Data efficient learning of implicit control strategies in Water Distribution Networks

Bayesian Optimization is proposed for data-efficient learning of optimal control strategies aimed at minimizing the energy related costs for operating pumps in a water distribution network. The control strategies are defined as pressure-based rules, whose parameters are the decision variables of the optimization problem. A probabilistic description is used to model the optimization problem from parameters to energy cost. The probabilistic model is learned from data obtained by testing a set of parameters via software hydraulic simulation. Bayesian Optimization selects the next values of the parameters to evaluate in a principled way, proving to be able to find globally optimal control strategies, within relatively few trials (i.e., software simulation runs). The proposed Bayesian Optimization framework deals with a quite general formalization of the control problem, including constraints, also black box. Relevant results on a real-life water distribution network are reported, also in comparison with Pure Random Search and Genetic Algorithms.