Abstract
The cross-entropy method is a relatively new method for combinatorial optimization. The idea of this method came from the simulation field and then was successfully applied to different combinatorial optimization problems. The method consists of an iterative stochastic procedure that makes use of the importance sampling technique. In this paper we prove the asymptotical convergence of some modifications of the cross-entropy method.
This is a preview of subscription content, log in via an institution to check access.
References
Dubin, U. (2002). “The Cross-Entropy Method with Applications for Combinatorial Optimization. ” Master’s thesis, The Technion, Israel Institute of Technology, Haifa, Israel.
Gutjahr, W.J. (2002). “ACO Algorithms with Guaranteed Convergence to the Optimal Solution. ” Information Processing Letters 82(3), 145–153.
Homem-de-Mello, T. and R.Y. Rubinstein (2002). “Rare Event Estimation for Static Models Via Cross-Entropy and Importance Sampling. ” Manuscript.
Margolin, L. (2002). “Cross-Entropy Method for Combinatorial Optimization. ” Master’s thesis, The Technion, Israel Institute of Technology, Haifa, Israel.
Rubinstein, R.Y. (1997). “Optimization of Computer Simulation Models with Rare Events. ” European Journal of Operational Research 99, 89–112.
Rubinstein, R.Y. (1999). “The Cross-Entropy Method for Combinatorial and Continuous Optimization. ” Methodology and Computing in Applied Probability 2, 127–190.
Rubinstein, R.Y. (2001a). “Combinatorial Optimization, Cross-Entropy, Ants and Rare Events.” In S. Uryasev and P.M. Pardalos (eds.), Stochastic Optimization: Algorithms and Applications, Kluwer, pp. 304–358.
Rubinstein, R.Y. (2001b). “Combinatorial Optimization Via Cross-Entropy. ” In S. Gass and C. Harris (eds.), Encyclopedia of Operations Research and Management Sciences, Kluwer, pp. 102–106.
Rubinstein, R.Y. (2002). “The Cross-Entropy Method and Rare-Events for Maximal Cut and Bipartition Problems. ” ACM Transactions on Modelling and Computer Simulation 12(1), 27–53.
Rubinstein, R.Y. and D.P. Kroese (2004). The Cross Entropy Method. Springer-Verlag.
Walker, A.J. (1977). “An Efficient Method for Generating Discrete Random Variables with General Distributions. ” ACM Transactions on Mathematical Software 3, 253–256.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Margolin, L. On the Convergence of the Cross-Entropy Method. Ann Oper Res 134, 201–214 (2005). https://doi.org/10.1007/s10479-005-5731-0
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10479-005-5731-0