31 October 2017
This lecture has two components: methodological and applied. On the methodological side, we consider a complex dynamical system, which depends on decision variables and random parameters. The state of this system evolves according to a set of complex rules, which may involve the solution of optimization or game theoretical problems. The evolution of the system over some time horizon is described by a simulation model implementing these rules. Some performance criterion is defined on the sample paths of this simulation model and we are interested in finding such values of decision variables, which yield the optimal expected value of this criterion, possibly under some risk constraints. We show how stochastic gradient methods can be employed in order to achieve this aim.
We apply this methodology to the optimal management of water resources network in Southern Sardinia. This network consists of several interconnected reservoirs and operates under substantial uncertainty about water inflows and general scarcity of water resources. The purpose of this network is to satisfy several different types of demand: agricultural, industrial, public, observing at the same time certain environmental constraints. In order to satisfy this demand the water should be transported upstream under certain circumstances, which generates substantial pumping costs. We simulate the operation of this system and apply stochastic gradient methods in order to find the optimal rules, which trigger the water transfer.
Last edited: 02 November 2017
International Institute for Applied Systems Analysis (IIASA)
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