Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach

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Title: Scalable Pareto set generation for multiobjective co-design problems in water distribution networks: a continuous relaxation approach
Authors: Pecci, F
Abraham, E
Stoianov, I
Item Type: Journal Article
Abstract: In this paper, we study the multiobjective co-design problem of optimal valve placement and operation in water distribution networks, addressing the minimization of average pressure and pressure variability indices. The presented formulation considers nodal pressures, pipe flows and valve locations as decision variables, where binary variables are used to model the placement of control valves. The resulting optimization problem is a multiobjective mixed integer nonlinear optimization problem. As conflicting objectives, average zone pressure and pressure variability can not be simultaneously optimized. Therefore, we present the concept of Pareto optima sets to investigate the trade-offs between the two conflicting objectives and evaluate the best compromise. We focus on the approximation of the Pareto front, the image of the Pareto optima set through the objective functions, using the weighted sum, normal boundary intersection and normalized normal constraint scalarization techniques. Each of the three methods relies on the solution of a series of single-objective optimization problems, which are mixed integer nonlinear programs (MINLPs) in our case. For the solution of each single-objective optimization problem, we implement a relaxation method that solves a sequence of nonlinear programs (NLPs) whose stationary points converge to a stationary point of the original MINLP. The relaxed NLPs have a sparse structure that come from the sparse water network graph constraints. In solving the large number of relaxed NLPs, sparsity is exploited by tailored techniques to improve the performance of the algorithms further and render the approaches scalable for large scale networks. The features of the proposed scalarization approaches are evaluated using a published benchmarking network model.
Issue Date: 20-Jul-2016
Date of Acceptance: 29-Jun-2016
ISSN: 1615-1488
Publisher: Springer Verlag
Start Page: 857
End Page: 869
Journal / Book Title: Structural and Multidisciplinary Optimization
Volume: 55
Issue: 3
Copyright Statement: © The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Science & Technology
Computer Science, Interdisciplinary Applications
Engineering, Multidisciplinary
Computer Science
Multiobjective optimization
Scalarization strategies
Mixed integer nonlinear programs
Complementarity constraints
Water distribution networks
Pressure management
09 Engineering
01 Mathematical Sciences
Design Practice & Management
Publication Status: Published
Appears in Collections:Faculty of Engineering
Civil and Environmental Engineering

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