A novel optimization framework for efficiently identifying high-quality Pareto-optimal solutions: maximizing resilience of water distribution systems under cost constraints
提出一种结合局部搜索差分进化算法的新框架，通过顺序单目标优化在成本约束下高效识别高质量帕累托最优解，在大型供水系统优化中优于传统多目标进化算法。
The design of water distribution systems (WDS) presents a classic multi-objective engineering optimization problem, involving maximizing network resilience within cost constraints. While multi-objective evolutionary algorithms (MOEAs) perform well in small WDS optimizations, they often yield low-quality Pareto optimal solutions (POSs) for large-scale networks. This paper proposes a novel optimization framework with the newly developed Localized Search Differential Evolution Algorithm (LS-DEA) for efficiently identifying high-quality POSs. The framework conducts sequential single-objective optimizations with a tailored objective function to improve resilience under cost constraints. LS-DEA employs a redesigned selection strategy to handle hydraulic and cost constraints simultaneously, achieving the optimization goal. Validation on three benchmark networks demonstrates that the proposed framework outperforms traditional MOEAs , particularly in finding low-cost POSs for large-scale WDS optimizations. It can also be readily applied to efficiently identify optimal solutions that maximize network resilience for a given cost, highlighting its practical value and versatility in engineering applications. Analysis of search behavior reveals that MOEAs, such as NSGA-II, are limited by their exploratory search due to the non-dominated sorting strategy. In contrast, LS-DEA excels in exploitative search through refined strategies, efficiently identifying high-quality POSs within specified cost constraints.