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

Dynamic multi-objective optimization problems (DMOPs) with a changing number of objectives 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 multi-modality and variable correlation, after the number of objectives 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 number of objective increases and decreases, respectively. It firstly 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. Lastly, PS is learnt to be expanded and contracted based on these most promising directions. Comprehensive studies using 13 DMOP benchmarks with a changing number of objectives 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.