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Journal of Global Optimization

, Volume 29, Issue 3, pp 315–334 | Cite as

An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes

  • Vladimir Ejov
  • Jerzy Filar
  • Jacek Gondzio
Article

Abstract

We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process (MDP). More specifically, we consider the HCP as an optimization problem over the space of long-run state-action frequencies induced by the MDP's stationary policies. We show that Hamiltonian cycles (if any) correspond to the global minima of a suitably constructed indefinite quadratic programming problem over the frequency space. We show that the above indefinite quadratic can be approximated by quadratic functions that are `nearly convex' and as such suitable for the application of logarithmic barrier methods. We develop an interior-point type algorithm that involves an arc elimination heuristic that appears to perform rather well in moderate size graphs. The approach has the potential for further improvements.

Hamiltonian cycles interior point methods Markov decision processes non-convex optimization 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Vladimir Ejov
    • 1
  • Jerzy Filar
    • 1
  • Jacek Gondzio
    • 2
  1. 1.School of MathematicsThe University of South AustraliaMawson LakesAustralia
  2. 2.School of MathematicsUniversity of EdinburghEdinburghUK

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