Adding Inferred Constraints Leads to Runtime Inefficiencies in the Optimization of Piped Water Networks

Pressure-constrained piped water network cost optimization is an important problem with significant real world impact. The main design decision to be made for a piped water network is the choice of pipe diameters from a set of commercially available pipe diameters. Rural water networks in the developing world are typically branched networks with a single water source. For such networks, existing methods either solve the constrainedoptimization problem heuristically, or optimally solve the specific case of single pipe segment per link. In the present study, we discuss two approaches to solve the general problem optimally. We show that the approach that attempts to model constraints capturing the inferred structure of the optimal solution results in much worse runtime performance compared to a more general approach. The general formulation proposed is optimal as well as faster than both the previous formulations for the specific problem of one pipe segment per link and the heuristic approach used to solve the general problem. We have implemented the general formulation in a constraint optimization tool and have made it publicly available.