A decomposition and multistage optimization approach applied to the optimization of water distribution systems with multiple supply sources

Abstract

The aim of this paper is to present a decomposition and multistage approach for optimizing the design of water distribution systems with multiple supply sources (WDS-MSS). An algorithm is first proposed to identify the optimal source partitioning cut-set for a WDS-MSS. A WDS with K supply sources is therefore decomposed to K disconnected subnetworks by the removal of the determined cut-set. Then, a total of K separate differential evolution (DE) algorithms are used to optimize the designs for the K subnetworks, respectively. This is the first optimization stage. The optimal solutions for the K subnetworks plus the optimal cut-set being the minimum allowable pipe sizes are used to create a tailored seeding table. This table is used to initialize a second-stage DE algorithm to optimize the whole of the original WDS, which is the second stage of the optimization process. Four WDS-MSS case studies are used to demonstrate the effectiveness of the proposed method. A standard DE algorithm seeded by the total choice table rather than the tailored seeding table is applied to the entire network for each case study, and the results are compared with those of the proposed method in terms of efficiency and solution quality. The comparison demonstrates that the proposed method (i.e., decomposition followed by multistage optimization) shows better performance than results from a whole of network optimization. In addition, the proposed method also exhibits significantly improved performance compared with the optimization techniques that have been previously used to optimize these case studies.