Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 801734, 9 pages
http://dx.doi.org/10.1155/2013/801734
Research Article

Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation

1Departamento de Física e Matemática, Centro Federal de Educaçäo Tecnológica de Minas Gerais, 30510-000 Belo Horizonte, MG, Brazil
2Departamento de Matemática, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil
3Departamento de Estatística, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil

Received 30 May 2013; Accepted 28 September 2013

Academic Editor: Lotfollah Najjar

Copyright © 2013 R. T. N. Cardoso et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Bellman, Dynamic Programming, Dover Books on Computer Science Series, Dover, Mineola, NY, USA, 2003. View at MathSciNet
  2. D. P. Bertsekas, Dynamic Programming and Optimal Control, vol. 3, Athena Scientific, Belmont, Mass, USA, 3rd edition, 2007.
  3. B. H. Dias, A. L. M. Marcato, R. C. Souza et al., “Stochastic dynamic programming applied to hydrothermal power systems operation planning based on the convex hull algorithm,” Mathematical Problems in Engineering, vol. 2010, Article ID 390940, 20 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. Y. Zhang, S. Song, C. Wu, and W. Yin, “Dynamic programming and heuristic for stochastic uncapacitated lot-sizing problems with incremental quantity discount,” Mathematical Problems in Engineering, vol. 2012, Article ID 582323, 21 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Ji, C. Sun, and Q. Wei, “The dynamic programming method of stochastic differential game for functional forward-backward stochastic system,” Mathematical Problems in Engineering, vol. 2013, Article ID 958920, 14 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  6. D. P. Bertsekas, Dynamic Programming: Deterministic and Stochastic Models, Prentice Hall, New York, NY, USA, 1987. View at MathSciNet
  7. C. Cervellera, V. C. P. Chen, and A. Wen, “Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization,” European Journal of Operational Research, vol. 171, no. 3, pp. 1139–1151, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. C. Cervellera, A. Wen, and V. C. P. Chen, “Neural network and regression spline value function approximations for stochastic dynamic programming,” Computers & Operations Research, vol. 34, no. 1, pp. 70–90, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. M. Ross, Simulation, Academic Press, San Diego, Calif, USA, 5th edition, 2012. View at MathSciNet
  10. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-Dynamic Programming, Athena Scientific, Belmont, Mass, USA, 1996.
  11. D. P. de Farias and B. van Roy, “Approximate linear programming for average-cost dynamic programming,” in Advances in Neural Information Processing Systems 15, S. T. Becker and K. Obermayer, Eds., pp. 1587–1594, The MIT Press, Cambridge, Mass, USA, 2003. View at Google Scholar
  12. A. M. Thompson and W. R. Cluett, “Stochastic iterative dynamic programming: a Monte Carlo approach to dual control,” Automatica, vol. 41, no. 5, pp. 767–778, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. Luus, Iterative Dynamic Programming, Chapman & Hall/CRC, New York, NY, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  14. H. Kushner, Introduction to Stochastic Control, Holt, Rinehart and Winston, 1971. View at MathSciNet
  15. R. T. N. Cardoso, R. H. C. Takahashi, F. R. B. Cruz, and C. M. Fonseca, “A multi-quantile approach for openloop stochastic dynamic programming problems,” in Proceedings of the IFAC Workshop on Control Applications of Optimization (CAO '09), vol. 7, pp. 52–57, 2009, http://www.scopus.com/inward/record.url?eid=2-s2.0-79960935120&partnerID=40&md5=7c3ed430fc2a0c425d0c182ac0ecf0d8.
  16. V. Chankong and Y. Y. Haimes, Multiobjective Decision Making: Theory and Methodology, Dover, Mineola, NY, USA, 2008.
  17. D. Li and Y. Y. Haimes, “Multiobjective dynamic programming. The state of the art,” Control, Theory and Advanced Technology, vol. 5, no. 4, pp. 471–483, 1989. View at Google Scholar · View at Scopus
  18. T. Trzaskalik and S. Sitarz, “Discrete dynamic programming with outcomes in random variable structures,” European Journal of Operational Research, vol. 177, no. 3, pp. 1535–1548, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. T. N. Cardoso, Algorithms for dynamic programming based on invariant families [M.S. thesis], Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil, 2005, (Portuguese), http://www.mat.ufmg.br/intranet-atual/pgmat/TesesDissertacoes/uploaded/Diss109.pdf.
  20. S. Robinson, “A statistical process control approach to selecting a warm-up period for a discrete-event simulation,” European Journal of Operational Research, vol. 176, no. 1, pp. 332–346, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus