Fuzzy optimization-based Water Distribution Network design using Self-Adaptive Cuckoo Search Algorithm

Water Distribution Network(s) (WDN) design is gaining prominence in the urban planning context. Several factors that play a significant role in design are uncertainty in data, non-linear relation of head loss & discharge, combinatorial nature of the problem, and high computational requirements. In addition, many conflicting objectives are possible and required for effective WDN design, such as cost, resilience, and leakage. Most of the research work published has used multiobjective evolutionary optimization in solving such complex WDN. However, the challenge of such population-based evolutionary approaches is that they provide multiple trade-off Pareto optimal solutions to the decision-maker who will have to choose another set of techniques to arrive at a single optimal solution. The present study employs a fuzzy optimization approach that would provide a single optimal WDN design for Hanoi and Pamapur, India. Maximization of network resilience (NR) and minimization of network cost (NC) are employed in a multiobjective context. Later, minimization of network leakages (NL) is also incorporated, leading to three objective problems. Hyperbolic membership function (HMF), exponential membership function (EMF), and non-linear membership function (NMF) are employed in Self-Adaptive Cuckoo Search Algorithm-based fuzzy optimization. HMF is found suitable to determine the best possible WDN design for chosen case studies based on the highest degree of satisfaction.