Evolutionary Intelligence

, Volume 5, Issue 2, pp 87–102 | Cite as

Analysing BioHEL using challenging boolean functions

  • María A. Franco
  • Natalio Krasnogor
  • Jaume Bacardit
Special Issue


In this work we present an extensive empirical analysis of the BioHEL genetics-based machine learning system using the k-Disjunctive Normal Form (k-DNF) family of boolean functions. These functions present a broad set of possible challenges for most machine learning techniques, such as different degrees of specificity, class imbalance and niche overlap. Moreover, as the ideal solutions are known, it is possible to assess if a learning system is able to find them, and how fast. Specifically, we study two aspects of BioHEL: its sensitivity to the coverage breakpoint parameter (that determines the degree of generality pressure applied by the fitness function) and the impact of the default rule policy. The results show that BioHEL is highly sensitive to the choice of coverage breakpoint and that using a default class suitable for the problem allows the system to learn faster than using other default class policies (e.g. the majority class policy). Moreover, the experiments indicate that BioHEL’s scalability depends directly on both k (the specificity of the k-DNF terms) and the number of terms in the problem. In the last part of the paper we discuss alternative policies to adjust the coverage breakpoint parameter.


Evolutionary algorithms Learning classifier systems Rule induction Large-scale datasets 



The authors would like to thank the UK Engineering and Physical Sciences Research Council (EPSRC) for its support under grant EP/H016597/1. They would also like to acknowledge the High Performance Computing facility at the University of Nottingham for providing the necessary framework for these experiments.


