Stochastic gradient methods for the optimization of water supply systems

Abstract

Reduction of water deficit for users and energy savings are frequently conflicting issues when optimizing large-scale multi-reservoirs and multi-users water supply system. Undoubtedly, a high uncertainty level due to hydrologic input variability and water demand behaviour characterizes these problems. The aim of this paper is to provide a decision support to the Water System Authority, in order to get a robust decision policy, minimizing the risk of wrong future decisions. It has been done through the optimization of emergency and costly water transfer activation. Hence, a costrisk balancing problem has been modelled to manage this problem, balancing the damages in terms of shortage water occurrences 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 few number of scenarios and a limited time horizon. Nevertheless, if we had 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 problems, it is necessary to apply a specialized approach for the optimization under uncertainty. We develop herein a simulation-optimization model using the stochastic gradient methods. The study case is a multi-reservoir and multiusers water supply system in a specific area in South-Sardinia (Italy), characterized by Mediterranean climate.