Application of Fuzzy Cluster Analysis and Decision Making Algorithms for Choosing the Optimal Water Distribution Network Design

Abstract Non-dominated Sorting Genetic Algorithm (NSGA-II) is employed to facilitate multi-objective optimization in Water Distribution Network(s) (WDN) framework for a benchmark problem of Hanoi Network and a real-world problem, Pamapur Network, Telangana, India. Maximization of resilience, minimization of cost and minimization of leakages are considered in a multiobjective context which result in generation of 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. Thereafter, Dunn’s Cluster Validity Index (DCVI) is used for identification of optimal cluster size. Representative NWDNS i.e. RNWDNS for each sub-cluster is based on the maximum membership of NWDNS in the respective sub-cluster. Ranking of RNWDNS is performed with three decision making algorithms, namely, Preference Ranking Organization METHod for Enrichment of Evaluations-2 (PROMETHEE-2), Multicriterion Q-analysis-2 (MCQA-2) and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR). Additive ranking rule is also applied to facilitate obtained ranks in group decision making environment to arrive at the optimal WDN. It is observed that 1020 NWDNS generated for Hanoi network are optimally classified into 18 clusters based on DCVI, and A13 representing RNWDNS 37 is found preferable. Whereas 272 NWDNS generated for Pamapur network are classified into 9 clusters where S6 is preferred (representing RNWDNS 203).