Stochastic optimization of simulation models: management of scarce water resources under risk and uncertainty

Alexei A. Gaivoronski

First

;Giovanni M. Sechi

Second

;Jacopo Napolitano

Penultimate

;Paola Zuddas

Last

2018-01-01

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Abstract

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. On the software side, we show how stochastic gradient methods can be eectively employed in order to optimize complex simulation models and describe stochastic optimization solver STOGRAD, which implements these methods. This solver is specifically designed to handle optimization of simulation models, but it is not limited to them. We apply this methodology to the optimal management of water resources networkv 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 dierent types of demand: agricultural, industrial, public, observing at the same time certain environmental constraints.