References
V. M. Glushkov, “On system optimization,”Kibernetika, No. 5, 89–90 (1980).
C. H. Papadimitriou and K. Steiglitz,Combinatorial Optimization: Algorithms and Complexity, Prentice Hall, Englewood Cliffs, NJ (1982).
I. V. Sergienko,Mathematical Models and Solution Methods for Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1985).
I. V. Sergienko, V. M. Grinchuk, L. F. Gulyanitskii, and L. B. Koshlai, “Algorithms to construct a mathematical model of preferences using expert judgments,”Kibernetika, No. 2, 16–22 (1991).
S. Kirkpatick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,”Science,220, No. 4598, 671–680 (1983).
P. I. M. van Laarhoven and E. H. L. Aarts,Simulated Annealing: Theory and Practice, Kluwer, Dordrecht (1987).
T. Elperin, “Monte Carlo structural optimization in discrete variables with annealing algorithm,”Int. J. Num. Meth. Eng.,26, 815–821 (1988).
F. A. Ogbu and D. K. Smith, “The application of the simulated annealing algorithm to the solution of the n/m/Cmax flowshop problem,”Comput. Oper. Res.,17, No. 3, 243–253 (1990).
D. S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon, “Optimization by simulated annealing: an experimental evaluation. I. Graph partitioning,”Oper. Res.,37, No. 6, 865–892 (1989).
E. H. L. Aarts, P. J. M. van Laarhoven, “Statistical cooling: a general approach to combinatorial optimization problems,”Philips J. Res.,40, 193–226 (1985).
M. Lundy and A. Mess, “Convergence of an annealing algorithm,”Math. Progr.,34, 111–124 (1986).
D. Mitra, F. Romeo, A. Sanglovanni-Vincentelli, “Convergence and finite-time behavior of simulated annealing,”Adv. Appl. Prob.,18, 747–771 (1986).
S. Geman and D. Geman, “Stochastic relaxation, Gibbs distribution, Bayesian restoration of image,”IEEE Trans., PAMI,6, 721–741 (1984).
B. Hajek, “Cooling schedules for optimal annealing,”Math. Oper. Res.,13, 311–329 (1988).
J. N. Tsitsiklis, “Markov chains with rare transitions and simulated annealing,”Math. Oper. Res.,14, No. 1, 70–90 (1989).
L. F. Gulyanitskii,Solution of Quadratic Assignment Problems by Probabilistic Simulation Algorithms [in Russian], Preprint 91-45, IK AN UkrSSR, Kiev (1991).
L. B. Koshlai,Development of Algorithms and Software for the Solution of One Class of Weakly Structured Optimization Problems [in Russian], Thesis, IK AN UkrSSR, Kiev (1992).
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The research is financed by State Foundation for Basic Research of the State Committee of Science and Technology of Ukraine.
Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 163–167, May–June, 1993.
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Gulyanitskii, L.F., Koshlai, L.B. & Sergienko, I.V. Convergence of a simulation method for solution of combinatorial optimization problems. Cybern Syst Anal 29, 445–449 (1993). https://doi.org/10.1007/BF01125551
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DOI: https://doi.org/10.1007/BF01125551