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Triangle-based consistencies for cost function networks

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Abstract

Cost Function Networks (aka Weighted CSP) allow to model a variety of problems, such as optimization of deterministic and stochastic graphical models including Markov random Fields and Bayesian Networks. Solving cost function networks is thus an important problem for deterministic and probabilistic reasoning. This paper focuses on local consistencies which define essential tools to simplify Cost Function Networks, and provide lower bounds on their optimal solution cost. To strengthen arc consistency bounds, we follow the idea of triangle-based domain consistencies for hard constraint networks (path inverse consistency, restricted or max-restricted path consistencies), describe their systematic extension to cost function networks, study their relative strengths, define enforcing algorithms, and experiment with them on a large set of benchmark problems. On some of these problems, our improved lower bounds seem necessary to solve them.

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Notes

  1. We use the terminology of Cost Function Networks by similarity to Constraint Networks. The Weighted Constraint Satisfaction Problem (WCSP) is the problem of solving a CFN. For outsiders, guessing what a Cost Function Network could be, is also much easier.

  2. There exists tiny variations on the definition of AC for CFNs. This paper uses the definition in [20] which simplifies the definition in [10] by not considering the propagation of inconsistent tuples.

  3. http://mulcyber.toulouse.inra.fr/projects/toulbar2/ version 0.9.6 branch maxrpc.

  4. We only excluded from the set all 35 Minizinc instances as well as two subcategories (UAI/DBN, 108 instances and CSP/warehouse, 55 instances) that contain no triangle of binary cost functions. Over the original 3,018 original instances, 2,820 remain.

  5. All the instances are available at http://genoweb.toulouse.inra.fr/degivry/evalgm.

  6. https://mulcyber.toulouse.inra.fr/scm/viewvc.php/trunk/?root=costfunctionlib

  7. http://www.cril.univ-artois.fr/CPAI08,../~lecoutre/benchmarks.html/

  8. http://www.cs.huji.ac.il/project/PASCAL/realBoard.php

  9. http://maxsat.ia.udl.cat:81/13/benchmarks/

  10. http://hci.iwr.uni-heidelberg.de/opengm2

References

  1. Allouche, D., Bessiere, C., Boizumault, P., Givry, S., Gutierrez, P., Loudni, S., Metivier, J., & Schiex, T. (2012). Decomposing global cost functions. In Proc. of AAAI.

  2. Bensana, E., Lemaître, M., & Verfaillie, G. (1999). Earth observation satellite management. Constraints, 4(3), 293–299.

    Article  MATH  Google Scholar 

  3. Berlandier, P. (1995). Improving domain filtering using restricted path consistency. In Proceedings IEEE Conference on Artificial Intelligenece and Applications (CAIA’95).

  4. Cabon, B., de Givry, S., Lobjois, L., Schiex, T., & Warners, J. (1999). Radio link frequency assignment. Constraints, 4, 79–89.

    Article  MATH  Google Scholar 

  5. Cooper, M., de Givry, S., Sanchez, M., Schiex, T., Zytnicki, M., & Werner, T. (2010). Soft arc consistency revisited. Artificial Intelligence, 174, 449–478.

    Article  MathSciNet  MATH  Google Scholar 

  6. Cooper, M., de Givry, S., Sanchez, M., Schiex, T., & Zytnicki, M. (2008). Virtual Arc Consistency for Weighted CSP. In Proc. of AAAI’2008. Chicago, USA.

  7. Cooper, M.C. (2003). Reduction operations in fuzzy or valued constraint satisfaction. Fuzzy Sets Systems, 134(3), 311–342.

    Article  MathSciNet  MATH  Google Scholar 

  8. Cooper, M.C. (2005). High-order consistency in Valued Constraint Satisfaction. Constraints, 10, 283–305.

    Article  MathSciNet  MATH  Google Scholar 

  9. Cooper, M.C., de Givry, S., & Schiex, T. (2007). Optimal soft arc consistency. In Proc. of IJCAI’2007, pp. 68–73. Hyderabad, India.

  10. Cooper, M.C., & Schiex, T. (2004). Arc consistency for soft constraints. Artificial Intelligence, 154(1-2), 199–227.

    Article  MathSciNet  MATH  Google Scholar 

  11. Debruyne, R., & Bessière, C. (1997). From restricted path consistency to max-restricted path consistency. In Proc. of CP’97, no. 1330 in LNCS, pp. 312–326. Springer-Verlag, Linz, Austria.

