Stochastic gradient methods for the optimization of water supply systems

Reductions of water deficits for users and energy savings are frequently conflicting issues when optimizing largescale multi-reservoir and multi-user water supply systems. Undoubtedly, a high level of uncertainty due to hydrologic input variability and water demand behaviour characterizes these problems. The aim of this paper is to provide a decision support for the water system authority, in order to realize a robust decision policy, minimizing the risk of wrong future decisions. This has been done through the optimization of emergency and costly water transfer activation. Hence, a cost–risk balancing problem has been modelled to manage this problem, balancing the damages in terms of occurrences of water shortages and energy and cost requirements for emergency transfers. In Napolitano et al. (2016), we dealt with this problem using a scenario analysis approach. The obtained results were appreciable considering a limited amount of scenarios and a short time horizon. Nevertheless, if we have to increase the number of considered scenarios, taking into account the effect of climate and hydrological changes, computational problems arise. Therefore, to solve this kind of problem, it is necessary to apply a specialized approach for optimization under uncertainty. We develop herein a simulation-optimization model using the stochastic gradient methods. The study case is a multi-reservoir and multi-user water supply system in a specific area in south Sardinia (Italy), characterized by Mediterranean climate.