Dual graph characteristics of water distribution networks—how optimal are design solutions?

Urban water infrastructures are an essential part of urban areas. For their construction and maintenance, major investments are required to ensure an efficient and reliable function. Vital parts of the urban water infrastructures are water distribution networks (WDNs), which transport water from the production (sources) to the spatially distributed consumers (sinks). To minimize the costs and at the same time maximize the resilience of such a system, multi-objective optimization procedures (e.g., meta-heuristic searches) are performed. Assessing the hydraulic behavior of WDNs in such an optimization procedure is no trivial task and is computationally demanding. Further, deciding how close to optimal design solutions the current solutions are, is difficult to assess and often results in an unnecessary extent of experiment. To tackle these challenges, an answer to the questions is sought: when is an optimization stage achieved from which no further improvements can be expected, and how can that be assessed? It was found that graph characteristics based on complex network theory (number of dual graph elements) converge towards a certain threshold with increasing number of generations. Furthermore, a novel method based on network topology and the demand distribution in WDNs, specifically based on changes in ‘demand edge betweenness centrality’, for identifying that threshold is developed and successfully tested. With the proposed novel approach, it is feasible, prior to the optimization, to determine characteristics that optimal design solutions should fulfill, and thereafter, test them during the optimization process. Therewith, numerous simulation runs of meta-heuristic search engines can be avoided.