Portfolio approaches for constraint optimization problems

  • Roberto Amadini
  • Maurizio Gabbrielli
  • Jacopo MauroEmail author


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.


Algorithm portfolio Artificial intelligence Combinatorial optimization Constraint programming Machine learning 

Mathematics Subject Classifications (2010)



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  1. 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)Google Scholar
  2. 2.
    Amadini, R., Gabbrielli, M., Mauro, J.: An enhanced features extractor for a portfolio of constraint solvers. In: SAC, pp. 1357–1359. ACM (2014)Google Scholar
  3. 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)Google Scholar
  4. 4.
    Amadini, R., Gabbrielli, M., Mauro, J.: SUNNY: A lazy portfolio approach for constraint solving. TPLP 14(4–5), 509–524 (2014)zbMATHGoogle Scholar
  5. 5.
    Amadini, R., Stuckey, P.: Sequential time splitting and bounds communication for a portfolio of optimization solvers. In: CP. (2014)
  6. 6.
    Arlot, S., Celisse, A.: A survey of cross-validation procedures for model selection. Stat. Surv. 4, 40–79 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Algorithm Selection Library (COSEAL project).
  8. 8.
    Baral, C: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press (2003)Google Scholar
  9. 9.
    Becket, R: Specification of FlatZinc - Version 1.6.
  10. 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)Google Scholar
  11. 11.
    Borenstein, Y., Riccardo, P.: Kolmogorov complexity, optimization and hardness. In: Evolutionary Computation, pp. 112–119 (2006)Google Scholar
  12. 12.
    Carchrae, T., Beck, J.C.: Applying machine learning to low-knowledge control of optimization algorithms. Comput. Intell. 21(4), 372–387 (2005)MathSciNetCrossRefGoogle Scholar
  13. 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)Google Scholar
  14. 14.
    Third International CSP Solver Competition 2008.
  15. 15.
    Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1–2), 43–62 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 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)Google Scholar
  17. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 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)Google Scholar
  19. 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)Google Scholar
  20. 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)Google Scholar
  21. 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. 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)Google Scholar
  23. 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)Google Scholar
  24. 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)Google Scholar
  25. 25.
    Kotthoff, L.: Algorithm selection for combinatorial search problems: A survey. CoRR, arXiv:1210.7959 (2012)
  26. 26.
    Kroer, C., Malitsky, Y.: Feature filtering for instance-specific algorithm configuration. In: ICTAI, pp. 849–855. IEEE (2011)Google Scholar
  27. 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)Google Scholar
  28. 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)Google Scholar
  29. 29.
    Mackworth, A.K.: Consistency in networks of relations. Artif. Intell. 8(1), 99–118 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm portfolios based on cost-sensitive hierarchical clustering. In: IJCAI. IJCAI/AAAI (2013)Google Scholar
  31. 31.
  32. 32.
    Merz, P.: Advanced fitness landscape analysis and the performance of memetic algorithms. Evol. Comput. 12(3), 303–325 (2004)MathSciNetCrossRefGoogle Scholar
  33. 33.
  34. 34.
  35. 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)Google Scholar
  36. 36.
    Rice, J.R.: The algorithm selection problem. Adv. Comput. 15, 65–118 (1976)CrossRefGoogle Scholar
  37. 37.
  38. 38.
    Smith-Miles, K.: Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Comput. Surv. 41(1) (2008)Google Scholar
  39. 39.
    Smith-Miles, K.A.: Towards insightful algorithm selection for optimisation using meta-learning concepts. In: IJCNN, pp. 4118–4124. IEEE (2008)Google Scholar
  40. 40.
    Telelis, O., Stamatopoulos, P.: Combinatorial optimization through statistical instance-based learning. In: ICTAI, pp. 203–209 (2001)Google Scholar
  41. 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)Google Scholar
  42. 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)Google Scholar
  43. 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)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Roberto Amadini
    • 1
  • Maurizio Gabbrielli
    • 1
  • Jacopo Mauro
    • 1
    Email author
  1. 1.Department of Computer Science and Engineering/Lab. Focus INRIAUniversity of BolognaBolognaItaly

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