Generalized Benders Decomposition to Reoptimize Water Production and Distribution Operations in a Real Water Supply Network

Water supply networks are designed to effectively and efficiently supply water to some originally targeted agglomerations. However, the dynamics over time of water-demand patterns and electricity cost schemes may render these designs inefficient and expensive to operate. This paper considers the challenging problem of optimizing water production and distribution operations in one of the largest water supply networks operating in Flanders (Belgium) while accounting for the water-demand and electricity cost dynamics. Optimizing operations in a real water supply network is a difficult task as it involves many constraints. In addition to the complex hydraulic nonlinear equality constraints stemming from friction losses and pump curves, specific constraints for accurate modeling of storage buffers must be taken into account. These constraints require additional binary variables to model free inflow or possible reinjection of water to the network. The resulting optimization problem is thus a nonconvex mixed-integer and nonlinear mathematical problem that is computationally expensive to solve. A particularly appealing method for solving such optimization problems is Generalized Benders Decomposition (GBD). This paper extends this method to the water supply network optimization problem mentioned previously. It is experimentally shown that the approach is successful through careful selection of the complicating variables and values for the penalty term. Results of the experiments carried out on two network instances show that the carefully fine-tuned model allows convergence to near-optimal solutions. Compared to state-of-the-art solvers, the proposed approach proved to be competitive on the tested networks in terms of solution quality and computational time.