Different from most other dynamic multi-objective optimization problems (DMOPs), DMOPs with a changing number of objectives usually result in expansion or contraction of the Pareto front or Pareto set manifold. 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 algorithm for DMOPs with a changing number of objectives lacks sufficient diversity when the fitness landscape and Pareto front shape present nonseparability, deceptiveness or other challenging features. Therefore, we propose a knowledge transfer dynamic multi-objective evolutionary algorithm (KTDMOEA) to enhance population diversity after changes by expanding/contracting the Pareto set in response to an increase/decrease in the number of objectives. This enables a solution set with good convergence and diversity to be obtained after optimization. Comprehensive studies using 13 DMOP benchmarks with a changing number of objectives demonstrate that our proposed KTDMOEA is successful in enhancing population diversity compared to state-of-the-art algorithms, improving optimization especially in fast changing environments.

翻译：与大多数动态多目标优化问题不同，目标数变化的动态多目标优化问题通常会导致帕累托前沿或帕累托解集流形的扩张或收缩。知识迁移已被用于求解动态多目标优化问题，因为它可以将解决一个问题实例时的有用信息迁移到求解另一个相关的问题实例。然而，我们发现在目标数变化的最先进动态多目标优化迁移算法中，当适应度景观和帕累托前沿形状呈现不可分离性、欺骗性或其他具有挑战性的特征时，其种群缺乏足够的多样性。因此，我们提出了一种知识迁移动态多目标进化算法，通过根据目标数的增加/减少对帕累托解集进行扩张/收缩，以增强变化后的种群多样性。这使得优化后能够获得具有良好收敛性和多样性的解集。基于13个目标数变化的动态多目标优化基准问题的综合研究表明，与最先进算法相比，我们提出的算法在增强种群多样性方面取得了成功，特别是在快速变化环境中显著提升了优化性能。