Optimal pipe-sizing design of water distribution networks using modified Rao-II algorithm

Several evolutionary algorithms (EAs) have been suggested in the last three decades for the least-cost design of water distribution networks (WDNs). EAs generally worked well to identify the global/near-global optimal solutions for small- to moderate-size networks in a reasonable time and computational effort. However, their applications to large-size networks are still challenging due to large computational effort. Recent developments in EAs are towards parameter-less techniques that avoid fine-tuning of case-specific parameters to reduce the computational effort. Further, several self-adaptive penalties and search-space reduction methodologies have been suggested to reduce the computational effort. A fast, efficient, and parameter-less Rao-II algorithm has been used earlier with penalty-based approaches for the optimal design of WDNs. In this study, the application of a Rao-II algorithm is further explored with three self-adaptive penalty approaches to compare the convergence characteristics. The Rao-II algorithm is observed to converge at an infeasible solution in cases that the applied penalty to an infeasible solution is not so substantial to make it inferior to the feasible solutions. Modifications are suggested to improve the Rao-II algorithm, named the modified Rao-II algorithm. The modified Rao-II algorithm with the self-adaptive penalty methods resulted in better solutions than those obtained earlier.