Relax-Tighten-Round Algorithm for Optimal Placement and Control of Valves and Chlorine Boosters in Water Networks

TL;DR

This paper introduces a relax-tighten-round algorithm to optimize the placement and operation of valves and chlorine boosters in water networks, effectively handling complex nonlinear constraints and outperforming standard solvers.

Contribution

The paper presents a novel relax-tighten-round algorithm for solving a challenging mixed integer nonlinear programming problem in water network optimization.

Findings

Algorithm outperforms standard solvers on benchmark networks.

Provides feasible solutions with small optimality gaps.

Effective for large-scale, real-world water network problems.

Abstract

In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of average zone pressure, while penalizing deviations from a target chlorine concentration. We propose a relax-tighten-round algorithm based on tightened polyhedral relaxations and a rounding scheme to compute feasible solutions, with bounds on their optimality gaps. This is because off-the-shelf global optimization solvers failed to compute feasible solutions for the considered non-convex mixed integer nonlinear program. The implemented algorithm is evaluated using three benchmarking water networks, and they are shown to outperform off-the-shelf solvers, for these case studies. The proposed heuristic has enabled the computation of good quality feasible solutions in most instances, with bounds on the optimality gaps that are comparable to the order of uncertainty observed in operational water network models.