Convex heuristics for optimal placement and operation of valves and chlorine boosters in water networks

This paper investigates the problem of optimal placement and operation of valves and chlorine boosters in water networks. The objective is to minimize average zone pressure while penalizing deviations from target chlorine concentrations. The problem formulation includes non-convex quadratic terms within constraints representing energy conservation law for each pipe, and discretized differential equations modelling advective transport of chlorine concentrations. Moreover, binary variables model the placement of valves and chlorine boosters. The resulting optimization problem is a non-convex mixed integer non-linear program, which is difficult to solve, especially when large water networks are considered. We develop a new convex heuristic to optimally place and operate valves and chlorine boosters in water networks, while estimating the optimality gaps for the computed solutions. We evaluate the proposed heuristic using case studies with varying sizes, and levels of connectivity and complexity including two large operational water networks. The convex heuristic is shown to generate good quality feasible solutions in all problem instances with bounds on the optimality gap comparable to the level of uncertainty inherent in hydraulic and water quality models.