Comparison of the Searching Behavior of NSGA-II, SAMODE, and Borg MOEAs Applied to Water Distribution System Design Problems

A number of multiobjective evolutionary algorithms (MOEAs) have been developed and applied to water resource optimization problems over the past decade. The comparative performance of these MOEAs has been investigated often according to their overall end-of-run results (quality of optimal fronts) within prespecified computational budgets. Despite the importance of such comparative analyses, these studies have provided little knowledge of how different MOEAs navigate through the decision space toward the Pareto front. To address this issue, this paper uses a range of metrics to quantitively characterize MOEAs' run-time searching behavior, with a focus on the statistics of search quality and convergence progress. The metrics are applied to three state-of-the-art MOEAs, including the nondominated sorting genetic algorithm-II (NSGA-II), self-adaptive multiobjective differential evolution (SAMODE), and Borg, for six water distribution system (WDS) design problems with the objectives of minimizing network cost and maximizing network resilience. Moreover, the relationship between algorithm operators and behavioral properties is discussed. The run-time behavioral results successfully capture the underlying search characteristics associated with each MOEA, thereby offering a significantly improved understanding of how different operators affect the MOEA's searching behavior. This insight not only offers guidance for practitioners to select appropriate MOEAs (and operators) for given optimization problems, but also builds fundamental understanding of MOEA operators, which can be used to develop further advanced optimization algorithms.