Multi-objective Optimisation Design of Water Distribution Systems ：Comparison of Two Evolutionary Algorithms

In order to compare two advanced multi-objective evolutionary algorithms, a multi-objective waterdistribution problem is for^nulated in this paper. The multi-objective optimization has received more attention inthe 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 handimproving the performance of water distribution systems is of equivalent importance, which is often conflictingwith the previous goal. Many performance metrics of water networks are developed in recent years, includingtotal or maximum pressure deficit, resilience, inequity, probabilistic robustness, and risk measure. In thispaper, a new resilience metric based on the energy analysis of water distribution systems is proposed. Twooptimization objectives are comprised of capital cost and the new resilience index. A heuristic algorithm, speedconstrainedmulti-objective particle swarm optimization （SMPSO） extended on the basis of the multi-objectiveparticle 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 ofSMPSO to efficiently identify good designs, two benchmark problems （two-loop network and Hanoi network） areemployed. From several aspects the results demonstrate that SMPSO is a competitive and potential tool to tacklewith the optimization problem of complex systems.