  12. Dehani, D., Lecoutre, C., & Roussel, O. (2013). Extension des cohérences wcsps aux tuples. In Proc. of JFPC-13.

  13. Favier, A., de Givry, S., Legarra, A., & Schiex, T. (2011). Pairwise decomposition for combinatorial optimization in graphical models. In Proc. of IJCAI’11. Barcelona, Spain.

  14. Freuder, E.C., & Elfe, C.D. (1996). Neighborhood inverse consistency preprocessing. In Proc. of AAAI’96. Portland, OR.

  15. Hurley, B., O’Sullivan, B., Allouche, D., Katsirelos, G., Schiex, T., Zytnicki, M., & de Givry, S. (2016). Multi-Language Evaluation of Exact Solvers in Graphical Model Discrete Optimization. In Proc. of CP-AI-OR’2016. Banff, Canada.

  16. Larrosa, J. (2002). On arc and node consistency in weighted CSP. In Proc. AAAI’02, pp. 48–53. Edmondton, CA.

  17. Larrosa, J., de Givry, S., Heras, F., & Zytnicki, M. (2005). Existential arc consistency: getting closer to full arc consistency in weighted CSPs. In Proc. of the 19 t h IJCAI, pp. 84–89. Edinburgh, Scotland.

  18. Larrosa, J., Heras, F., & de Givry, S. (2008). A logical approach to efficient max-sat solving. Artificial Intelligence, 172(2-3), 204–233.

    Article  MathSciNet  MATH  Google Scholar 

  19. Larrosa, J., & Schiex, T. (2003). In the quest of the best form of local consistency for weighted CSP. In Proc. of the 18 t h IJCAI, pp. 239–244. Acapulco, Mexico.

  20. Larrosa, J., & Schiex, T. (2004). Solving weighted CSP by maintaining arc consistency. Artificial Intelligence, 159(1-2), 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  21. Lee, J., & Leung, K. (2009). Towards efficient consistency enforcement for global constraints in weighted constraint satisfaction. In Proc. of the 21 r d IJCAI, pp. 559–565. Pasadena (CA), USA.

  22. Lee, J., & Leung, K. (2012). Consistency techniques for flow-based projection-safe global cost functions in weighted constraint satisfaction. Artificial Intelligence, 43, 257–292.

    MathSciNet  MATH  Google Scholar 

  23. Sánchez, M., de Givry, S., & Schiex, T. (2008). Mendelian error detection in complex pedigrees using weighted constraint satisfaction techniques. Constraints, 13(1-2), 130–154.

    Article  MathSciNet  MATH  Google Scholar 

  24. Schiex, T. (2000). Arc consistency for soft constraints. In Principles and Practice of Constraint Programming - CP 2000, LNCS, vol. 1894, pp. 411–424. Singapore.

  25. Schiex, T., Fargier, H., & Verfaillie, G. (1995). Valued constraint satisfaction problems: hard and easy problems. In Proc. of the 14 th IJCAI, pp. 631–637. Montréal, Canada.

  26. Simoncini, D., Allouche, D., de Givry, S., Delmas, C., Barbe, S., & Schiex, T. (2015). Guaranteed discrete energy optimization on large protein design problems. Journal of Chemical Theory and Computation, 11(12), 5980–5989.

    Article  Google Scholar 

  27. Traoré, S., Allouche, D., André, I., de Givry, S., Katsirelos, G., Schiex, T., & Barbe, S. (2013). A new framework for computational protein design through cost function network optimization. Bioinformatics, 29(17), 2129–2136.

    Article  Google Scholar 

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Acknowledgements

This work has been partly funded by the “Agence nationale de la Recherche”, reference ANR-10-BLA-0214

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Authors and Affiliations

  1. MIAT, UR 875, Université de Toulouse, INRA, Castanet-Tolosan, France

    Hiep Nguyen, Simon de Givry & Thomas Schiex

  2. University of Montpellier, Montpellier, France

    Christian Bessiere

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  1. Hiep Nguyen
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  2. Christian Bessiere
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  3. Simon de Givry
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  4. Thomas Schiex
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Correspondence to Thomas Schiex.

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Nguyen, H., Bessiere, C., Givry, S.d. et al. Triangle-based consistencies for cost function networks. Constraints 22, 230–264 (2017). https://doi.org/10.1007/s10601-016-9250-1

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