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Mathematical Programming

, Volume 52, Issue 1–3, pp 359–375 | Cite as

Multi-stage stochastic optimization applied to energy planning

  • M. V. F. Pereira
  • L. M. V. G. Pinto
Article

Abstract

This paper presents a methodology for the solution of multistage stochastic optimization problems, based on the approximation of the expected-cost-to-go functions of stochastic dynamic programming by piecewise linear functions. No state discretization is necessary, and the combinatorial “explosion” with the number of states (the well known “curse of dimensionality” of dynamic programming) is avoided. The piecewise functions are obtained from the dual solutions of the optimization problem at each stage and correspond to Benders cuts in a stochastic, multistage decomposition framework. A case study of optimal stochastic scheduling for a 39-reservoir system is presented and discussed.

Keywords

Linear Function Mathematical Method Dynamic Programming Stochastic Optimization Piecewise Linear Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. J.F. Benders, “Partitioning procedures for solving mixed variables programming problems,”Numerische Mathematik 4 (1962) 238–252.Google Scholar
  2. J.R. Birge, “Solution methods for stochastic dynamic linear programs,” Report 80/29, Systems Optimization Laboratory, Department of Operations Research, Stanford University (Stanford, CA, 1980).Google Scholar
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  4. J.L. Kennington and R.V. Helgason,Algorithms for Network Programming (Wiley, New York, 1984).Google Scholar
  5. M.V.F. Pereira and L.M.V.G. Pinto, “Stochastic optimization of a multireservoir hydroelectric system—a decomposition approach”,Water Resources Research 21(6) (1985).Google Scholar
  6. R. J.-B. Wets, “Large scale linear programming techniques,” in: Y. Ermoliev and R. Wets, eds.,Numerical Methods for Stochastic Optimization (Springer, Berlin, 1988) Chapter 3.Google Scholar

Copyright information

© The Mathematical Programming Society, Inc. 1991

Authors and Affiliations

  • M. V. F. Pereira
    • 1
  • L. M. V. G. Pinto
    • 1
  1. 1.Electric Engineering DepartmentCatholic University of Rio de JaneiroGavea, Rio de JaneiroBrazil

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