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.
Similar content being viewed by others
References
Bellman, R., Dynamic Programming, Princeton: Princeton Univ. Press, 1957. Translated under the title Dinamicheskoe programmirovanie, Moscow: Inostrannaya Literatura, 1960.
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.
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.
Baryshnikov, Yu.M., On Expectation of the Number of Variants Undominated in the Binary Relation, Avtom. Telemekh., 1985, no. 6, pp. 111–116.
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.
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.
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.
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.
Peregudov, F.I. and Tarasenko, F.P., Vvedenie v sistemnyi analiz (Introduction to System Analysis), Moscow: Vysshaya Shkola, 1989.
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.
Plott, C.B., Path Independence, Rationality and Social Choice, Econometrica, 1973, vol. 41, no. 6, pp. 1075–1091.
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.
Yudin, D.B., Vychislitel’nye metody teorii prinyatiya reshenii (Computer Methods of the Decision Theory), Moscow: Nauka, 1989.
Berezovskii, B.A., Baryshnikov, Yu.M., Borzenko, V.I., and Kempner, L.M., Multicriteria Optimization: Mathematical Aspects, Moscow: Nauka, 1989.
Bellman, R. and Kalaba, R., On k th-best Policies, J. SIAM., 1960, no. 8, p. 582.
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.
Author information
Authors and Affiliations
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.