In order to compare two advanced multi⁃objective evolutionary algorithms, a multi⁃objective water distribution problem is formulated in this paper. The multi⁃objective optimization has received more attention in the water distribution system design. On the one hand the cost of water distribution system including capital, operational, and maintenance cost is mostly concerned issue by the utilities all the time; on the other hand improving the performance of water distribution systems is of equivalent importance, which is often conflicting with the previous goal. Many performance metrics of water networks are developed in recent years, including total or maximum pressure deficit, resilience, inequity, probabilistic robustness, and risk measure. In this paper, a new resilience metric based on the energy analysis of water distribution systems is proposed. Two optimization objectives are comprised of capital cost and the new resilience index. A heuristic algorithm, speed⁃constrained multi⁃objective particle swarm optimization ( SMPSO) extended on the basis of the multi⁃objective particle swarm algorithm, is introduced to compare with another state⁃of⁃the⁃art heuristic algorithm, NSGA⁃II. The solutions are evaluated by two metrics, namely spread and hypervolume. To illustrate the capability of SMPSO to efficiently identify good designs, two benchmark problems ( two⁃loop network and Hanoi network) are employed. From several aspects the results demonstrate that SMPSO is a competitive and potential tool to tackle with the optimization problem of complex systems.
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