Optimal design of water networks using fuzzy genetic algorithm

A fuzzy genetic algorithm (FGA) is used to obtain the least-cost design of looped water distribution networks (WDNs). The FGA is a GA-based search method in which fitness evaluation is carried out using a fuzzy decision system (FDS). Unlike previous fuzzy water network optimisation techniques in which different properties were introduced by fuzzy membership functions and the decisions were made by the means of crisp logic, a fully FDS is used to simulate the tolerance in constraint deviation in network elements. The method is applied to two well-known networks currently appearing in the literature as case studies. For each case, based on network layout and optimisation constraints, a FDS is introduced by determining fuzzy parameters, membership functions and the rule set. The results prove the capability of the FGA method of finding optimum solutions in addition to providing a dynamic algorithm that gives engineers more practical insight into easily applying system uncertainty in the optimisation algorithm.