MILPNet: A Mixed Integer Linear Programming Framework to Model Water Distribution Systems Problems

Water distribution systems (WDSs) are critical infrastructure that are used to convey water from sources to consumers. The operation of WDSs is constrained by supply quantities, energy costs, and limits on the operation of control elements like pumps and valves. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDS lends itself to application in a wide range of optimization problems. Several studies have performed optimization of pump scheduling, valve control, and network design using a variety of both deterministic and heuristic optimization techniques. In particular, adapting a classical mixed integer linear programming (MILP) approach to model WDSs guarantees a convex solution space and, by extension, high solution accuracy and low computational effort and time devoted to solving the problem. However, adapting WDS to conform to a MILP formulation has proven challenging because of the intrinsic non-linearity of system hydraulics as well as the complexity associated with modeling hydraulic devices that influence the state of the WDS. This work discusses MILPNet, an adjustable MILP model for WDSs that can be used to build and solve an extensive array of simulations and optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, as well as the behavior of hydraulic devices, control rules, and status checks. To conform with MILP structure, MILPNet’s methodology employs piece-wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Sensitivity analyses were conducted to examine the impacts of our modeling assumptions and the performance of MILPNet was shown to be comparable to EPANET, an industry standard software for hydraulic modeling. Additionally, application of the framework was demonstrated using a pump scheduling optimization example. Our results show that MILPNet can facilitate quick, accurate optimization problem solving for a wide range of applications.