Advertisement

Structure-Preserving Instance Generation

  • Yuri Malitsky
  • Marius Merschformann
  • Barry O’Sullivan
  • Kevin TierneyEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10079)

Abstract

Real-world instances are critical for the development of state-of-the-art algorithms, algorithm configuration techniques, and selection approaches. However, very few true industrial instances exist for most problems, which poses a problem both to algorithm designers and methods for algorithm selection. The lack of enough real data leads to an inability for algorithm designers to show the effectiveness of their techniques, and for algorithm selection it is difficult or even impossible to train a portfolio with so few training examples. This paper introduces a novel instance generator that creates instances that have the same structural properties as industrial instances. We generate instances through a large neighborhood search-like method that combines components of instances together to form new ones. We test our approach on the MaxSAT and SAT problems, and then demonstrate that portfolios trained on these generated instances perform just as well or even better than those trained on the real instances.

Notes

Acknowledgements

We thank the Paderborn Center for Parallel Computing for the use of the OCuLUS cluster for the experiments in this paper. Barry O’Sullivan was supported in part by Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289.

References

  1. 1.
    Ansótegui, C., Béjar, R., Fernàndez, C., Mateu, C.: Edge matching puzzles as hard SAT/CSP benchmarks. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 560–565. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-85958-1_42 CrossRefGoogle Scholar
  2. 2.
    Ansótegui, C., Bonet, M.L., Levy, J., Li, C.M.: Analysis and generation of pseudo-industrial maxsat instances. In: CCIA. FAIA, vol. 248, pp. 173–184. IOS Press (2012)Google Scholar
  3. 3.
    Ansótegui, C., Giráldez-Cru, J., Levy, J.: The community structure of SAT formulas. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 410–423. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31612-8_31 CrossRefGoogle Scholar
  4. 4.
    Ansótegui, C., Levy, J.: On the modularity of industrial sat instances. In: Fernández, C., Geffner, H., Manyà, F. (eds.) CCIA. FAIA, vol. 232, pp. 11–20. IOS Press, Amsterdam (2011)Google Scholar
  5. 5.
    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). doi: 10.1007/978-3-642-04244-7_14 CrossRefGoogle Scholar
  6. 6.
    Ansotegui, C., Malitsky, Y., Sellmann, M.: MaxSAT by improved instance-specific algorithm configuration. In: AAAI (2014)Google Scholar
  7. 7.
    Argelich, J., Li, C.M., Manyà, F., Planes, J.: Eighth Max-SAT evaluation (2013)Google Scholar
  8. 8.
    Balint, A., Belov, A., Heule, M., Järvisalo, M.: Proceedings of SAT competition 2013; solver and benchmark descriptions. Technical report, University of Helsinki (2013)Google Scholar
  9. 9.
    Barták, R.: On generators of random quasigroup problems. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds.) CSCLP 2005. LNCS (LNAI), vol. 3978, pp. 164–178. Springer, Heidelberg (2006). doi: 10.1007/11754602_12 CrossRefGoogle Scholar
  10. 10.
    Bastian, M., Heymann, S., Jacomy, M.: Gephi: an open source software for exploring and manipulating networks. In: AAAI Conference on Weblogs and Social Media (2009)Google Scholar
  11. 11.
    Bayless, S., Tompkins, D.A.D., Hoos, H.H.: Evaluating instance generators by configuration. In: Pardalos, P.M., Resende, M.G.C., Vogiatzis, C., Walteros, J.L. (eds.) LION 2014. LNCS, vol. 8426, pp. 47–61. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-09584-4_6 Google Scholar
  12. 12.
    Bejar, R., Cabiscol, A., Manya, F., Planes, J.: Generating hard instances for MaxSAT. In: International Symposium on Multiple-Valued Logic (ISMVL 2009), pp. 191–195, May 2009Google Scholar
  13. 13.
    Burg, S., Kottler, S., Kaufmann, M.: Creating industrial-like SAT instances by clustering and reconstruction. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 471–472. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-31612-8_40 CrossRefGoogle Scholar
  14. 14.
