Multi-objective design of the Water distribution systems using SPEA2

As a complicated and combinatorial optimization problem, the design of Water distribution systems (WDSs) is difficult to be solved. In this paper, in order to design WDSs better, three objectives are considered, including the initial construction cost, the sum of node surplus head and the variance of node surplus head. The consideration of the variance of node surplus head can reflect the distribution of the node surplus head in WDSs. This problem is solved by the strength pareto evolutionary algorithm (SPEA2). Finally, the model is applied into two well-known benchmark case studies, the two-loop network and the New York Tunnels network. By comparing with some algorithms, such as Tabu search algorithm and non-dominated sorting genetiv algorithm (NSGA2), the performance of SPEA2 shows the effectiveness in terms of reliability, convergence, as well as diversity.