Robust least-cost design of water distribution networks using redundancy and integration-based methodologies

Two approaches to solving the problem of robust least-cost design of water distribution systems under uncertainty in input parameters are considered. The first approach (redundant design) is based on redundancy in design, where "safety margins" are added to the uncertain parameters and the resulting deterministic optimization problem is then solved. The values of safety margins are determined iteratively. This method requires no changes to the objective function or constraints formulation when used in conjunction with existing deterministic tools. The second approach (integration method) includes within the objective function the influence of uncertainty on system robustness. A fast numerical integration method is used to quantify uncertainties. System robustness is defined here as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in a network. The sources of uncertainty analyzed here are future water consumption (at each node in the network) and hydraulic roughness (for each pipe in the network), which are assumed to be independent random variables with known probability density functions. The objective is to minimize the total design cost subject to a target level of system robustness. A genetic algorithm is used as the optimization tool. The two methodologies considered in this paper are applied to the New York Tunnels case study. The optimal solutions are identified for different levels of robustness. The best solutions obtained are also compared to the previously identified optimal deterministic solution. The results obtained show that both methodologies are capable of identifying robust least-cost designs while achieving significant computational savings when compared to a full sampling methodology. The results obtained also show that, even though slightly more expensive, solutions obtained using the redundant design method can be obtained with significantly less computational effort than the solutions obtained using the integration method.