    Dinur, I., Goldwasser, S., Lin, H.: The computational benefit of correlated instances. In: Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science. pp. 219–228. ACM (2015)Google Scholar
  15. 15.
    Gent, I.P., Hoos, H.H., Prosser, P., Walsh, T.: Morphing: combining structure and randomness. In: Hendler, J., Subramanian, D. (eds.) AAAI, pp. 654–660 (1999)Google Scholar
  16. 16.
    Gomes, C.P., Selman, B.: Problem structure in the presence of perturbations. In: Kuipers, B., Webber, B.L. (eds.) AAAI, pp. 221–226 (1997)Google Scholar
  17. 17.
    Hamerly, G., Elkan, C.: Learning the k in k-means. In: Neural Information Processing Systems (NIPS) (2003)Google Scholar
  18. 18.
    Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential model-based optimization for general algorithm configuration. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 507–523. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-25566-3_40 CrossRefGoogle Scholar
  19. 19.
    Kadioglu, S., Malitsky, Y., Sellmann, M., Tierney, K.: ISAC - instance-specific algorithm configuration. In: ECAI. FAIA, vol. 215, pp. 751–756. IOS Press (2010)Google Scholar
  20. 20.
    Katsirelos, G., Simon, L.: Eigenvector centrality in industrial sat instances. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 348–356. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-33558-7_27 Google Scholar
  21. 21.
    Krzakala, F., Zdeborová, L.: Hiding quiet solutions in random constraint satisfaction problems. Phys. Rev. Lett. 102(23), 238701 (2009)CrossRefGoogle Scholar
  22. 22.
    Lopes, L., Smith-Miles, K.: Generating applicable synthetic instances for branch problems. Oper. Res. 61(3), 563–577 (2013)CrossRefzbMATHGoogle Scholar
  23. 23.
    Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm portfolios based on cost-sensitive hierarchical clustering. In: IJCAI (2013)Google Scholar
  24. 24.
    Motoki, M.: Test instance generation for MAX 2SAT. In: Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 787–791. Springer, Heidelberg (2005). doi: 10.1007/11564751_65 CrossRefGoogle Scholar
  25. 25.
    Nallaperuma, S., Wagner, M., Neumann, F.: Parameter prediction based on features of evolved instances for ant colony optimization and the traveling salesperson problem. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN XIII 2014. LNCS, vol. 8672, pp. 100–109. Springer, Heidelberg (2014). doi: 10.1007/978-3-319-10762-2_10 Google Scholar
  26. 26.
    Nudelman, E., Leyton-Brown, K., Hoos, H.H., Devkar, A., Shoham, Y.: Understanding random SAT: beyond the clauses-to-variables ratio. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 438–452. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30201-8_33 CrossRefGoogle Scholar
  27. 27.
    Pari, P.R., Lin, J., Yuan, L., Qu, G.: Generating ‘random’ 3-SAT instances with specific solution space structure. In: McGuinness, D.L., Ferguson, G. (eds.) AAAI, pp. 960–961 (2004)Google Scholar
  28. 28.
    Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998). doi: 10.1007/3-540-49481-2_30 CrossRefGoogle Scholar
  29. 29.
    Slater, A.: Modelling more realistic SAT problems. In: McKay, B., Slaney, J. (eds.) AI 2002. LNCS (LNAI), vol. 2557, pp. 591–602. Springer, Heidelberg (2002). doi: 10.1007/3-540-36187-1_52 CrossRefGoogle Scholar
  30. 30.
    Smith-Miles, K., Bowly, S.: Generating new test instances by evolving in instance space. Comput. Oper. Res. 63, 102–113 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Smith-Miles, K., van Hemert, J.: Discovering the suitability of optimisation algorithms by learning from evolved instances. Ann. Math. Artif. Intell. 61(2), 87–104 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Van Gelder, A., Spence, I.: Zero-one designs produce small hard SAT instances. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 388–397. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-14186-7_37 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Yuri Malitsky
    • 1
  • Marius Merschformann
    • 2
  • Barry O’Sullivan
    • 3
  • Kevin Tierney
    • 2
    Email author
  1. 1.IBM T.J. Watson Research CenterNew YorkUSA
  2. 2.Decision Support and Operations Research LabUniversity of PaderbornPaderbornGermany
  3. 3.Insight Centre for Data AnalyticsUniversity College CorkCorkIreland

Personalised recommendations