Lower bounding aggregation and direct computation for an infinite horizon one-reservoir model |
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| Institution: | 1. Institute for Sustainable Plant Protection, National Research Council, Bari 70122, Italy;2. Molecular Plant Pathology Laboratory, US Department of Agriculture, Agricultural Research Service, Beltsville, MD 20705, USA;3. Instituto de Biología Molecular y Celular de Plantas (Consejo Superior de Investigaciones Científicas–Universitat Politècnica de València), Valencia 46022, Spain;4. Institute for Agribiotechnology Research (CIALE), Department of Microbiology and Genetics, University of Salamanca, Villamayor 37185, Salamanca, Spain;5. Instituto Agroforestal Mediterráneo (IAM-UPV), Camino de Vera, s/n 46022, Valencia, Spain;6. Institute of Biochemistry and Biotechnology, Section Microbial Biotechnology, Martin Luther University Halle-Wittenberg, Halle/Saale 06120, Germany |
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| Abstract: | We present a specialized policy iteration method for the computation of optimal and approximately optimal policies for a discrete-time model of a single reservoir whose discharges generate hydroelectric power. The model is described in (Lamond et al., 1995) and (Drouin et al., 1996), where the special structure of optimal policies is given and an approximate value iteration method is presented, using piecewise affine approximations of the optimal return functions. Here, we present a finite method for computing an optimal policy in O(n3) arithmetic operations, where n is the number of states in the associated Markov decision process, and a finite method for computing a lower bound on the optimal value function in O(m2n) where m is the number of nodes of the piecewise affine approximation. |
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