Abstract
This manuscript investigates the problem of optimal placement of control valves in water supply networks, where the objective is to minimize average zone pressure. The problem formulation results in a nonconvex mixed integer nonlinear program (MINLP). Due to its complex mathematical structure, previous literature has solved this nonconvex MINLP using heuristics or local optimization methods, which do not provide guarantees on the global optimality of the computed valve configurations. In our approach, we implement a branch and bound method to obtain certified bounds on the optimality gap of the solutions. The algorithm relies on the solution of mixed integer linear programs, whose formulations include linear relaxations of the nonconvex hydraulic constraints. We investigate the implementation and performance of different linear relaxation schemes. In addition, a tailored domain reduction procedure is implemented to tighten the relaxations. The developed methods are evaluated using two benchmark water supply networks and an operational water supply network from the UK. The proposed approaches are shown to outperform state-of-the-art global optimization solvers for the considered benchmark water supply networks. The branch and bound algorithm converges to good quality feasible solutions in most instances, with bounds on the optimality gap that are comparable to the level of parameter uncertainty usually experienced in water supply network models.
Highlights
The efficient management of hydraulic pressure in pipes results in reduction of leakage (Lambert 2000; Wright et al 2015) and risk of pipe failure (Lambert and Thornton 2011), and it is one of the main operational challenges in water supply networks (WSNs)
The Mixed Integer Linear Programming (MILP) and linear programs (LPs) involved in Algorithms 1 and 2 are solved using GUROBI (v7.5) (Gurobi Optimization 2017), which is accessed via its MATLAB interface
We have investigated the application of branch and bound strategies to compute -sub-optimal solutions for the problem of optimal valve placement and operation in water supply networks
Summary
The efficient management of hydraulic pressure in pipes results in reduction of leakage (Lambert 2000; Wright et al 2015) and risk of pipe failure (Lambert and Thornton 2011), and it is one of the main operational challenges in water supply networks (WSNs). We investigate the problem of simultaneously optimizing the placement and operational settings of control valves in WSNs, where the objective is to minimize average zone pressure (AZP). The solution of process network optimization problems frequently relies on the solution of MINLPs. Some examples include synthesis of heat exchanger networks (Zamora and Grossmann 1998), multi-period blending (Kolodziej et al 2013), optimal design and operation of gas networks (Pfetsch et al 2015; Humpola and Fügenschuh 2015), and water supply networks (DAmbrosio et al 2015). In the framework of WSNs, MINLP formulations are ubiquitous and employed in a variety of applications, ranging from optimal network design (Bragalli et al 2012; Sherali et al 1999) to pump scheduling (Menke et al 2015; Gleixner et al 2012)
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