A novel optimization framework for efficiently identifying high-quality Pareto-optimal solutions: maximizing resilience of water distribution systems under cost constraints

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.