence after NObj increases and decreases, respectively. It first learns potentially good directions for expansion and contraction separately via principal component analysis. Then, the most promising expansion and contraction directions are selected from their candidates according to whether they help diversity and convergence, respectively. Finally, PS is learned to be expanded and contracted based on these most promising directions. Comprehensive studies using 13 DMOP benchmarks with a changing NObjs demonstrate that our proposed LEC is effective on improving solution quality, not only right after changes but also after optimization of different generations, compared to state-of-the-art algorithms.