Decision Tree Learning-Inspired Dynamic Variable Ordering for the Weighted CSP

The weighted constraint satisfaction problem (WCSP) is a powerful mathematical framework for combinatorial optimization. The branch-and-bound search paradigm is very successful in solving the WCSP but critically depends on the ordering in which variables are instantiated. In this paper, we introduce a new framework for dynamic variable ordering for solving the WCSP. This framework is inspired by regression decision tree learning. Variables are ordered dynamically based on samples of random assignments of values to variables as well as their corresponding total weights. Within this framework, we propose four variable ordering heuristics (sdr, inv-sdr, rr and inv-rr). We compare them with many stateof-the-art dynamic variable ordering heuristics, and show that sdr and rr outperform them on many real-world and random benchmark instances.

[1]  Javier Larrosa,et al.  Intelligent variable orderings and re-orderings in DAC-based solvers for WCSP , 2006, J. Heuristics.

[2]  William T. Freeman,et al.  Understanding belief propagation and its generalizations , 2003 .

[3]  Rina Dechter,et al.  Best-First AND/OR Search for Graphical Models , 2007, AAAI.

[4]  Lakhdar Sais,et al.  Boosting Systematic Search by Weighting Constraints , 2004, ECAI.

[5]  Hong Xu,et al.  A Constraint Composite Graph-Based ILP Encoding of the Boolean Weighted CSP , 2017, CP.

[6]  Olga Veksler,et al.  Fast approximate energy minimization via graph cuts , 2001, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[7]  Martin C. Cooper,et al.  Soft arc consistency revisited , 2010, Artif. Intell..

[8]  Ronen I. Brafman,et al.  CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements , 2011, J. Artif. Intell. Res..

[9]  Pascal Van Hentenryck,et al.  Activity-Based Search for Black-Box Constraint Programming Solvers , 2011, CPAIOR.

[10]  Wei-Yin Loh,et al.  Classification and regression trees , 2011, WIREs Data Mining Knowl. Discov..

[11]  Hong Xu,et al.  The Nemhauser-Trotter Reduction and Lifted Message Passing for the Weighted CSP , 2017, CPAIOR.

[12]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[13]  Barry O'Sullivan,et al.  Dead-End Elimination for Weighted CSP , 2013, CP.

[14]  Rina Dechter,et al.  Dynamic Orderings for AND/OR Branch-and-Bound Search in Graphical Models , 2006, ECAI.

[15]  Thomas Schiex,et al.  DARN! A Weighted Constraint Solver for RNA Motif Localization , 2007, Constraints.

[16]  Philippe Refalo,et al.  Impact-Based Search Strategies for Constraint Programming , 2004, CP.

[17]  P. Pandurang Nayak,et al.  Remote Agent: To Boldly Go Where No AI System Has Gone Before , 1998, Artif. Intell..

[18]  Mateu Villaret,et al.  Solving Intensional Weighted CSPs by Incremental Optimization with BDDs , 2014, CP.

[19]  Thomas Schiex,et al.  Solving weighted CSP by maintaining arc consistency , 2004, Artif. Intell..

[20]  V. Kolmogorov.  Primal-dual Algorithm for Convex Markov Random Fields , 2005 .

[21]  Isabel Milho,et al.  An Auxiliary System for Medical Diagnosis Based on Bayesian Belief Networks , 2003 .

[22]  Thomas Schiex,et al.  Semiring-Based CSPs and Valued CSPs: Frameworks, Properties, and Comparison , 1999, Constraints.

[23]  Simon de Givry,et al.  Existential arc consistency: Getting closer to full arc consistency in weighted CSPs , 2005, IJCAI.

[24]  Barry O'Sullivan,et al.  Multi-language evaluation of exact solvers in graphical model discrete optimization , 2016, Constraints.

[25]  Vladimir Kolmogorov,et al.  Convergent Tree-Reweighted Message Passing for Energy Minimization , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.