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Quantifying Homogeneity of Instance Sets for Algorithm Configuration

  • Marius Schneider
  • Holger H. Hoos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7219)

Abstract

Automated configuration procedures play an increasingly prominent role in realising the performance potential inherent in highly parametric solvers for a wide range of computationally challenging problems. However, these configuration procedures have difficulties when dealing with inhomogenous instance sets, where the relative difficulty of problem instances varies between configurations of the given parametric algorithm. In the literature, instance set homogeneity has been assessed using a qualitative, visual criterion based on heat maps. Here, we introduce two quantitative measures of homogeneity and empirically demonstrate these to be consistent with the earlier qualitative criterion. We also show that according to our measures, homogeneity increases when partitioning instance sets by means of clustering based on observed runtimes, and that the performance of a prominent automatic algorithm configurator increases on the resulting, more homogenous subsets.

Keywords

Quantifying Homogeneity Empirical Analysis Parameter Optimization Algorithm Configuration 

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References

  1. 1.
    Hutter, F., Babić, D., Hoos, H., Hu, A.: Boosting verification by automatic tuning of decision procedures. In: Procs. FMCAD 2007, pp. 27–34. IEEE Computer Society Press (2007)Google Scholar
  2. 2.
    KhudaBukhsh, A., Xu, L., Hoos, H., Leyton-Brown, K.: SATenstein: Automatically building local search sat solvers from components. In: Boutilier, C. (ed.) Procs. IJCAI 2009, pp. 517–524. AAAI Press/The MIT Press (2009)Google Scholar
  3. 3.
    Tompkins, D.A.D., Balint, A., Hoos, H.H.: Captain Jack: New Variable Selection Heuristics in Local Search for SAT. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 302–316. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Hutter, F., Hoos, H.H., Leyton-Brown, K.: Automated Configuration of Mixed Integer Programming Solvers. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 186–202. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Vallati, M., Fawcett, C., Gerevini, A., Hoos, H.H., Saetti, A.: Generating fast domain-specic planners by automatically conguring a generic parameterised planner. In: Procs. PAL 2011, pp. 21–27 (2011)Google Scholar
  6. 6.
    Hoos, H.H.: Programming by optimisation. Communications of the ACM (to appear, 2012)Google Scholar
  7. 7.
    Ansótegui, C., Sellmann, M., Tierney, K.: A Gender-Based Genetic Algorithm for the Automatic Configuration of Algorithms. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 142–157. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Birattari, M., Stützle, T., Paquete, L., Varrentrapp, K.: A racing algorithm for configuring metaheuristics. In: Kaufmann, M. (ed.) Procs. GECCO 2009, pp. 11–18. ACM Press (2002)Google Scholar
  9. 9.
    Hutter, F., Hoos, H.H., Leyton-Brown, K., Stützle, T.: ParamILS: An automatic algorithm configuration framework. Journal of Artificial Intelligence Research 36, 267–306 (2009)zbMATHGoogle Scholar
  10. 10.
    Hutter, F., Hoos, H.H., Stützle, T.: Automatic algorithm configuration based on local search. In: Procs. AAAI 2007, pp. 1152–1157. AAAI Press (2007)Google Scholar
  11. 11.
    Hutter, F., Hoos, H.H., Leyton-Brown, K.: Tradeoffs in the Empirical Evaluation of Competing Algorithm Designs. Annals of Mathematics and Artificial Intelligenc (AMAI), Special Issue on Learning and Intelligent Optimization 60(1), 65–89 (2011)MathSciNetGoogle Scholar
  12. 12.
    Kadioglu, S., Malitsky, Y., Sellmann, M., Tierney, K.: ISAC - Instance-Specific Algorithm Configuration. In: Coelho, H., Studer, R., Wooldridge, M. (eds.) Procs. ECAI 2008, pp. 751–756. IOS Press (2010)Google Scholar
  13. 13.
