Skip to main content
Log in

Generalization of the dynamic programming scheme

  • Discrete Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

A new generalization of the Bellman optimality principle and the scheme of dynamic programming in terms of the language of choice functions was proposed. Proved were their correctness and applicability to the multistage decision making.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bellman, R., Dynamic Programming, Princeton: Princeton Univ. Press, 1957. Translated under the title Dinamicheskoe programmirovanie, Moscow: Inostrannaya Literatura, 1960.

    Google Scholar 

  2. Velichko, D.A., Methods of Multicriteria Search of the Optimal Variants of Production Line Configuration and Technology (Exemplified by the Semiconductor Production), Cand. Sci. (Eng.) Dissertation, Voronezh: VTI, 1983.

    Google Scholar 

  3. Sysoev, V.V., Strukturnye i algoritmicheskie modeli avtomatizirovannogo proektirovaniya proizvodstva izdelii elektronnoi tekhniki (Structural and Algorithmic Models of Computer-aided Design of Electronic Devices), Voronezh: VTI, 1993.

    Google Scholar 

  4. Baryshnikov, Yu.M., On Expectation of the Number of Variants Undominated in the Binary Relation, Avtom. Telemekh., 1985, no. 6, pp. 111–116.

  5. Ivanin, V.M., On One Estimate of the Expectation of the Number of Elements of the Pareto Set, Kibernetika, 1975, no. 3, pp. 145–147.

  6. Bugaev, Yu.V., Application of the Direct Generalization of the Scalar Algorithms in the Vector Optimization on Graphs, Diskretn. Mat., 2001, vol. 13, no. 3, pp. 110–124.

    MathSciNet  Google Scholar 

  7. Chikunov, S.V., Structural-Parametric Design of the Models of Multicriteria Step-by-Step Choice of Decisions in Technological Systems, Cand. Sci. (Eng.) Dissertation, Voronezh: VGTA, 2003.

    Google Scholar 

  8. Bugaev, Yu.V. and Chikunov, S.V., Experimental Studies of the Algorithms of Multicriteria Step-by-Step Choice of Decisions in the Technological Systems, in Teoreticheskie osnovy proektirovaniya tekhnologicheskikh sistem i oborudovaniya avtomatizirovannykh proizvodstv. Sb. nauch. tr. (Theoretical Fundamentals of Design of Technological Systems and Equipment of the Computer-aided Manufacturing. Collected Papers), Voronezh: VGTA, 2007, no. 5, part 1, pp. 68–82.

    Google Scholar 

  9. Peregudov, F.I. and Tarasenko, F.P., Vvedenie v sistemnyi analiz (Introduction to System Analysis), Moscow: Vysshaya Shkola, 1989.

    Google Scholar 

  10. Bugaev, Yu.V., Design of the Models of Choice of Technological Decisions on the Basis of Two-stage Majority Schemes, Doctoral (Phys.-Math.) Dissertation, Voronezh: VGTA, 2005.

    Google Scholar 

  11. Plott, C.B., Path Independence, Rationality and Social Choice, Econometrica, 1973, vol. 41, no. 6, pp. 1075–1091.

    Article  MATH  MathSciNet  Google Scholar 

  12. Aizerman, M.A. and Malishevskii, A.V., Some Aspects of the General Theory of Choice of the Best Variants, Avtom. Telemekh., 1981, no. 2, pp. 65–82.

  13. Yudin, D.B., Vychislitel’nye metody teorii prinyatiya reshenii (Computer Methods of the Decision Theory), Moscow: Nauka, 1989.

    Google Scholar 

  14. Berezovskii, B.A., Baryshnikov, Yu.M., Borzenko, V.I., and Kempner, L.M., Multicriteria Optimization: Mathematical Aspects, Moscow: Nauka, 1989.

    Google Scholar 

  15. Bellman, R. and Kalaba, R., On k th-best Policies, J. SIAM., 1960, no. 8, p. 582.

  16. Kravtsov, M.K., Insolvability of the Problems of Vector Discrete Optimization in the Class of Algorithms of Linear Convolution of Criteria, Diskretn. Mat., 1996, vol. 8, no. 2, pp. 89–96.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © Yu.V. Bugaev, S.V. Chikunov, 2009, published in Avtomatika i Telemekhanika, 2009, No. 2, pp. 90–100.

This work was supported by the Russian Foundation for Basic Research, project no. 06-07-89189.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bugaev, Y.V., Chikunov, S.V. Generalization of the dynamic programming scheme. Autom Remote Control 70, 253–262 (2009). https://doi.org/10.1134/S0005117909020076

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117909020076

PACS numbers

Navigation