Hybridizing the cross-entropy method: An application to the max-cut problem

Cross-entropy has been recently proposed as a heuristic method for solving combinatorial optimization problems. We briefly review this methodology and then suggest a hybrid version with the goal of improving its performance. In the context of the well-known max-cut problem, we compare an implementation of the original cross-entropy method with our proposed version. The suggested changes are not particular to the max-cut problem and could be considered for future applications to other combinatorial optimization problems.

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

[2]  A. H. Roscoe,et al.  A Subjective Rating Scale for Assessing Pilot Workload in Flight: A decade of Practical Use , 1990 .

[3]  David P. Williamson,et al.  Improved approximation algorithms for MAX SAT , 2000, SODA '00.

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

[5]  Patrick J. Driscoll,et al.  Decision Making in Systems Engineering and Management , 2007 .

[6]  Scott A. Shappell,et al.  The Human Factors Analysis and Classification System : HFACS : final report. , 2000 .

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

[8]  Andres Sousa-Poza,et al.  System of systems engineering , 2003, IEEE Engineering Management Review.

[9]  Crowley Js Simulator Sickness: A Problem for Army Aviation , 1987 .

[10]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[11]  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..

[12]  S. Uryasev,et al.  Stochastic optimization : Algorithms and Applications , 2001 .

[13]  Daniel J. Garland,et al.  Situation Awareness Analysis and Measurement , 2009 .

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

[15]  Panos M. Pardalos,et al.  Randomized heuristics for the Max-Cut problem , 2002, Optim. Methods Softw..

[16]  Samuel G. Charlton,et al.  Handbook of Human Factors Testing and Evaluation , 1996 .

[17]  Dirk P. Kroese,et al.  Preface : From the issue entitled "The Cross-Entropy Method for Combinatorial Optimization, Rare Event Simulation and Neural Computation" , 2005 .

[18]  Yin Zhang,et al.  Rank-Two Relaxation Heuristics for MAX-CUT and Other Binary Quadratic Programs , 2002, SIAM J. Optim..

[19]  D. M. Deighton,et al.  Computers in Operations Research , 1977, Aust. Comput. J..

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

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

[22]  Franz Rendl,et al.  A Spectral Bundle Method for Semidefinite Programming , 1999, SIAM J. Optim..

[23]  Andrew P. Sage,et al.  Introduction to systems engineering , 2000 .

[24]  Manuel Laguna,et al.  Fine-Tuning of Algorithms Using Fractional Experimental Designs and Local Search , 2006, Oper. Res..