Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks

Filippo Pecci, Edo Abraham, Ivan Stoianov

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.

Original languageEnglish
Pages (from-to)201-223
Number of pages23
JournalComputational Optimization and Applications
Volume67
Issue number1
DOIs
Publication statusPublished - 1 May 2017
Externally publishedYes

Keywords

  • Mathematical programs with complementarity constraints
  • Mixed integer nonlinear programming
  • Nonlinear programming
  • Water distribution networks

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