Two new approaches for the stochastic least cost design of water distribution systems

Abstract

The problem of stochastic (i.e. robust) water distribution system (WDS) design is formulated and solved here as an optimisation problem under uncertainty. The objective is to minimise total design costs subject to a target level of system robustness. System robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. The decision variables are the alternative design options available for each pipe in the WDS. The only source of uncertainty analysed is the future water consumption uncertainty. Uncertain nodal demands are assumed to be independent random variables following some pre-specified probability density function (PDF). Two new methods are developed to solve the aforementioned problem. In the Integration method, the stochastic problem formulation is replaced with a deterministic one. After some simplifications, a fast numerical integration method is used to quantify the uncertainties. The optimisation problem is solved using the standard genetic algorithm (GA). The Sampling method solves the stochastic optimisation problem directly by using the newly developed robust chance constrained GA. In this approach, a small number of Latin Hypercube (LH) samples are used to evaluate each solution's fitness. The fitness values obtained this way are then averaged over the chromosome age. Both robust design methods are applied to a New York Tunnels rehabilitation 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 lead to the following conclusions: (1) Neglecting demand uncertainty in WDS design may lead to serious under-design of such systems; (2) Both methods shown here are capable of identifying (near) optimal robust least cost designs achieving significant computational savings.