Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation
A heuristic algorithm is proposed for a class of stochastic discrete-time continuous-variable dynamic programming problems submitted to non-Gaussian disturbances. Instead of using the expected values of the objective function, the randomness nature of the decision variables is kept along the process...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/801734 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849408364995411968 |
|---|---|
| author | R. T. N. Cardoso R. H. C. Takahashi F. R. B. Cruz |
| author_facet | R. T. N. Cardoso R. H. C. Takahashi F. R. B. Cruz |
| author_sort | R. T. N. Cardoso |
| collection | DOAJ |
| description | A heuristic algorithm is proposed for a class of stochastic discrete-time continuous-variable dynamic programming problems submitted to non-Gaussian disturbances. Instead of using the expected values of the objective function, the randomness nature of the decision variables is kept along the process, while Pareto fronts weighted by all quantiles of the objective function are determined. Thus, decision makers are able to choose any quantile they wish. This new idea is carried out by using Monte Carlo simulations embedded in an approximate algorithm proposed to deterministic dynamic programming problems. The new method is tested in instances of the classical inventory control problem. The results obtained attest for the efficiency and efficacy of the algorithm in solving these important stochastic optimization problems. |
| format | Article |
| id | doaj-art-7992735e64604e8abfc5d53c38114ebd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7992735e64604e8abfc5d53c38114ebd2025-08-20T03:35:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/801734801734Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo SimulationR. T. N. Cardoso0R. H. C. Takahashi1F. R. B. Cruz2Departamento de Física e Matemática, Centro Federal de Educaçäo Tecnológica de Minas Gerais, 30510-000 Belo Horizonte, MG, BrazilDepartamento de Matemática, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, BrazilDepartamento de Estatística, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, BrazilA heuristic algorithm is proposed for a class of stochastic discrete-time continuous-variable dynamic programming problems submitted to non-Gaussian disturbances. Instead of using the expected values of the objective function, the randomness nature of the decision variables is kept along the process, while Pareto fronts weighted by all quantiles of the objective function are determined. Thus, decision makers are able to choose any quantile they wish. This new idea is carried out by using Monte Carlo simulations embedded in an approximate algorithm proposed to deterministic dynamic programming problems. The new method is tested in instances of the classical inventory control problem. The results obtained attest for the efficiency and efficacy of the algorithm in solving these important stochastic optimization problems.http://dx.doi.org/10.1155/2013/801734 |
| spellingShingle | R. T. N. Cardoso R. H. C. Takahashi F. R. B. Cruz Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation Journal of Applied Mathematics |
| title | Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation |
| title_full | Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation |
| title_fullStr | Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation |
| title_full_unstemmed | Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation |
| title_short | Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation |
| title_sort | pareto optimal solutions for stochastic dynamic programming problems via monte carlo simulation |
| url | http://dx.doi.org/10.1155/2013/801734 |
| work_keys_str_mv | AT rtncardoso paretooptimalsolutionsforstochasticdynamicprogrammingproblemsviamontecarlosimulation AT rhctakahashi paretooptimalsolutionsforstochasticdynamicprogrammingproblemsviamontecarlosimulation AT frbcruz paretooptimalsolutionsforstochasticdynamicprogrammingproblemsviamontecarlosimulation |