In this study, a novel density-based spatial clustering method is developed to maintain a diverse set of solutions for stochastic multi-objective optimization algorithms. This method dynamically clusters solutions in the decision space after solutions evaluations. Dominance check is localized to maintain solutions that are globally dominated but locally non-dominated in their cluster. Unlike the original solution archiving, the proposed method implemented for Pareto Archived-Dynamically Dimensioned Search successfully finds optimal and near-optimal fronts with different cluster labels in two mathematical case studies. Two environmental benchmark problems are also solved and a three-stage screening process is applied to their archive sets to identify the number of dissimilar options. The dissimilarity index devised for this study shows a significantly higher distinction level and archive size for the cluster-based solution archiving, which allows decision-makers to have higher flexibility in refining their preferences for robust decision-making in the environmental problems, compared with the original archiving.

在这项研究中，开发了一种新颖的基于密度的空间聚类方法，以维护随机多目标优化算法的多种解决方案。此方法在解决方案评估之后在决策空间中动态地对解决方案进行聚类。优势检查已本地化，以维护在其集群中全局支配但本地不支配的解决方案。与原始解决方案存档不同，在两个数学案例研究中，为Pareto存档动态尺寸搜索实施的拟议方法成功找到了具有不同聚类标签的最优和近乎最优的前沿。还解决了两个环境基准问题，并将三个阶段的筛选过程应用于其存档集，以识别不同选项的数量。