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Cross-entropy method

About: Cross-entropy method is a research topic. Over the lifetime, 745 publications have been published within this topic receiving 28244 citations.


Papers
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Journal ArticleDOI
TL;DR: It is conjecture that the analogy with thermodynamics can offer a new insight into optimization problems and can suggest efficient algorithms for solving them.
Abstract: We present a Monte Carlo algorithm to find approximate solutions of the traveling salesman problem. The algorithm generates randomly the permutations of the stations of the traveling salesman trip, with probability depending on the length of the corresponding route. Reasoning by analogy with statistical thermodynamics, we use the probability given by the Boltzmann-Gibbs distribution. Surprisingly enough, using this simple algorithm, one can get very close to the optimal solution of the problem or even find the true optimum. We demonstrate this on several examples. We conjecture that the analogy with thermodynamics can offer a new insight into optimization problems and can suggest efficient algorithms for solving them.

3,061 citations

Book
01 Jan 1983
TL;DR: In this article, problem complexity and method efficiency in optimisation are discussed in terms of problem complexity, method efficiency, and method complexity in the context of OO optimization, respectively.
Abstract: (1984). Problem Complexity and Method Efficiency in Optimization. Journal of the Operational Research Society: Vol. 35, No. 5, pp. 455-455.

2,382 citations

Journal ArticleDOI
TL;DR: This tutorial presents the CE methodology, the basic algorithm and its modifications, and discusses applications in combinatorial optimization and machine learning.
Abstract: The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning.

2,367 citations

Journal ArticleDOI
TL;DR: The mode of a unimodal importance sampling distribution, like the mode of beta distribution, is used as an estimate of the optimal solution for continuous optimization and Markov chains approach for combinatorial optimization.
Abstract: We present a new and fast method, called the cross-entropy method, for finding the optimal solution of combinatorial and continuous nonconvex optimization problems with convex bounded domains. To find the optimal solution we solve a sequence of simple auxiliary smooth optimization problems based on Kullback-Leibler cross-entropy, importance sampling, Markov chain and Boltzmann distribution. We use importance sampling as an important ingredient for adaptive adjustment of the temperature in the Boltzmann distribution and use Kullback-Leibler cross-entropy to find the optimal solution. In fact, we use the mode of a unimodal importance sampling distribution, like the mode of beta distribution, as an estimate of the optimal solution for continuous optimization and Markov chains approach for combinatorial optimization. In the later case we show almost surely convergence of our algorithm to the optimal solution. Supporting numerical results for both continuous and combinatorial optimization problems are given as well. Our empirical studies suggest that the cross-entropy method has polynomial in the size of the problem running time complexity.

902 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20234
20229
202114
202018
201920
201825