The Cross-Entropy Method

The cross-entropy method is a recent versatile Monte Carlo technique. This article provides a brief introduction to the cross-entropy method and discusses how it can be used for rare-event probability estimation and for solving combinatorial, continuous, constrained, and noisy optimization problems. A comprehensive list of references on cross-entropy methods and applications is included.

[1]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[2]  Reuven Y. Rubinstein,et al.  Optimization of computer simulation models with rare events , 1997 .

[3]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[4]  Reuven Y. Rubinstein,et al.  Modern simulation and modeling , 1998 .

[5]  R. Rubinstein The Cross-Entropy Method for Combinatorial and Continuous Optimization , 1999 .

[6]  Pieter Tjerk de Boer,et al.  Analysis and efficient simulation of queueing models of telecommunications systems , 2000 .

[7]  Bjarne E. Helvik,et al.  Using the Cross-Entropy Method to Guide/Govern Mobile Agent's Path Finding in Networks , 2001, MATA.

[8]  R. Rubinstein Combinatorial Optimization, Cross-Entropy, Ants and Rare Events , 2001 .

[9]  Dirk P. Kroese,et al.  Sequence alignment by rare event simulation , 2002, Proceedings of the Winter Simulation Conference.

[10]  Reuven Y. Rubinstein,et al.  Cross-entropy and rare events for maximal cut and partition problems , 2002, TOMC.

[11]  Shie Mannor,et al.  The Cross Entropy Method for Fast Policy Search , 2003, ICML.

[12]  Dirk P. Kroese,et al.  The Transform Likelihood Ratio Method for Rare Event Simulation with Heavy Tails , 2004, Queueing Syst. Theory Appl..

[13]  Dirk P. Kroese,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning , 2004 .

[14]  Dirk P. Kroese,et al.  Combinatorial Optimization via Cross-Entropy , 2004 .

[15]  Arnaud Doucet,et al.  The cross-entropy method for blind multiuser detection , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[16]  Dirk P. Kroese,et al.  A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks , 2004, Manag. Sci..

[17]  Dirk P. Kroese,et al.  HEAVY TAILS, IMPORTANCE SAMPLING AND CROSS–ENTROPY , 2005 .

[18]  Dirk P. Kroese,et al.  Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment , 2005, Ann. Oper. Res..

[19]  Avraham Shtub,et al.  Managing Stochastic, Finite Capacity, Multi-Project Systems through the Cross-Entropy Methodology , 2005, Ann. Oper. Res..

[20]  Ad Ridder,et al.  Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy , 2005, Ann. Oper. Res..

[21]  Shie Mannor,et al.  Basis Function Adaptation in Temporal Difference Reinforcement Learning , 2005, Ann. Oper. Res..

[22]  L. Margolin,et al.  On the Convergence of the Cross-Entropy Method , 2005, Ann. Oper. Res..

[23]  Dirk P. Kroese,et al.  Designing an Optimal Network Using the Cross-Entropy Method , 2005, IDEAL.

[24]  Miro Kraetzl,et al.  The Cross-Entropy Method for Network Reliability Estimation , 2005, Ann. Oper. Res..

[25]  M. Caserta,et al.  A Cross-Entropy Based Algorithm for Combinatorial Optimization Problems , 2005 .

[26]  Shie Mannor,et al.  A Tutorial on the Cross-Entropy Method , 2005, Ann. Oper. Res..

[27]  S. Nariai,et al.  On the design of multi-type networks via the cross-entropy method , 2005, DRCN 2005). Proceedings.5th International Workshop on Design of Reliable Communication Networks, 2005..

[28]  Tito Homem-de-Mello,et al.  Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method , 2005, Ann. Oper. Res..

[29]  Dirk P. Kroese,et al.  The Cross-Entropy Method for Continuous Multi-Extremal Optimization , 2006 .

[30]  Jiguo Cao,et al.  Parameter estimation for differential equations: a generalized smoothing approach , 2007 .

[31]  Xiaoguang Gao,et al.  Double Unmanned Aerial Vehicle's Path Planning for Scout via Cross-Entropy Method , 2007 .

[32]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[33]  Gregory Levitin,et al.  Computational Intelligence in Reliability Engineering , 2007 .

[34]  Vasyl Pihur,et al.  Weighted rank aggregation of cluster validation measures: a Monte Carlo cross-entropy approach , 2007, Bioinform..

[35]  Gareth E. Evans,et al.  Parallel cross-entropy optimization , 2007, 2007 Winter Simulation Conference.

[36]  Dirk P. Kroese,et al.  Application of the cross-entropy method to clustering and vector quantization , 2007, J. Glob. Optim..

[37]  Tito Homem-de-Mello,et al.  A Study on the Cross-Entropy Method for Rare-Event Probability Estimation , 2007, INFORMS J. Comput..

[38]  Dirk P. Kroese,et al.  Convergence properties of the cross-entropy method for discrete optimization , 2007, Oper. Res. Lett..

[39]  Dirk P. Kroese,et al.  Network Reliability Optimization via the Cross-Entropy Method , 2007, IEEE Transactions on Reliability.

[40]  Adnan Acan,et al.  Multi-objective optimization with cross entropy method: Stochastic learning with clustered pareto fronts , 2007, 2007 IEEE Congress on Evolutionary Computation.

[41]  Gareth E. Evans Parallel and Sequential Monte Carlo Methods with Applications , 2008 .

[42]  Dirk P. Kroese,et al.  Randomized methods for solving the Winner Determination Problem in combinatorial auctions , 2008, 2008 Winter Simulation Conference.

[43]  Dirk P. Kroese,et al.  Controlling the number of HIV infectives in a mobile population. , 2008, Mathematical biosciences.

[44]  Sébastien Paris,et al.  Application of the cross entropy method to the GLVQ algorithm , 2008, Pattern Recognit..

[45]  Ying Wu,et al.  Topology perserving mappings using cross entropy adaptation , 2008 .

[46]  András Lörincz,et al.  Spike-based cross-entropy method for reconstruction , 2008, Neurocomputing.

[47]  A. Sani Stochastic Modelling and Intervention of the Spread of HIV/AIDS , 2009 .

[48]  T. Taimre ADVANCES IN CROSS-ENTROPY METHODS , 2009, Bulletin of the Australian Mathematical Society.

[49]  Marco Caserta,et al.  A cross entropy based algorithm for reliability problems , 2009, J. Heuristics.

[50]  Marco Caserta,et al.  A cross entropy-Lagrangean hybrid algorithm for the multi-item capacitated lot-sizing problem with setup times , 2009, Comput. Oper. Res..

[51]  Joshua C. C. Chan Advanced Monte Carlo Methods with Applications in Finance , 2010 .

[52]  Boaz Golany,et al.  Setting gates for activities in the stochastic project scheduling problem through the cross entropy methodology , 2011, Ann. Oper. Res..

[53]  Dirk P. Kroese,et al.  Rare-event probability estimation with conditional Monte Carlo , 2011, Ann. Oper. Res..

[54]  Joseph Kreimer,et al.  An optimal routing policy for unmanned aerial vehicles (analytical and cross-entropy simulation approach) , 2011, Ann. Oper. Res..

[55]  Jerzy A. Filar,et al.  A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem , 2011, Ann. Oper. Res..