Multiobjective Optimization for the Least-Cost Design of Water Distribution System Under Correlated Uncertain Parameters

Abstract

The problem of the stochastic (i.e. robust) water distribution system (WDS) design is formulated and solved here as a multiobjective optimization problem under uncertainty. The objectives are to minimize two parameters – a) cost of the network design/rehabilitation; b) probability of network failure due to uncertainty in input parameters. The sources of uncertainty analyzed here are future water consumption and pipe roughnesses. All uncertain model input parameters are assumed to be random variables following some known probability density function (PDF). We also assume that those random variables are not necessarily independent and the matrix giving the correlations between all pairs of uncertain parameters (correlation matrix) is specified. To avoid using a computationally demanding sampling-based technique for uncertainty quantification, the original stochastic formulation is replaced by a deterministic one. After some simplifications, a fast numerical integration method is used to quantify the uncertainties. The optimization problem is solved by a Genetic Algorithm (GA), which finds the Pareto front by using the non-dominating sorting GA (NSGAII) for multi-objective optimisation. The proposed methodology was tested on the New York tunnel problem.