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A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation*

Abstract

We present a new method, called the minimum cross-entropy (MCE) method for approximating the optimal solution of NP-hard combinatorial optimization problems and rare-event probability estimation, which can be viewed as an alternative to the standard cross entropy (CE) method. The MCE method presents a generic adaptive stochastic version of Kull-back’s classic MinxEnt method. We discuss its similarities and differences with the standard cross-entropy (CE) method and prove its convergence. We show numerically that MCE is a little more accurate than CE, but at the same time a little slower than CE. We also present a new method for trajectory generation for TSP and some related problems. We finally give some numerical results using MCE for rare-events probability estimation for simple static models, the maximal cut problem and the TSP, and point out some new areas of possible applications.

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Correspondence to R. Y. Rubinstein.

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AMS 2000 Subject Classification: 65C05, 60C05, 68W20, 90C59

*This reseach was supported by the Israel Science Foundation (grant no 191-565).

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Rubinstein, R.Y. A Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-event Estimation*. Methodol Comput Appl Probab 7, 5–50 (2005). https://doi.org/10.1007/s11009-005-6653-7

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  • DOI: https://doi.org/10.1007/s11009-005-6653-7

Keywords

  • combinatorial optimization
  • cross-entropy
  • rare-event estimation
  • Monte Carlo simulation
  • stochastic optimization