分解多目标优化的不完全列表匹配选择算法
Matching-Based Selection with Incomplete Lists for Decomposition Multi-Objective Optimization
摘要：
收敛性与多样性的平衡是进化多目标优化的关键问题。最近提出的基于稳定匹配的选择提供了一个新的视角来处理这种平衡下的分解多目标优化的框架。特别是，子问题和解决方案之间的稳定匹配，实现了他们的相互偏好之间的平衡，隐含的收敛性和多样性之间的平衡。然而，原有的稳定匹配模型具有很高的风险，匹配的解决方案与一个不利的子问题，最终导致不平衡的选择结果。本文提出了一种基于自适应两级稳定匹配选择的分解多目标优化方法。具体来说，借用不完整列表的稳定匹配的思想，我们匹配每个解决方案与它最喜欢的子问题之一，通过限制其偏好列表的长度在第一级稳定匹配。在第二级稳定匹配过程中，剩余的子问题根据经典的稳定匹配模型与它们最喜欢的解进行匹配。特别是，我们开发了一个自适应机制，自动设置的偏好列表的长度为每个解决方案，根据其本地的竞争力。我们提出的方法的性能进行了验证，并与几个国家的最先进的进化多目标优化算法的62个基准问题的实例进行比较。实验结果充分证明了我们所提出的方法在复杂的Pareto集和具有三个以上目标的问题上的竞争力。
英文摘要：
The balance between convergence and diversity is a key issue of evolutionary multi-objective optimization. The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of decomposition multi-objective optimization. In particular, the stable matching between subproblems and solutions, which achieves an equilibrium between their mutual preferences, implicitly strikes a balance between the convergence and diversity. Nevertheless, the original stable matching model has a high risk of matching a solution with a unfavorable subproblem which finally leads to an imbalanced selection result. In this paper, we propose an adaptive two-level stable matching-based selection for decomposition multi-objective optimization. Specifically, borrowing the idea of stable matching with incomplete lists, we match each solution with one of its favorite subproblems by restricting the length of its preference list during the first-level stable matching. During the second-level stable matching, the remaining subproblems are thereafter matched with their favorite solutions according to the classic stable matching model. In particular, we develop an adaptive mechanism to automatically set the length of preference list for each solution according to its local competitiveness. The performance of our proposed method is validated and compared with several state-of-the-art evolutionary multi-objective optimization algorithms on 62 benchmark problem instances. Empirical results fully demonstrate the competitive performance of our proposed method on problems with complicated Pareto sets and those with more than three objectives.
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