Enhanced Branch & Check for Pump Scheduling in Water Networks

International audiencePump scheduling in drinking water distribution networks is the problem to plan, on the day-ahead typically, the operation of the pumps and the storage usage of the water tanks, in order to meet the dynamic demand in water at minimum costs.In G. Bonvin, S. Demassey, A. Lodi. Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound. Optimization Engineering 2021, a general-purpose global optimization solver has been proposed for this nonconvex minlp. In this approach, a polyhedral outer approximation is solved with a branch-and-cut algorithm where the feasibility of the relaxed nonlinear constrained is checked externally at each integer solution.This talk is made of two parts. We first present the algorithm in a more general way for mixed binary nonlinear programs with some improvements, and how to implement it efficiently in modern milp solvers using callbacks and lazy cut functionalities.In a second part, we devise new cuts for the pump scheduling problem based on duality theory