    Lindawati, Lau, H.C., Lo, D.: Instance-Based Parameter Tuning via Search Trajectory Similarity Clustering. In: Coello, C.A.C. (ed.) LION 5. LNCS, vol. 6683, pp. 131–145. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Gomes, C., Selman, B.: Algorithm portfolios. Journal of Artificial Intelligence 126(1-2), 43–62 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Xu, L., Hutter, F., Hoos, H., Leyton-Brown, K.: SATzilla: Portfolio-based algorithm selection for SAT. Journal of Artificial Intelligence Research 32, 565–606 (2008)zbMATHGoogle Scholar
  16. 16.
    Hutter, F., Hamadi, Y., Hoos, H.H., Leyton-Brown, K.: Performance Prediction and Automated Tuning of Randomized and Parametric Algorithms. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 213–228. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Xu, L., Hoos, H.H., Leyton-Brown, K.: Hydra: Automatically configuring algorithms for portfolio-based selection. In: Fox, M., Poole, D. (eds.) Procs. AAAI 2010, pp. 210–216. AAAI Press (2010)Google Scholar
  18. 18.
    Rice, J.: The algorithm selection problem. Advances in Computers 15, 65–118 (1976)CrossRefGoogle Scholar
  19. 19.
    Xu, L., Hoos, H.H., Leyton-Brown, K.: Hierarchical Hardness Models for SAT. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 696–711. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    Leyton-Brown, K., Nudelman, E., Shoham, Y.: Empirical hardness models: Methodology and a case study on combinatorial auctions. Journal of the ACM 56(4), 1–52 (2009)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T., Schneider, M.T., Ziller, S.: A Portfolio Solver for Answer Set Programming: Preliminary Report. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol. 6645, pp. 352–357. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential Model-Based Optimization for General Algorithm Configuration. In: Coello, C.A.C. (ed.) LION 5. LNCS, vol. 6683, pp. 507–523. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    Smith-Miles, K.: Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Computing Surveys 41(1), 6:1–6:25 (2008)CrossRefGoogle Scholar
  24. 24.
    Guerri, A., Milano, M.: Learning Techniques for Automatic Algorithm Portfolio Selection. In: de Mántaras, R.L., Saitta, L. (eds.) Procs. ECAI 2004, pp. 475–479. IOS Press (2004)Google Scholar
  25. 25.
    Kotthoff, L., Gent, I., Miguel, I.: A Preliminary Evaluation of Machine Learning in Algorithm Selection for Search Problems. In: Borrajo, D., Likhachev, M., López, C. (eds.) Procs. SoCS 2011, pp. 84–91. AAAI Press (2011)Google Scholar
  26. 26.
    Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set solving. In: Veloso, M. (ed.) Procs. IJCAI 2007, pp. 386–392. AAAI Press/The MIT Press (2007)Google Scholar
  27. 27.
    MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Cam, L., Neyman, J. (eds.) Procs. Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press (1967)Google Scholar
  28. 28.
    Bishop, C.: Pattern Recognition and Machine Learning (Information Science and Statistics), 1st edn. 2006. corr. 2nd printing edn. Springer (2007)Google Scholar
  29. 29.
    Ward, J.: Hierarchical Grouping to Optimize an Objective Function. Journal of the American Statistical Association 58(301), 236–244 (1963)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press (2003)Google Scholar
  31. 31.
    Zarpas, E.: Benchmarking SAT Solvers for Bounded Model Checking. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 340–354. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  32. 32.
    Hamerly, G., Elkan, C.: Learning the k in k-means. In: Procs. NIPS 2003, MIT Press, Cambridge (2003)Google Scholar
  33. 33.
    Hamadi, Y., Jabbour, S., Sais, L.: ManySAT: a parallel SAT solver. Journal on Satisfiability, Boolean Modeling and Computation 6, 245–262 (2009)zbMATHGoogle Scholar
  34. 34.
    Streeter, M., Golovin, D., Smith, S.: Combining Multiple Heuristics Online. In: Procs. AAAI 2007, pp. 1197–1203. AAAI Press (2007)Google Scholar
  35. 35.
    Kadioglu, S., Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm Selection and Scheduling. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 454–469. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marius Schneider
    • 1
  • Holger H. Hoos
    • 2
  1. 1.University of PotsdamGermany
  2. 2.Unversity of British ColumbiaCanada

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