Skip to main content
Log in

Portfolio approaches for constraint optimization problems

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Within the Constraint Satisfaction Problems (CSP) context, a methodology that has proven to be particularly performant consists of using a portfolio of different constraint solvers. Nevertheless, comparatively few studies and investigations have been done in the world of Constraint Optimization Problems (COP). In this work, we provide a generalization to COP as well as an empirical evaluation of different state of the art existing CSP portfolio approaches properly adapted to deal with COP. The results obtained by measuring several evaluation metrics confirm the effectiveness of portfolios even in the optimization field, and could give rise to some interesting future research.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Amadini, R., Gabbrielli, M., Mauro, J.: An empirical evaluation of portfolios approaches for solving CSPs. In: CPAIOR, Volume 7874 of Lecture Notes in Computer Science. Springer (2013)

  2. Amadini, R., Gabbrielli, M., Mauro, J.: An enhanced features extractor for a portfolio of constraint solvers. In: SAC, pp. 1357–1359. ACM (2014)

  3. Amadini, R., Gabbrielli, M., Mauro, J.: Portfolio approaches for constraint optimization problems. In: LION, Volume 8426 of Lecture Notes in Computer Science, pp. 21–35. Springer (2014)

  4. Amadini, R., Gabbrielli, M., Mauro, J.: SUNNY: A lazy portfolio approach for constraint solving. TPLP 14(4–5), 509–524 (2014)

    MATH  Google Scholar 

  5. Amadini, R., Stuckey, P.: Sequential time splitting and bounds communication for a portfolio of optimization solvers. In: CP. http://ww2.cs.mu.oz.au/pjs/papers/cp2014d.pdf (2014)

  6. Arlot, S., Celisse, A.: A survey of cross-validation procedures for model selection. Stat. Surv. 4, 40–79 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Algorithm Selection Library (COSEAL project). https://code.google.com/p/coseal/wiki/AlgorithmSelectionLibrary

  8. Baral, C: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press (2003)

  9. Becket, R: Specification of FlatZinc - Version 1.6. http://www.minizinc.org/downloads/doc-1.6/flatzinc-spec.pdf

  10. Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, volume 185 of Frontiers in Artificial Intelligence and Applications. IOS Press (2009)

  11. Borenstein, Y., Riccardo, P.: Kolmogorov complexity, optimization and hardness. In: Evolutionary Computation, pp. 112–119 (2006)

  12. Carchrae, T., Beck, J.C.: Applying machine learning to low-knowledge control of optimization algorithms. Comput. Intell. 21(4), 372–387 (2005)

    Article  MathSciNet  Google Scholar 

  13. Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: A short introduction to computational social choice. In: SOFSEM, volume 4362 of LNCS, pp. 51–69. Springer (2007)

  14. Third International CSP Solver Competition 2008. http://www.cril.univ-artois.fr/CPAI09/

  15. Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1–2), 43–62 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gomes, C.P., Selman, B., Crato, N.: Heavy-tailed distributions in combinatorial search. In: CP, Volume 1330 of Lecture Notes in Computer Science, pp. 121–135. Springer (1997)

  17. Guo, H., Hsu, WH.: A machine learning approach to algorithm selection for NP-hard optimization problems: A case study on the MPE problem. Annals OR 156(1), 61–82 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hall, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The WEKA data mining software: An update. SIGKDD Explor. Newsl. 11(1) (2009)

  19. Hebrard, E., O’Mahony, E., O’Sullivan, B.: Constraint programming and combinatorial optimisation in numberjack. In: CPAIOR-10, Volume 6140 of LNCS, pp. 181–185. Springer-Verlag (2010)

  20. Hoos, H.H., Kaufmann, B., Schaub, T., Schneider, M.: Robust benchmark set selection for boolean constraint solvers. In: LION, Volume 7997 of Lecture Notes in Computer Science, pp. 138–152. Springer (2013)

  21. Hutter, F., Xu, L., Hoos, H.H., Leyton-Brown, K.: Algorithm runtime prediction: The state of the art. CoRR, arXiv:1211.0906 (2012)

