Fuzzy cluster analysis and decision-making algorithms for optimal water distribution network design

ABSTRACT Three objectives, maximization of resilience, minimization of cost, and minimization of leakages, were considered in the Water Distribution Network (WDN) framework for a benchmark problem of Hanoi WDN and a real-world problem, Pamapur WDN, Telangana, India. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is employed to generate Non-dominated WDN Strategies (NWDNS). In order to simplify the decision-making process of engineers, Fuzzy Cluster Analysis (FCA) is employed to categorize NWDNS into groups. An optimum number of clusters are based on the Elbow method. Representative NWDNS, i.e. RNWDNS for each sub-cluster, is based on the membership values. Ranking of RNWDNS is performed with two decision-making algorithms, namely, Preference Ranking Organization METHod for Enrichment of Evaluations-2 (PROMETHEE-2) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR). The additive ranking rule is also applied to obtain ranks in a group decision-making environment to arrive at the optimal WDN. It is observed that 1020 NWDNSH (H represents Hanoi) generated for the Hanoi are optimally classified into 18 clusters based on the Elbow method, and A13 representing RNWDNSH 37 (cost, resilience, and leakages, respectively, are 7.8818 × 106 $, 0.3194, 0.2024 × 10−3 m3/s) is preferable, respectively. Whereas 272 NWDNSP (P represents Pamapur) generated for the Pamapur are classified into 9 clusters where S6 representing RNWDNSP 203 (cost, resilience, and leakages, respectively, are 3.5159 × 106 Rs., 0.8367, 0.5317 × 10−3 m3/s) is preferred, respectively. The present study facilitated seamless integration of NSGA-II (generation of Pareto front), FCA (reducing to manageable set) and MCDM methods (to rank the reduced manageable set) in a robust manner. GRAPHICAL ABSTRACT