Optimal Design-for-Control of Chlorine Booster Systems in Water Networks via Convex Optimization

In this manuscript, we investigate the design-for-control problem to optimize locations and operational settings of chlorine boosters in water networks. The objective is to minimize deviations from target chlorine concentrations. The problem formulation includes discretized linear PDEs modeling advective transport of chlorine concentrations. Moreover, binary variables model the placement of chlorine boosters. The resulting optimization problem is a convex mixed integer program (MIP), which is difficult to solve, especially when large water networks are considered. We develop a new swapping heuristic to optimally place and control chlorine boosters in water networks. The proposed method relies on a continuous relaxation of the original MIP. We evaluate the heuristic using two case studies, including one large operational water network from the UK.