A non-standard branch and bound method for the Hamiltonian cycle problem

J.A. Filar, Jean B. Lasserre


In this note, we consider an embedding of a Hamiltonian cycle problem in a Markov decision process (MDP). We propose a branch and bound type method based on the frequency polytope resulting from this embedding. Among the special features of the proposed scheme are the properties that: (i) a three-way branching is the biggest that can occur, (ii) no integer-valued variable is required, and (iii), the size of the LPs solved at the nodes of the branch and bound tree can only decrease as one moves down the tree. We hope that this note will encourage researchers in combinatorial optimization to experiment with the Markov decision process embedding as a basis for new algorithmic procedures.

Full Text:


DOI: http://dx.doi.org/10.21914/anziamj.v42i0.614

Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.