Non-dominated sorting harmony search differential evolution (NS-HS-DE): A hybrid algorithm for multi-objective design of water distribution networks

We developed a hybrid algorithm for multi-objective design of water distribution networks (WDNs) in the present study. The proposed algorithm combines the global search schemes of differential evolution (DE) with the local search capabilities of harmony search (HS) to enhance the search proficiency of evolutionary algorithms. This method was compared with other multi-objective evolutionary algorithms (MOEAs) including NSGA2, SPEA2, MOEA/D and extended versions of DE and HS combined with non-dominance criteria using several metrics. We tested the compared algorithms on four benchmark WDN design problems with two objective functions, (i) the minimization of cost and (ii) the maximization of resiliency as reliability measure. The results showed that the proposed hybrid method provided better optimal solutions and outperformed the other algorithms. It also exhibited significant improvement over previous MOEAs. The hybrid algorithm generated new optimal solutions for a case study that dominated the best-known Pareto-optimal solutions in the literature.