论文标题
多模式多目标优化的决策和目标空间的分解
Decomposition in Decision and Objective Space for Multi-Modal Multi-Objective Optimization
论文作者
论文摘要
多模式多目标多目标优化问题（MMMOPS）在帕累托最佳设置中具有多个子集，每个子集独立映射到同一pareto-front。普遍的多目标进化算法并非纯粹是为搜索多个溶液子集而设计的，而专为MMMOPS设计的算法表明，在目标空间中表现出降低的性能。这激发了更好地解决MMMOP的更好算法的设计。目前的工作确定了拥挤的幻觉问题，该问题源于在整个决策空间中全球使用拥挤距离。随后，提出了一个使用参考矢量辅助分解（LORD）的进化框架，称为图形laplacian优化，该框架在客观和决策空间中都使用分解来处理MMMOP。它的过滤步骤进一步扩展到列为II算法，该算法证明了其在多模式多目标多目标问题上的动态。框架的功效是通过比较CEC 2019多模式多目标测试套件和多边形问题的测试实例中的性能与MMMOPS和其他多种多数和其他多目标进化算法的最新算法的。通过提及拟议框架的局限性和设计的未来方向的局限性仍然是MMMOP的算法，可以得出结论。源代码可在https://worksupplements.droppages.com/lord上找到。
Multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to the same Pareto-Front. Prevalent multi-objective evolutionary algorithms are not purely designed to search for multiple solution subsets, whereas, algorithms designed for MMMOPs demonstrate degraded performance in the objective space. This motivates the design of better algorithms for addressing MMMOPs. The present work identifies the crowding illusion problem originating from using crowding distance globally over the entire decision space. Subsequently, an evolutionary framework, called graph Laplacian based Optimization using Reference vector assisted Decomposition (LORD), is proposed, which uses decomposition in both objective and decision space for dealing with MMMOPs. Its filtering step is further extended to present LORD-II algorithm, which demonstrates its dynamics on multi-modal many-objective problems. The efficacies of the frameworks are established by comparing their performance on test instances from the CEC 2019 multi-modal multi-objective test suite and polygon problems with the state-of-the-art algorithms for MMMOPs and other multi- and many-objective evolutionary algorithms. The manuscript is concluded by mentioning the limitations of the proposed frameworks and future directions to design still better algorithms for MMMOPs. The source code is available at https://worksupplements.droppages.com/lord.
