Global optimality bounds for the placement of control valves in water supply networks

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-ofthe-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.

An MINLP-Based Approach for the Design-for-Control of Resilient Water Supply Systems

“…In this work, we modify the method, which generates a sequence of lower and upper bounds to the optimal value of the original problem, to include additional optimality-based bound tightening (OBBT). This further reduces the domain of the problem variables and improves the computed lower bounds compared to the algorithm presented in [22].…”

“…Previous attempts to solve MINLPs to global optimality for the design and/or control of water distribution networks use branch-and-bound methods [19]- [22]. For an introduction to mixed-integer non-linear problems and a review of methods for solving convex and non-convex MINLPs (in particular branch-and-bound), see Belotti et al [23].…”

“…For an introduction to mixed-integer non-linear problems and a review of methods for solving convex and non-convex MINLPs (in particular branch-and-bound), see Belotti et al [23]. We propose to solve the problem of optimal link addition and pressure control implementing a spatial branch-and-bound (sBB) method based on the work of [22], which was shown to outperform state-ofthe-art global optimization solvers for the problem of optimal valve placement in water networks. In this work, we modify the method, which generates a sequence of lower and upper bounds to the optimal value of the original problem, to include additional optimality-based bound tightening (OBBT).…”

Sequential Convex Optimization for Detecting and Locating Blockages in Water Distribution Networks

“…Because of non-convexity, mathematical optimization methods to compute globally optimal solutions for Problem (8) requires the implementation of global optimization techniques (Tawarmalani and Sahinidis 2002). However, these algorithms require a large computational effort, and can be impractical when large water networks are considered (Pecci et al 2018). For this reason, we investigate the implementation of gradient-based optimization algorithms, and develop a trust-region based sequential convex optimization algorithm for solving Problem (8).…”

Laboratory Analysis of a Piston-Actuated Pressure-Reducing Valve under Low Flow Conditions

“…In the literature, diaphragm pressure-reducing valves have been extensively investigated, from device modelling, possibly in combination with an electronic control apparatus [18][19][20][21][22][23][24] also under transient regimes [25], to the optimisation of their location in networks and their setting value [26][27][28][29][30][31][32][33][34][35][36][37]. The efficiency of the use of PRVs in reducing losses has been demonstrated in several studies [13,14,16,17,38].…”