AND/OR Branch-and-Bound search for combinatorial optimization in graphical models

  • Authors:

  • Radu Marinescu;Rina Dechter

  • Affiliations:

  • Cork Constraint Computation Centre, University College Cork, Ireland;Donald Bren School of Information and Computer Science, University of California, Irvine, CA 92697, USA

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2009

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Abstract

This is the first of two papers presenting and evaluating the power of a new framework for combinatorial optimization in graphical models, based on AND/OR search spaces. We introduce a new generation of depth-first Branch-and-Bound algorithms that explore the AND/OR search tree using static and dynamic variable orderings. The virtue of the AND/OR representation of the search space is that its size may be far smaller than that of a traditional OR representation, which can translate into significant time savings for search algorithms. The focus of this paper is on linear space search which explores the AND/OR search tree. In the second paper we explore memory intensive AND/OR search algorithms. In conjunction with the AND/OR search space we investigate the power of the mini-bucket heuristics in both static and dynamic setups. We focus on two most common optimization problems in graphical models: finding the Most Probable Explanation in Bayesian networks and solving Weighted CSPs. In extensive empirical evaluations we demonstrate that the new AND/OR Branch-and-Bound approach improves considerably over the traditional OR search strategy and show how various variable ordering schemes impact the performance of the AND/OR search scheme.