Computers & Operations Research 36 (2009) 487 – 498 www.elsevier.com/locate/cor Hybridizing the cross-entropy method: An application to the max-cut problem Manuel Laguna a , ∗ , Abraham Duarte b , Rafael Martí c a Leeds School of Business, University of Colorado at Boulder, USA b Departamento de Ciencias de la Computación, Universidad Rey Juan Carlos, Spain c Departamento de Estadística e Investigación Operativa, Universidad de Valencia, Spain Available online 9 October 2007 Abstract 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.  2007 Elsevier Ltd. All rights reserved. Keywords: Combinatorial optimization; Metaheuristics; Max-cut problem; Local search; Cross-entropy 1. Introduction The cross-entropy (CE) method was conceived by Rubinstein [1] as a way of adaptively estimating probabilities of rare events in complex stochastic networks. The method was soon adapted to tackle combinatorial optimization problems [2,3]. Recently, the Annals of Operations Research devoted a volume to the cross-entropy method [4]. Applications of the CE method to combinatorial optimization include vehicle routing [5], buffer allocation [6], the traveling salesman problem (TSP) [7], and the max-cut problem [8]. The description of other applications, a list of references and computer implementations of the CE method can be found at http://www.cemethod.org. As stated by de Boer et al. [7], the CE method, in its most basic form, is a fairly straightforward procedure that consists of iterating the following two steps: 1. Generate a random sample from a pre-specified probability distribution function. 2. Use the sample to modify the parameters of the probability distribution in order to produce a “better” sample in the next iteration. The basic CE method is very easy to implement, particularly when dealing with combinatorial optimization problems for which the natural representation of solutions is a binary string. The methodology is quite intuitive, focusing on the ∗ Corresponding author. Tel.: +1 303 492 6368; fax: +1 303 492 5962. E-mail addresses: laguna@colorado.edu (M. Laguna), Abraham.Duarte@urjc.es (A. Duarte), Rafael.Marti@uv.es (R. Martí). 0305-0548/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2007.10.001