On the Evolution of the Optimal Design of WDS: Shifting towards the Use of a Fractal Criterion

Abstract

Several researchers have proposed methodologies for addressing the problem of designing optimal water distribution systems. Metaheuristic approximations are studied the most due to the vast solution space. In search of reducing computational time, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) has been tested with retrofitting from the Optimal Power Use Surface (OPUS) methodology. A previous study demonstrates how OPUS significantly improves the results since it seeks to reduce energy losses in the network, in order to approximate minimum-cost designs using fewer hydraulic executions. However, more research is still needed to determine applicable hydraulic criteria that allow an enhanced comprehension of optimal designs. Therefore, this paper aims to understand the characteristics of near-optimal solutions using designs from the retrofitted OPUS/NSGA-II Pareto fronts of four distinct networks (Hanoi, Balerma, Fossolo, and Modena). Moreover, fractal characteristics of the networks’ energy dissipation, flow, and diameter distribution have been analyzed for this purpose. In this way, outcomes suggest that the hydraulic gradient line box dimension in optimal designs approaches a value of two, demonstrating that objects resemble a single-plane surface. These promising results propose fractal analysis as a practical design criterion due to its hydraulic significance and low computational cost.