Trade-off between total cost and reliability for Anytown water distribution network

This paper investigates the application of multiobjective evolutionary algorithms to the identification of the payoff characteristic between total cost and reliability of a water distribution system using the well-known ‘Anytown’ network as an example. An expanded rehabilitation problem is considered where the design variables are the pipe rehabilitation decisions, tank sizing, tank siting, and pump operation schedules. To provide flexibility, the network is designed and operated under multiple loading conditions. Inclusion of pump operation schedules requires consideration of water system operation over an extended period. The cost of the solution includes the capital costs of pipes and tanks as well as the present value of the energy consumed during a specified period. Optimization tends to reduce costs by reducing the diameter of, or completely eliminating, some pipes, thus leaving the system with insufficient capacity to respond to pipe breaks or demands that exceed design values without violating required performance levels. A resilience index is considered as a second objective to increase the hydraulic reliability and availability of water during pipe failures. Sensitivity analysis of solutions on the payoff curve generated by twin-objective optimization shows poor performance of these networks under random pipe failure or a pump being out of service. The minimum surplus head is added as a third objective to overcome the shortcomings of the resilience index. Results are presented for the payoff characteristics between total cost and reliability for 24 h design and five loading conditions.