Multiobjective Optimization for the LeastCost Design of Water Distribution System Under Correlated Uncertain Parameters
by A. V. Babayan, (Research Fellow, Department of Engineering, School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter, EX4 4QF, UK Email: A.V.Babayan@ex.ac.uk), D. A. Savic, (Professor, Department of Engineering, School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter, EX4 4QF, UK Email: D.Savic@ex.ac.uk), and G. A. Walters, (Professor, Department of Engineering, School of Engineering, Computer Science and Mathematics, University of Exeter, North Park Road, Exeter, EX4 4QF, UK Email: G.A.Walters@ex.ac.uk) Section: 7th Annual Symposium on Water Distribution Systems Analysis, pp. 111, (doi: http://dx.doi.org/10.1061/40792(173)36)
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Document type: 
Conference Proceeding Paper 
Part of: 
Impacts of Global Climate Change 
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 samplingbased 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 nondominating sorting GA (NSGAII) for multiobjective optimisation. The proposed methodology was tested on the New York tunnel problem. 
