A graph decomposition‐based approach for water distribution network optimization

Abstract

[1] A novel optimization approach for water distribution network design is proposed in this paper. Using graph theory algorithms, a full water network is first decomposed into different subnetworks based on the connectivity of the network's components. The original whole network is simplified to a directed augmented tree, in which the subnetworks are substituted by augmented nodes and directed links are created to connect them. Differential evolution (DE) is then employed to optimize each subnetwork based on the sequence specified by the assigned directed links in the augmented tree. Rather than optimizing the original network as a whole, the subnetworks are sequentially optimized by the DE algorithm. A solution choice table is established for each subnetwork (except for the subnetwork that includes a supply node) and the optimal solution of the original whole network is finally obtained by use of the solution choice tables. Furthermore, a preconditioning algorithm is applied to the subnetworks to produce an approximately optimal solution for the original whole network. This solution specifies promising regions for the final optimization algorithm to further optimize the subnetworks. Five water network case studies are used to demonstrate the effectiveness of the proposed optimization method. A standard DE algorithm (SDE) and a genetic algorithm (GA) are applied to each case study without network decomposition to enable a comparison with the proposed method. The results show that the proposed method consistently outperforms the SDE and GA (both with tuned parameters) in terms of both the solution quality and efficiency.

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

“…The efficiency advantage of the graph decomposition based optimization techniques has been consistently reported based on testing a number of WDS case studies (Kadu et al, 2008;Krapivka and Ostfeld, 2009;Zheng et al, 2011;, 2013b, 2013c, 2013a, 2013b, 2013c as reviewed above. All these methods were developed to seek least-cost design solutions for WDSs (single-objective optimization).…”

“…Subsequently, Zheng et al (2013bZheng et al ( , 2013c further developed two graph decomposition based optimization algorithms. In Zheng et al (2013b), the water network was decomposed into the core and multiple trees, where the DE was used to optimize the core, and the integer linear programming (ILP) was employed to optimize the trees.…”

“…In Zheng et al (2013b), the water network was decomposed into the core and multiple trees, where the DE was used to optimize the core, and the integer linear programming (ILP) was employed to optimize the trees. While in Zheng et al (2013c), the water network was partitioned into several sub-networks to facilitate the optimization process.…”

Optimization of Potable Water Distribution and Wastewater Collection Networks: A Systematic Review and Future Research Directions

“…The whole network was finally determined by again employing DE given the initial solution gathered from each of the optimized subnetworks and the optimal source partitioning cut-set. Another subnetwork decomposition based optimization approach with the aid of DE was also recently reported in [85].…”

Automated sub-zoning of water distribution systems

“…Zheng et al (2013) and Zheng and Zecchin (2014) utilized network decomposition for an optimal design of water distribution systems. The full network is decomposed into sub-networks followed by a solution of a set of sub-problems representing each of the sub-networks using evolutionary algorithms.…”