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.
Highlights
Water utilities are facing unprecedented operational challenges from growing water demand, ageing water infrastructure and more stringent environmental standards.utilities are required to continuously improve the quality of service and satisfy customers’ expectations for a cost-efficient operation
In the present work we focus on the mathematical optimization for network pressure management, minimizing average zone pressure through the optimal placement and operation of pressure control valves
Various techniques to handle nonconvex, ill-conditioned problems without a strict relative interior are adopted by advanced nonlinear programming solvers—see as example [42]. These algorithmic modifications are not sufficient to deal with general badly posed problems, the analysis reported in Sect. 6 shows that, in practice, an mathematical program with complementarity constraints (MPCC) reformulation represents a valid alternative to standard mixed integer nonlinear programming (MINLP) techniques for the solution of optimal valve placement and operation in water distribution networks
Summary
Water utilities are facing unprecedented operational challenges from growing water demand, ageing water infrastructure and more stringent environmental standards. Since the optimization problem is nonconvex, like most nonlinear programming algorithms, under suitable assumptions all the methods can guarantee convergence only to local minimum points and the quality of the solutions will depend on the initial points. We take this into account when comparing different approaches and we consider a solution qualitatively good if it is obtained with various random initial guesses and provides an average zone pressure close to the best known solution
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