Minimizing the variance of flow series using a genetic algorithm for reliability-based design of looped water distribution networks

A network design based on the flow uniformity in various pipes improves the reliability of the network. One way to obtain such a flow distribution is by minimizing the variance of pipe flows. The available analytical method is critically studied, and observed to fail in providing global minimum variance of flow series. The analytical method accounts for the flow directions, while a variance evaluation requires that only the magnitude of flows is considered. A general nonlinear programming approach is tried, and it is observed that it requires correct knowledge of the flow direction. This article presents a genetic algorithm-based method to avoid this limitation. A linear programming-based algorithm is then suggested for selecting the optimal pipe sizes considering reliability. The proposed method is found to provide better design solutions than those obtained using some of the methodologies previously suggested for expansion of a water main system.