Cost Optimization of Water Distribution Networks: Model Refinement Is Better Than Problem-Specific Solving Techniques

Abstract: Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a rich set of model refinement techniques. The networks that we study contain a single source and multiple demand nodes with residual pressure constraints. Indeterminism of flow values and flow direction in the network leads to non-linearity in these constraints making the optimization problem non-convex. While the physical network is cyclic, flow through the network is necessarily acyclic and thus enforces an acyclic orientation. We devise different strategies of finding acyclic orientations and explore the benefit of enforcing such orientations explicitly as a constraint. Finally, we propose a parallel link formulation that models flow in each link as two separate flows with opposing directions. This allows us to tackle numerical difficulties in optimization when flow in a link is near zero. We find that all our proposed formulations give results at par with least cost solutions obtained in the literature on benchmark networks. We also introduce a suite of large test networks since existing benchmark networks are small in size, and find that the parallel link approach outperforms all other approaches on these bigger networks, resulting in a more tractable technique of cost optimization.