Model Reduction and Outer Approximation for Optimizing the Placement of Control Valves in Complex Water Networks

Filippo Pecci, Edo Abraham, Ivan Stoianov

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)
145 Downloads (Pure)


The optimal placement and operation of pressure control valves in water distribution networks is a challenging engineering problem. When formulated in a mathematical optimization framework, this problem results in a nonconvex mixed integer nonlinear program (MINLP), which has combinatorial computational complexity. As a result, the considered MINLP becomes particularly difficult to solve for large-scale looped operational networks. We extend and combine network model reduction techniques with the proposed optimization framework in order to lower the computational burden and enable the optimal placement and operation of control valves in these complex water distribution networks. An outer approximation algorithm is used to solve the considered MINLPs on reduced hydraulic models. We demonstrate that the restriction of the considered optimization problem on a reduced hydraulic model is not equivalent to solving the original larger MINLP, and its solution is therefore sub-optimal. Consequently, we investigate the trade-off between reducing computational complexity and the potential sub-optimality of the solutions that can be controlled with a parameter of the model reduction routine. The efficacy of the proposed method is evaluated using two large scale water distribution network models.
Original languageEnglish
Article number04019014
Number of pages13
JournalJournal of Water Resources Planning and Management
Issue number5
Publication statusPublished - 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project

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  • Outer approximation
  • Optimization
  • Mixed integer nonlinear programming
  • water distribution networks
  • valve placement
  • leakage control


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