  22. Kadioglu, S., Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm selection and scheduling. In: CP, Volume 6876 of Lecture Notes in Computer Science. Springer (2011)

  23. Kadioglu, S., Malitsky, Y., Sellmann, M., Tierney, K.: ISAC - instance-specific algorithm configuration. In: ECAI, Volume 215 of Frontiers in Artificial Intelligence and Applications. IOS Press (2010)

  24. Knowles, J.D., Corne, D.: Towards landscape analyses to inform the design of hybrid local search for the multiobjective quadratic assignment problem. In: HIS, Volume 87 of Frontiers in Artificial Intelligence and Applications, pp. 271–279. IOS Press (2002)

  25. Kotthoff, L.: Algorithm selection for combinatorial search problems: A survey. CoRR, arXiv:1210.7959 (2012)

  26. Kroer, C., Malitsky, Y.: Feature filtering for instance-specific algorithm configuration. In: ICTAI, pp. 849–855. IEEE (2011)

  27. Leyton-Brown, K., Nudelman, E., Shoham, Y.: Learning the empirical hardness of optimization problems: The case of combinatorial auctions. In: CP, Volume 2470 of Lecture Notes in Computer Science, pp. 556–572. Springer (2002)

  28. Lobjois, L., Lemaître, M.: Branch and bound algorithm selection by performance prediction. In: AAAI/IAAI, pp. 353–358. AAAI Press / The MIT Press (1998)

  29. Mackworth, A.K.: Consistency in networks of relations. Artif. Intell. 8(1), 99–118 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  30. Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm portfolios based on cost-sensitive hierarchical clustering. In: IJCAI. IJCAI/AAAI (2013)

  31. Max-SAT 2013. http://maxsat.ia.udl.cat/introduction/

  32. Merz, P.: Advanced fitness landscape analysis and the performance of memetic algorithms. Evol. Comput. 12(3), 303–325 (2004)

    Article  MathSciNet  Google Scholar 

  33. Minizinc version 1.6. http://www.minizinc.org/download.html

  34. MiniZinc Challenge. http://www.minizinc.org/challenge2014/rules2014.html

  35. OMahony, E., Hebrard, E., Holland, A., Nugent, C., OSullivan, B.: Using case-based reasoning in an algorithm portfolio for constraint solving. In: AICS 08 (2009)

  36. Rice, J.R.: The algorithm selection problem. Adv. Comput. 15, 65–118 (1976)

    Article  Google Scholar 

  37. SAT Challenge 2012. http://baldur.iti.kit.edu/SAT-Challenge-2012/

  38. Smith-Miles, K.: Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Comput. Surv. 41(1) (2008)

  39. Smith-Miles, K.A.: Towards insightful algorithm selection for optimisation using meta-learning concepts. In: IJCNN, pp. 4118–4124. IEEE (2008)

  40. Telelis, O., Stamatopoulos, P.: Combinatorial optimization through statistical instance-based learning. In: ICTAI, pp. 203–209 (2001)

  41. Xu, L., Hutter, F., Shen, J., Hoos, H., Leyton-Brown, K.: SATzilla2012: Improved algorithm selection based on cost-sensitive classification models. Solver description, SAT Challenge 2012 (2012)

  42. Lin, X., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla-07: The design and analysis of an algorithm portfolio for SAT. In: CP, Volume 4741 of Lecture Notes in Computer Science. Springer (2007)

  43. Lin, X., Hutter, F., Hoos, H.H., Leyton-brown, K.: Hydra-MIP: Automated algorithm configuration and selection for mixed integer programming. In: RCRA Workshop on Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion (2011)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jacopo Mauro.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amadini, R., Gabbrielli, M. & Mauro, J. Portfolio approaches for constraint optimization problems. Ann Math Artif Intell 76, 229–246 (2016). https://doi.org/10.1007/s10472-015-9459-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-015-9459-5

Keywords

Mathematics Subject Classifications (2010)

Navigation