Optimal Design of Water Distribution Network Using Parallel Slime Mould Algorithm for Cost Minimization

Water distribution networks (WDNs) are vital infrastructures designed to ensure a minimum acceptable supply level to consumers under different operating conditions throughout the design period. Due to their complexity and the substantial investment required for their construction and maintenance, economic aspects have become a primary focus for researchers and engineers. Various evolutionary algorithms (EAs), such as the genetic algorithm (GA), have been utilized to achieve cost minimization while fulfilling hydraulic requirements. This study uses the Parallel Slime Mould Algorithm (PSMA), a variant of the slime mould algorithm (SMA) developed by Wang et al., and implemented to solve the mathematical and hydraulic optimization of WDNs. The PSMA incorporates the Hazen-Williams equation for calculating head loss and pressure constraints to ensure the feasibility of the solution. The proposed method is applied to a benchmark network and compared with results from the GA used by Savic. The PSMA proved effective in optimizing a WDN, achieving a cost reduction of approximately 6.08% compared to the GA while maintaining hydraulic feasibility. However, the pipe sizes showed notable differences, with the PSMA favoring larger diameters for most pipes except pipe 2. These results highlight the potential of PSMA as a powerful tool for WDN optimization, particularly when cost reduction is a priority.