Model-Based Stochastic Search Methods

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Handbook of Simulation Optimization

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 216))

Abstract

Model-based algorithms are a class of stochastic search methods that have successfully addressed some hard deterministic optimization problems. However, their application to simulation optimization is relatively undeveloped. This chapter reviews the basic structure of model-based algorithms, describes some recently developed frameworks and approaches to the design and analysis of a class of model-based algorithms, and discusses their extensions to simulation optimization.

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References

  1. G. Allon, D. P. Kroese, T. Raviv, and R. Y. Rubinstein. Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment. Annals of Operations Research, 134:137–151, 2005.

    Article  Google Scholar 

  2. S. Andradóttir. An overview of simulation optimization with random search. In S. G. Henderson and B. L. Nelson, editors, Handbooks in Operations Research and Management Science: Simulation. Elsevier, 2006.

    Google Scholar 

  3. R. R. Barton and M. Meckesheimer. Metamodel-based simulation optimization. In S. G. Henderson and B. L. Nelson, editors, Handbooks in Operations Research and Management Science: Simulation. Elsevier, 2006.

    Google Scholar 

  4. M. Benaim. A dynamical system approach to stochastic approximations. SIAM Journal on Control and Optimization, 34:437–472, 1996.

    Article  Google Scholar 

  5. V. S. Borkar. Stochastic approximation: a dynamical systems viewpoint. Cambridge University Press; New Delhi: Hindustan Book Agency, 2008.

    Google Scholar 

  6. Y. Cai, X. Sun, and P. Jia. Probabilistic modeling for continuous eda with boltzmann selection and kullback-leibeler divergence. In Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pages 389–396, 2006.

    Google Scholar 

  7. A. Costa, O. D. Jones, and D. Kroese. Convergence properties of the cross-entropy method for discrete optimization. Operations Research Letters, 35(5):573–580, 2007.

    Article  Google Scholar 

  8. M. Dorigo and L. M. Gambardella. Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1:53–66, 1997.

    Article  Google Scholar 

  9. F. W. Glover. Tabu search: A tutorial. Interfaces, 20:74–94, 1990.

    Article  Google Scholar 

  10. D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Kluwer Academic Publishers, Boston, MA, 1989.

    Google Scholar 

  11. W. B. Gong, Y. C. Ho, and W. Zhai. Stochastic comparison algorithm for discrete optimization with estimation. SIAM Journal on Optimization, 10:384–404, 1999.

    Article  Google Scholar 

  12. W. J. Gutjahr. A converging aco algorithm for stochastic combinatorial optimization. In Proceedings of SAGA 2003 Stochastic Algorithms: Foundations and Applications, pages 10–25, 2003.

    Google Scholar 

  13. T. Homem-de-Mello. A study on the cross-entropy method for rare-event probability estimation. INFORMS Journal on Computing, 19:381–394, 2007.

    Article  Google Scholar 

  14. T. Homem-de-Mello. On rates of convergence for stochastic optimization problems under non-independent and identically distributed sampling. SIAM Journal on Optimization, 19:524–551, 2008.

    Article  Google Scholar 

  15. L. J. Hong and B. L. Nelson. Discrete optimization via simulation using compass. Operations Research, 54:115–129, 2006.

    Article  Google Scholar 

  16. J. Hu and H. S. Chang. An approximate stochastic annealing algorithm for finite horizon markov decision processes. In Proceedings of the 49th IEEE Conference on Decision and Control, pages 5338–5343, 2010.

    Google Scholar 

  17. J. Hu, H. S. Chang, M. C. Fu, and S. I. Marcus. Dynamic sample budget allocation in model-based optimization. Journal of Global Optimization, 50:575–596, 2011.

    Article  Google Scholar 

  18. J. Hu, M. C. Fu, and S. I. Marcus. A model reference adaptive search method for global optimization. Operations Research, 55:549–568, 2007.

    Article  Google Scholar 

  19. J. Hu, M. C. Fu, and S. I. Marcus. A model reference adaptive search method for stochastic global optimization. Communications in Information and Systems, 8:245–276, 2008.

    Article  Google Scholar 

  20. J. Hu and P. Hu. On the performance of the cross-entropy method. In Proceedings of the 2009 Winter Simulation Conference, pages 459–468. IEEE, Piscataway, NJ, 2009.

    Google Scholar 

  21. J. Hu and P. Hu. Annealing adaptive search, cross-entropy, and stochastic approximation in global optimization. Naval Research Logistics, 58:457–477, 2011.

    Article  Google Scholar 

  22. J. Hu, P. Hu, and H. S. Chang. A stochastic approximation framework for a class of randomized optimization algorithms. IEEE Transactions on Automatic Control, 57:165–178, 2012.

