An efficient decomposition and dual-stage multi-objective optimization method for water distribution systems with multiple supply sources

This paper proposes an efficient decomposition and dual-stage multi-objective optimization (DDMO) method for designing water distribution systems with multiple supply sources (WDS-MSSs). Three phases are involved in the proposed DDMO approach. In Phase 1, an optimal source partitioning cut-set is identified for a WDS-MSS, allowing the entire WDS-MSS to be decomposed into sub-networks. Then in Phase 2 a non-dominated sorting genetic algorithm (NSGA-II) is employed to optimize the sub-networks separately, thereby producing an optimal front for each sub-network. Finally in Phase 3, another NSGA-II implementation is used to drive the combined sub-network front (an approximate optimal front) towards the Pareto front for the original complete WDS-MSS. Four WDS-MSSs are used to demonstrate the effectiveness of the proposed approach. Results obtained show that the proposed DDMO significantly outperforms the NSGA-II that optimizes the entire network as a whole in terms of efficiently finding good quality optimal fronts.