Dynamic edge betweenness centrality and optimal design of water distribution networks

Abstract

The multi-objective design of water distribution networks (WDNs) as a nonlinear optimization problem is a challenging task. With two contradicting objectives (e.g., minimizing costs and maximizing resilience), Pareto fronts of optimal solutions can be obtained with, e.g., evolutionary algorithms. However, the main drawback of these algorithms is the high computational effort required to optimize large WDNs. Recently, a highly efficient method based on complex network theory (CNT) was developed, where within seconds, a wide range of Pareto near-optimal solutions can be obtained for the design of WDNs (i.e., determining optimal diameters). The developed method is based on a customized graph measure called demand edge betweenness centrality (EBCQ). This measure is based on the frequency of occurrence of an edge in the shortest path from a source node to a demand node. In addition, EBCQ sums up the demands routed through that edge, giving a valid flow estimation for an optimal design. In the graph of a WDN, the edges can have different weights. The weighting function used for calculations can be ‘static’ or ‘dynamic’. A constant value is utilized for edge weights in the static weighting approach, while a dynamic weighting function implies that edge weights are modified when iterating through all demand nodes. In this context, using dynamic weighting functions for (i.e., dynamic ) avoids concentrating values in just a few edges (shortest-path trees) by considering redundancy in flow paths and better approximation of the hydraulic behavior. However, it is not clear how the parameters of dynamic weighting functions should be defined to achieve the best approximation of the Pareto-optimal front. This work performs a systematic investigation of dynamic weighting functions and gives guidance for optimal parameter selection. The comparative study between the CNT approach (with static and dynamic weights) and evolutionary optimizations on four WDN design problems confirms the capability of the proposed dynamic functions in providing optimal/near-optimal solutions.