Optimal design for control of water supply networks by mixed integer programming

Abstract

The efficient management of hydraulic pressure in pipes is one of the main operational challenges in water supply networks. This thesis considers pressure management that is actuated by pressure control valves. The research investigates the problem of optimising valve locations and their operational settings simultaneously - this approach is referred to as the design-for-control optimisation problem. Initially, the thesis focuses on the minimisation of average zone pressure. The problem formulation employs quadratic approximations of the non-smooth friction head loss formulae, and results in a nonconvex mixed integer nonlinear program (MINLP). Building upon previous work, the research studies two numerical schemes, namely penalty and relaxation methods, for the solution of the formulated MINLP problem. While these methods are shown to be effective on a published benchmark network model, their limitations for the solution of the problem of optimal valve placement in large operational water networks are highlighted. A new problem formulation is proposed, reducing the degree of nonlinearity within optimisation constraints. This reformulation allows the application of outer approximation based schemes, enabling the solution of the considered MINLP when large operational water supply networks are considered. Since the MINLP for optimal valve placement is nonconvex, previously developed approaches do not provide theoretical guarantees on the global optimality of the computed valve configurations. Here, the research implements a branch and bound method to obtain certified bounds on the optimality gap of the solutions. The branch and bound algorithm is shown to converge to good quality feasible solutions, with bounds on the optimality gap comparable to the level of uncertainty inherent in water network models. Finally, the problem formulation for optimal valve placement is extended to the framework of multiobjective optimisation, to evaluate the trade-offs between the minimisation of average zone pressure and pressure variability. Scalarisation schemes are used to convert the original multiobjective MINLP into series of single-objective MINLPs that are individually solved using outer approximation methods. The proposed approaches have enabled the generation of wide and uniform Pareto fronts for a large operational water network.