Cluster-based multi-objective optimization for identifying diverse design options: Application to water resources problems

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.