The CrossEntropy Method for Combinatorial and Continuous Optimization
 Reuven Rubinstein
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We present a new and fast method, called the crossentropy 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 KullbackLeibler crossentropy, 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 KullbackLeibler crossentropy 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 crossentropy method has polynomial in the size of the problem running time complexity.
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 Title
 The CrossEntropy Method for Combinatorial and Continuous Optimization
 Journal

Methodology And Computing In Applied Probability
Volume 1, Issue 2 , pp 127190
 Cover Date
 19990901
 DOI
 10.1023/A:1010091220143
 Print ISSN
 13875841
 Online ISSN
 15737713
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 combinatorial optimization
 global optimization
 importance sampling
 markov chain monte carlo
 simulated annealing
 simulation
 Authors