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Annals of Operations Research

, Volume 189, Issue 1, pp 103–125 | Cite as

A hybrid simulation-optimization algorithm for the Hamiltonian cycle problem

  • Ali Eshragh
  • Jerzy A. FilarEmail author
  • Michael Haythorpe
Article

Abstract

In this paper, we propose a new hybrid algorithm for the Hamiltonian cycle problem by synthesizing the Cross Entropy method and Markov decision processes. In particular, this new algorithm assigns a random length to each arc and alters the Hamiltonian cycle problem to the travelling salesman problem. Thus, there is now a probability corresponding to each arc that denotes the probability of the event “this arc is located on the shortest tour.” Those probabilities are then updated as in cross entropy method and used to set a suitable linear programming model. If the solution of the latter yields any tour, the graph is Hamiltonian. Numerical results reveal that when the size of graph is small, say less than 50 nodes, there is a high chance the algorithm will be terminated in its cross entropy component by simply generating a Hamiltonian cycle, randomly. However, for larger graphs, in most of the tests the algorithm terminated in its optimization component (by solving the proposed linear program).

Keywords

Hamiltonian cycle problem Markov decision process Cross-entropy method 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Ali Eshragh
    • 1
  • Jerzy A. Filar
    • 1
    Email author
  • Michael Haythorpe
    • 1
  1. 1.School of Mathematics and StatisticsThe University of South AustraliaMawson LakesAustralia

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