Annealing adaptive search, cross-entropy, and stochastic approximation in global optimization

Naval Research Logistics

Volumn 58, Issue 5, 2011, Pages 457-477

  Hu, Jiaqiao ^a   Hu, Ping ^a  

^a Stony Brook University   (United States)

Author keywords

annealing adaptive search (AAS); cross entropy method (CE); global optimization; stochastic approximation (SA)

Indexed keywords

ADAPTIVE SEARCH; ASYMPTOTIC CONVERGENCE RATE; BOLTZMANN DISTRIBUTION; CROSS ENTROPY; CROSS-ENTROPY METHOD; EMPIRICAL RESULTS; GLOBAL CONVERGENCE; MODEL REFERENCE ADAPTIVE; OPTIMIZATION PROBLEMS; RANDOM SEARCHES; SAMPLING TECHNIQUE; SOLUTION SPACE; STOCHASTIC APPROXIMATION METHODS; STOCHASTIC APPROXIMATIONS;

ANNEALING; APPROXIMATION THEORY; BOLTZMANN EQUATION; CONVERGENCE OF NUMERICAL METHODS; ENTROPY; GLOBAL OPTIMIZATION; MARKOV PROCESSES; OPTIMIZATION; STOCHASTIC SYSTEMS;

APPROXIMATION ALGORITHMS;

EID: 79960273055     PISSN: 0894069X     EISSN: 15206750     Source Type: Journal    
DOI: 10.1002/nav.20462     Document Type: Article

References (32)

1. Y. Cai, X. Sun, and, P. Jia, "Probabilistic modeling for continuous EDA with Boltzmann selection and Kullback-Leibeler divergence," Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, Seattle, WA, 2006, pp. 389-396.
2. M. Dorigo, and, L.M. Gambardella, Ant colony system: A cooperative learning approach to the traveling salesman problem, IEEE Trans Evol Comput 1 (1997), 53-66. (Pubitemid 127771018)
3. A. Dukkipati, M.N. Murty, and, S. Bhatnagar, "Cauchy annealing schedule: An annealing schedule for Boltzmann selection scheme in evolutionary algorithms," in: Proceedings of the 2004 Congress on Evolutionary Computation: CEC 2004, June 19-23, 2004, Portland OR, USA.
4. S.N. Evans, and, N.C. Weber, On the almost sure convergence of a general stochastic approximation procedure, Bull Australian Math Soc 34 (1986), 335-342.
5. V. Fabian, On asymptotic normality in stochastic approximation, Ann Math Stat 39 (1968), 1327-1332.
6. M. Fu, J. Hu, and, S.I. Marcus, "Model-based randomized methods for global optimization," Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan, 2006, 355-363.
7. F.W. Glover, Tabu search: A tutorial, Interfaces 20 (1990), 74-94.
8. D.E. Goldberg, Genetic algorithms in search, optimization, and machine learning, Kluwer Academic Publishers, Boston, MA, 1989.
9. J. Hu, M.C. Fu, and, S.I. Marcus, A model reference adaptive search algorithm for global optimization, Oper Res 55 (2007), 549-568. (Pubitemid 351159509)
10. W. Hoeffding, Probability inequalities for sums of bounded random variables, J Am Statist Assoc 58 (1963), 13-30.
11. S. Kirkpatrick, C.D. Gelatt, and, M.P. Vecchi, Optimization by simulated annealing, Science 220 (1983), 671-680.
12. H.J. Kushner, and, D.S. Clark, Stochastic approximation methods for constrained and unconstrained systems, Springer-Verlag, New York, NY, 1978.
13. H.J. Kushner, and, G.G. Yin, Stochastic approximation algorithms and applications, Springer-Verlag, New York, NY, 1997.
14. P.J.M. Laarhoven, and, E.H.L. Aarts, Simulated annealing: Theory and applications, Kluwer Academic Publisher, Norwell, MA, 1987.
15. P. Larrañaga, and, J.A. Lozano, (Editors), Estimation of distribution algorithms: A new tool for evolutionary computation, Kluwer Academic Publisher, Boston, MA, 2002.
16. C.N. Morris, Natural exponential families with quadratic variance functions, Ann Statist 10 (1982), 65-80.
17. J.D. Pintér, Global optimization in action, Kluwer Academic Publisher, The Netherlands, 1996.
18. H.E. Romeijn, and, R.L. Smith, Simulated annealing and adaptive search in global optimization, Probab Eng Inform Sci 8 (1994), 571-590.
19. H.E. Romeijn, and, R.L. Smith, Simulated annealing for constrained global optimization, J Global Optim 5 (1994), 101-126.
20. H. Robbins, and, S. Monro, A stochastic approximation method, Ann Math Statist 22 (1951), 400-407.
21. R.Y. Rubinstein, and, D.P. Kroese, The cross-entropy method: A unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning, Springer, New York, NY, 2004.
22. Y. Shen, S. Kiatsupaibul, Z.B. Zabinsky, and, R.L. Smith, An analytically derived cooling schedule for simulated annealing, J Global Optim 38 (2007), 333-365. (Pubitemid 46872965)
23. L. Shi, and, S. Ãlafsson, Nested partitions method for stochastic optimization, Methodol Comput Appl Probab 2 (2000), 271-291.
24. J.C. Spall, Introduction to stochastic search and optimization, Wiley, New York, NY, 2003.
25. J.C. Spall, and, J.A. Cristion, Model-free control of nonlinear stochastic systems with discrete-time measurements, IEEE Trans Automat Control 43 (1998), 1198-1210. (Pubitemid 128736510)
26. F. Topsoe, Bounds for entropy and divergence for distributions over a two-element set, J Inequal Pure Appl Math 2 (2001), Article 25.
27. D.H. Wolpert, "Finding bounded rational equilibria part I: Iterative focusing," Proceedings of the Eleventh International Symposium on Dynamic Games and Applications, in:, T. Vincent, (Editor), Tucson AZ, USA, December, 2004.
28. X. Yao, and, Y. Liu, "Fast evolutionary programming," Proceedings of the 5th Annual Conference on Evolutionary Programming, MIT Press, 1996, pp. 451-460.
29. Z.B. Zabinsky, and, R.L. Smith, Pure adaptive search in global optimization, Math Program 53 (1992), 323-338.
30. Z.B. Zabinsky, Stochastic adaptive search for global optimization, Kluwer Academic Publishers, Boston, MA, 2003.
31. Z.B. Zabinsky, R.L. Smith, J.F. McDonald, H.E. Romeijn, and, D.E. Kaufman, Improving hit-and-run for global optimization, J Global Optim 3 (1993), 171-192.
32. M. Zlochin, M. Birattari, N. Meuleau, and, M. Dorigo, Model-based search for combinatorial optimization: A critical survey, Ann Oper Res 131 (2004), 373-395. (Pubitemid 39187387)