Refined MDP-based branch-and-fix algorithm for the Hamiltonian cycle problem

Date

2009

Authors

Ejov, V.
Filar, J.
Haythorpe, M.
Nguyen, G.

Editors

Advisors

Journal Title

Journal ISSN

Volume Title

Type:

Journal article

Citation

Mathematics of Operations Research, 2009; 34(3):758-768

Statement of Responsibility

Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe, Giang T. Nguyen

Conference Name

Abstract

We consider the famous Hamiltonian cycle problem (HCP) embedded in a Markov decision process (MDP). More specifically, we consider the HCP as an optimisation problem over the space of occupation measures induced by the MDP's stationary policies. In recent years, this approach to the HCP has led to a number of alternative formulations and algorithmic approaches. In this paper, we focus on a specific embedding, because of the work of Feinberg. We present a “branch-and-fix” type algorithm that solves the HCP. At each branch of the algorithm, only a linear program needs to be solved and the dimensions of the successive linear programs are shrinking rather than expanding. Because the nodes of the branch-and-fix tree correspond to specially structured 1-randomised policies, we characterise the latter. This characterisation indicates that the total number of such policies is significantly smaller than the subset of all 1-randomised policies. Finally, we present some numerical results.

School/Discipline

Dissertation Note

Provenance

Description

Access Status

Rights

Copyright status unknown

License

Grant ID

Call number

Persistent link to this record