Fast Non-Linear Optimization for Design Problems on Water Networks

As water infrastructure ages and repair costs increase, optimization techniques are increasingly used for the design and operation of water networks. A key challenge for optimization of water systems is the fast and accurate simulation of hydraulic equations. Conventional simulation tools such as Epanet are fast but cannot perform optimization alone and so must be coupled to an optimization engine, typically a meta-heuristic such as a genetic algorithm. In contrast, mathematical optimization methods take into account hydraulic equations as constraints. The energy equation for pipe flow is a challenging constraint because it is non-linear and given by an explicit function with a rational exponent (Hazen-Williams) or an implicit function (Colebrook-White). This paper uses a quadratic approximation for pipe head loss that provides very good accuracy. The approximation is applied to pose and solve a mixed integer non-linear program (MINLP) for placing and setting pressure-reducing valves. The problem is addressed using both local and global solvers. Computational results show accuracy comparable to Epanet and significant potential to reduce nonrevenue water by deploying optimal solutions.