Pareto-optimal design of water distribution networks: an improved graph theory-based approach

Abstract

One of the main drawbacks of using evolutionary algorithms for the multi-objective design of water distribution networks (WDNs) is their computational inefficiency, particularly for large-scale problems. Recently, graph theory-based approaches (GTAs) have gained attention as they can help with the optimal WDN design (i.e., determining optimal diameters). This study aims to extend a GTA to further improve the quality of design solutions. The GTA design is based on a customized metric called ‘demand edge betweenness centrality’, which spatially distributes nodal demands through the weighted edges of a WDN graph and provides an estimation of water flows. Assigned edge weights can be constant (i.e., static) or modified iteratively (i.e., dynamic) during the design process, leading to different flow estimations and alternative design options. Three hydraulic-inspired dynamic weights are developed in this study to better reproduce hydraulic behavior and, consequently, find better solutions. Additionally, this work proposes a framework for the optimal design of multi-source WDNs and provides guidelines for obtaining near-optimal solutions in such networks. A comparative study between GTAs and evolutionary optimizations confirms the efficiency of the improved GTA in providing optimal/near-optimal solutions, especially for large WDNs, with a runtime reduction of up to seven orders of magnitude. HIGHLIGHTS An improved graph theory-based approach for determining optimal diameters is developed.; The proposed approach uses hydraulic-inspired dynamic weights to better reproduce hydraulic behavior.; The newly developed framework is highly efficient, particularly for large-scale networks with thousands of pipes.;

Keywords

• complex network analysis
• multi-objective evolutionary algorithms
• pareto fronts
• resilience