    Article  Google Scholar 

  23. J. Hu and C. Wang. Discrete optimization via approximate annealing adaptive search with stochastic averaging. In Proceedings of the 2011 Winter Simulation Conference, pages 4206–4216. IEEE, Piscataway, NJ, 2011.

    Google Scholar 

  24. J. Hu, E. Zhou, and Q. Fan. Model-based annealing random search with stochastic averaging. ACM Transactions on Modeling and Computer Simulation, forthcoming, 2014.

    Google Scholar 

  25. J. Kennedy and R. Eberhart. Particle swarm optimization. In Proceedings of IEEE International Conference on Neural Networks, pages 1942–1948, 1995.

    Google Scholar 

  26. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220:671–680, 1983.

    Article  Google Scholar 

  27. A. Kleywegt, A. Shapiro, and T. Homem-de-Mello. The sample average approximation method for stochastic discrete optimization. SIAM Journal on Optimization, 12:479–502, 2001.

    Article  Google Scholar 

  28. H. J. Kushner and D. S. Clark. Stochastic Approximation Methods for Constrained and Unconstrained Systems and Applications. Springer-Verlag, New York, 1978.

    Book  Google Scholar 

  29. H. J. Kushner and G. G. Yin. Stochastic Approximation Algorithms and Applications. Springer-Verlag, New York, 1997.

    Book  Google Scholar 

  30. P. Larrañaga and J. A. Lozano. Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publisher, Boston, MA, 2002.

    Book  Google Scholar 

  31. S. Mannor, R. Y. Rubinstein, and Y. Gat. The cross-entropy method for fast policy search. In Proceedings of the 20th International Conference on Machine Learning, pages 512–519, 2003.

    Google Scholar 

  32. H. E. Romeijn and R. L. Smith. Simulated annealing and adaptive search in global optimization. Probability in the Engineering and Informational Sciences, 8:571–590, 1994.

    Article  Google Scholar 

  33. R. Y. Rubinstein. Optimization of computer simulation models with rare events. European Journal of Operational Research, 99:89–112, 1997.

    Article  Google Scholar 

  34. R. Y. Rubinstein. Combinatorial optimization, ants and rare events. In S. Uryasev and P. M. Pardalos, editors, Stochastic Optimization: Algorithms and Applications, pages 304–358, 2001.

    Google Scholar 

  35. 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, 2004.

    Book  Google Scholar 

  36. L. Shi and S. Ólafsson. Nested partitions method for global optimization. Operations Research, 48:390–400, 2000.

    Article  Google Scholar 

  37. D. H. Wolpert. Finding bounded rational equilibria part i: Iterative focusing. In T. Vincent, editor, Proceedings of the Eleventh International Symposium on Dynamic Games and Applications, 2004.

    Google Scholar 

  38. D. Yan and H. Mukai. Stochastic discrete optimization. SIAM Journal on Control and Optimization, 30:594–612, 1992.

    Article  Google Scholar 

  39. Z. B. Zabinsky. Stochastic Adaptive Search for Global Optimization. Kluwer Academic Publishers, 2003.

    Google Scholar 

  40. Z. B. Zabinsky, R. L. Smith, J. F. McDonald, H. E. Romeijn, and D. E. Kaufman. Improving hit-and-run for global optimization. Journal of Global Optimization, 3:171–192, 1993.

    Article  Google Scholar 

  41. Q. Zhang and H. Mühlenbein. On the convergence of a class of estimation of distribution algorithm. IEEE Transactions on Evolutionary Computation, 8:127–136, 2004.

    Article  Google Scholar 

  42. E. Zhou, M. C. Fu, and S. I. Marcus. A particle filtering framework for randomized optimization algorithms. In Proceedings of the 2008 Winter Simulation Conference, pages 647–654. IEEE, Piscataway, NJ, 2008.

    Google Scholar 

  43. E. Zhou and J. Hu. Gradient guided adaptive stochastic search. IEEE Transactions on Automatic Control, 59:1818–1832, 2014.

    Article  Google Scholar 

  44. M. Zlochin, M. Birattari, N. Meuleau, and M. Dorigo. Model-based search for combinatorial optimization: A critical survey. Annals of Operations Research, 131:373–395, 2004.

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the National Science Foundation (NSF) under Grant CMMI-1130761 and by the Air Force Office of Scientific Research (AFOSR) under Grant FA95501010340.

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Correspondence to Jiaqiao Hu .

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Hu, J. (2015). Model-Based Stochastic Search Methods. In: Fu, M. (eds) Handbook of Simulation Optimization. International Series in Operations Research & Management Science, vol 216. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1384-8_12

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