Application of the multi-objective particle swarm optimisation (MOPSO) algorithm to design of water distribution systems is described. An earlier MOPSO algorithm is augmented with (a) local search, (b) a modified strategy for assigning the leader, and (c) a modified mutation scheme. For one of the benchmark problems described in the literature, the effect of each of the above features on the algorithm performance is demonstrated. The augmented MOPSO algorithm (called MOPSO+) is applied to five benchmark problems, and in each case, it finds non-dominated solutions not reported earlier.In addition, for the purpose of comparing Pareto fronts (sets of non-dominated solutions) obtained by different algorithms, a new criterion is suggested, and its usefulness is pointed out with an example. Finally, some suggestions regarding future research directions are made.

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Hybridisation of the multi-objective optimisation algorithm NSGA-II and local search is proposed for water distribution system design.Results obtained with the proposed algorithm are presented for four medium-size water networks taken from the literature. Local search is found to be beneficial for one of the networks in terms of finding new solutions not reported earlier. It is also shown that simply using an external archive to save all non-dominated solutions visited by the population, even without local search, leads to substantial improvement in the non-dominated set produced by the algorithm.

Optimally designed water distribution networks (WDNs) make engineers’ tasks difficult due to various challenges like non-linearity between head-loss and flow, commercially available distinct diameters, combinatorial, nondeterministic polynomial time hard problems and a large number of decision variables. This paper develops a new hybrid NSGA-II algorithm augmented with a random multi-point crossover operator and a local search denoted by RLNSGA-II to design the multiobjective WDN. The efficiency of the proposed algorithm (RLNSGA-II) is tested on three benchmark problems, namely New York, Hanoi and Balerma networks. The results obtained are compared with the best-known algorithms available in the literature. The results have shown that the proposed algorithm RLNSGA-II has found better converged and distributed solutions for all three representative benchmark problems considered in the literature consistently and evidently when compared with the best-known approximation of solutions published. Furthermore, as the complexity of the WDN increases, its advantages over other algorithms become more significant.

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).

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