Improved MOSADE algorithm incorporating Sobol sequences for multi-objective design of Water Distribution Networks

Abstract

Design of Water Distribution Networks (WDNs) is a tremendously hard optimization problem, and consideration of reliability further adds to the complexity, which may involve huge computational effort. As several past studies stressed that Evolutionary Algorithms (EAs) could be efficient tools for WDN design, so this study, presents an effective methodology, Multi-Objective Self Adaptive Differential Evolution (MOSADE) algorithm using Sobol sequences for random number generation, termed as (S-MOSADE) for WDN design. The efficacy of the S-MOSADE framework is evaluated by application on a few benchmark WDNs, by considering cost minimization and mechanical reliability maximization and comparing the results with that of NSGA-II algorithm. The results illustrated that S-MOSADE algorithm leads to a better Pareto-optimal front than NSGA-II with respect to uniformly spaced and wide range of non-dominated solutions, and converges faster as compared to other algorithms. To further reduce the computational burden, minimizing the cost and maximizing the network resilience is carried out to generate the initial population for S-MOSADE algorithm. This has reduced the computational burden by almost three times as compared to random initialization of population, thus saving a lot of computational time. The study concludes that the proposed S-MOSADE algorithm with the strategy of solutions initialized with minimum cost and maximum network resilience could be used effectively for speeding-up the multi-objective design of WDNs.