  1. 1.
    Bacardit J (2004) Pittsburgh Genetics-Based machine learning in the data mining era: representations, generalization, and run-time. phdthesis. Ramon Llull University, Barcelona, SpainGoogle Scholar
  2. 2.
    Bacardit J, Burke E, Krasnogor N (2009) Improving the scalability of rule-based evolutionary learning. Memetic Computing 1(1):55–67. doi: 10.1007/s12293-008-0005-4 Google Scholar
  3. 3.
    Bacardit J, Garrell JM (2003) Bloat control and generalization pressure using the minimum description length principle for a pittsburgh approach learning classifier system. In: Proceedings of the 6th International Workshop on Learning Classifier SystemsGoogle Scholar
  4. 4.
    Bacardit J, Goldberg DE, Butz MV (2007) Improving the performance of a pittsburgh learning classifier system using a default rule. In: Learning classifier systems, revised selected papers of the international workshop on learning classifier systems 2003–2005. Springer, LNCS 4399, pp. 291–307Google Scholar
  5. 5.
    Bacardit J, Goldberg DE, Butz MV, Llorá X, Garrell JM (2004) Speeding-Up pittsburgh learning classifier systems: modeling time and accuracy. In: Parallel problem solving from nature—PPSN VIII, Lecture Notes in Computer Science, vol. 3242, chap. 103. Springer, Berlin, Heidelberg, pp 1021–1031.
  6. 6.
    Bacardit J, Hirst JD, Stout M, Blazewicz J, Krasnogor N (2006) Coordination number prediction using learning classifier systems: performance and interpretability. In: In GECCO ’06: Proceedings of the 8th annual conference on Genetic and evolutionary computation. ACM Press, New York, NY, pp 247–254Google Scholar
  7. 7.
    Bacardit J, Krasnogor N (2009) A mixed discrete-continuous attribute list representation for large scale classification domains. In: GECCO ’09: Proceedings of the 11th annual conference on genetic and evolutionary computation, pp 1155–1162. ACM Press, New York, NY. doi: 10.1145/1569901.1570057
  8. 8.
    Bacardit J, Stout M, Hirst JD, Sastry K, Llorà X, Krasnogor N (2007) Automated alphabet reduction method with evolutionary algorithms for protein structure prediction. In: GECCO ’07: Proceedings of the 9th annual conference on genetic and evolutionary computation. ACM, New York, NY, pp 346–353. doi: 10.1145/1276958.1277033
  9. 9.
    Bacardit J, Stout M, Hirst JD, Valencia A, Smith R, Krasnogor N (2009) Automated alphabet reduction for protein datasets. BMC Bioinformatics 10(1):6. doi: 10.1186/1471-2105-10-6 Google Scholar
  10. 10.
    Bassel GW, Glaab E, Marquez J, Holdsworth MJ, Bacardit J (2011) Functional network construction in arabidopsis using rule-based machine learning on large-scale data sets. Plant Cell Online 23(9):3101–3116. doi: 10.1105/tpc.111.088153 CrossRefGoogle Scholar
  11. 11.
    Butz MV (2006) Rule-based evolutionary online learning systems: a principled approach to LCS analysis and design, studies in fuzziness and soft computing. vol 109, Springer, BerlinGoogle Scholar
  12. 12.
    Butz MV, Pelikan M (2006) Studying XCS/BOA learning in boolean functions: structure encoding and random boolean functions. In: GECCO ’06: Proceedings of the 8th annual conference on Genetic and evolutionary computation. ACM, New York, NY, pp 1449–456. doi: 10.1145/1143997.1144236
  13. 13.
    Ehrenfeucht A, Haussler D, Kearns MJ, Valiant L (1988) A general lower bound on the number of examples needed for learning. In: Proceedings of the first annual workshop on Computational learning theory. Morgan Kaufmann Publishers Inc., MIT, Cambridge, MA, pp 139–154.
  14. 14.
    Franco MA, Krasnogor N, Bacardit J (2010) Speeding up the evaluation of evolutionary learning systems using GPGPUs. In: GECCO ’10: Proceedings of the 12th annual conference on genetic and evolutionary computation. ACM, New York, NY, pp. 1039–1046. doi: 10.1145/1830483.1830672
  15. 15.
    Franco MA, Krasnogor N, Bacardit J (2011) Modelling the initialisation stage of the alkr representation for discrete domains and gabil encoding. In: Proceedings of the 13th annual conference on Genetic and evolutionary computation, GECCO ’11. ACM, New York, NY, pp 1291–1298. doi: 10.1145/2001576.2001750
  16. 16.
    Hernández-Aguirre A, Buckles BP, Coello CAC (2001) On learning kDNF nss boolean formulas. In: Evolvable hardware, NASA/DoD conference on, vol 0. IEEE Computer Society, Los Alamitos, CA, p 0240.doi: 10.1109/EH.2001.937967
  17. 17.
    Hirschberg DS, Pazzani MJ, Ali KM (1994) Average case analysis of k-CNF and k-DNF learning algorithms. In: Proceedings of the workshop on computational learning theory and natural learning systems (vol 2): intersections between theory and experiment. MIT Press, Cambridge, MA, pp 15–28Google Scholar
  18. 18.
    Ioannides C, Barrett G, Eder K (2011) Xcs cannot learn all boolean functions. In: Proceedings of the 13th annual conference on Genetic and evolutionary computation, GECCO ’11, pp. 1283–1290. ACM, New York, NY. doi: 10.1145/2001576.2001749
  19. 19.
    Jong KD, Spears WM (1991) Learning concept classification rules using genetic algorithms. In: Proceedings of the 12th international joint conference on Artificial intelligence, vol 2. Morgan Kaufmann Publishers Inc., Sydney, New South Wales, pp 651–656.
  20. 20.
    Kearns MJ (1990) The computational complexity of machine learning. MIT Press, Cambridge, MAGoogle Scholar
  21. 21.
    Orriols-Puig A, Bernadó-Mansilla E (2008) Evolutionary rule-based systems for imbalanced data sets. Soft Comput 13(3):213–225. Google Scholar
  22. 22.
    Orriols-Puig A, Bernadó-Mansilla E, Goldberg DE, Sastry K, Lanzi PL (2009) Facetwise analysis of XCS for problems with class imbalances. Trans Evol Comp 13(5):1093–1119. Google Scholar
  23. 23.
    Rissanen J (1978) Modeling by shortest data description. Automatica 14:465–471zbMATHCrossRefGoogle Scholar
  24. 24.
    Stone C, Bull L (2003) For real! XCS with continuous-valued inputs. Evol Comput 11:299–336. doi: 10.1162/106365603322365315 Google Scholar
  25. 25.
    Stout M, Bacardit J, Hirst JD, Krasnogor N (2008) Prediction of recursive convex hull class assignments for protein residues. Bioinformatics 24(7):916–923. doi: 10.1093/bioinformatics/btn050. Google Scholar
  26. 26.
    Venturini G (1993) SIA: a supervised inductive algorithm with genetic search for learning attributes based concepts. In: Brazdil PB (eds), Machine learning: ECML-93—Proceedings of the European Conference on Machine Learning. Springer, New York, pp 280–296Google Scholar
  27. 27.
    Wilson SW (1995) Classifier fitness based on accuracy. Evol Comput 3(2):149–175. doi: 10.1162/evco.1995.3.2.149 Google Scholar
  28. 28.
    Wilson SW (2001) Mining oblique data with XCS. In: Luca Lanzi P, Stolzmann W, Wilson S (eds), Advances in learning classifier systems, lecture notes in computer science, vol 1996. Springer, Berlin/Heidelberg, pp 283–290. doi: 10.1007/3-540-44640-0_11
  29. 29.
    Witten IH, Frank E (2005) Data mining: practical machine learning tools and techniques. Morgan Kaufmann, Waltham, MAzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • María A. Franco
    • 1
  • Natalio Krasnogor
    • 1
  • Jaume Bacardit
    • 1
    • 2
  1. 1.ICOS Research Group, School of Computer ScienceUniversity of NottinghamNottinghamUK
  2. 2.Multi-disciplinary Centre for Integrative Biology (MyCIB), School of BiosciencesUniversity of NottinghamSutton BoningtonUK

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