Skip to main content
SpringerLink
Log in
Book cover

International Conference on Parallel Problem Solving from Nature

PPSN 2018: Parallel Problem Solving from Nature – PPSN XV pp 436–448Cite as

Learning Bayesian Networks with Algebraic Differential Evolution

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11102))

Abstract

In this paper we introduce DEBN, a novel evolutionary algorithm for learning the structure of a Bayesian Network. DEBN is an instantiation of the Algebraic Differential Evolution which is designed and applied to a particular (product) group whose elements encode all the Bayesian Networks of a given set of random variables. DEBN has been experimentally investigated on a set of standard benchmarks and its effectiveness is compared with BFO-B, a recent and effective bacterial foraging algorithm for Bayesian Network learning. The experimental results show that DEBN largely outperforms BFO-B, thus validating our algebraic approach as a viable solution for learning Bayesian Networks.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Baioletti, M., Milani, A., Santucci, V.: Algebraic particle swarm optimization for the permutations search space. In: Proceedings of 2017 IEEE Congress on Evolutionary Computation (CEC 2017), pp. 1587–1594 (2017). https://doi.org/10.1109/CEC.2017.7969492

  2. Baioletti, M., Milani, A., Santucci, V.: Linear ordering optimization with a combinatorial differential evolution. In: Proceedings of 2015 IEEE International Conference on Systems, Man, and Cybernetics (IEEE SMC 2015), pp. 2135–2140 (2015). https://doi.org/10.1109/SMC.2015.373

  3. Baioletti, M., Milani, A., Santucci, V.: An extension of algebraic differential evolution for the linear ordering problem with cumulative costs. In: Handl, J., Hart, E., Lewis, P.R., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds.) PPSN 2016. LNCS, vol. 9921, pp. 123–133. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45823-6_12

    Chapter  Google Scholar 

  4. Baioletti, M., Milani, A., Santucci, V.: Automatic algebraic evolutionary algorithms. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds.) WIVACE 2017. CCIS, vol. 830, pp. 271–283. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78658-2_20

    Chapter  Google Scholar 

  5. Baioletti, M., Milani, A., Santucci, V.: MOEA/DEP: an algebraic decomposition-based evolutionary algorithm for the multiobjective permutation flowshop scheduling problem. In: Liefooghe, A., López-Ibáñez, M. (eds.) EvoCOP 2018. LNCS, vol. 10782, pp. 132–145. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-77449-7_9

    Chapter  Google Scholar 

  6. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)

    Article  Google Scholar 

  7. Daly, R., Shen, Q.: Learning Bayesian networks equivalence with ant colony optimization. J. Artif. Intell. Res. 35, 391–447 (2009)

    Article  MathSciNet  Google Scholar 

  8. Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)

    Article  Google Scholar 

  9. Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)

    Article  Google Scholar 

  10. de Campos, L.M., Fernández-Luna, J.M., Gámez, J.A., Puerta, J.M.: Ant colony optimization for learning Bayesian networks. Int. J. Approx. Reason. 31(3), 291–311 (2002)

    Article  MathSciNet  Google Scholar 

  11. de Campos, L.M., Gámez, J.A., Puerta, J.M.: Learning Bayesian networks by ant colony optimization: searching in two different spaces. Mathw. Soft Comput. 9(2–3), 251–268 (2002)

    MATH  Google Scholar 

  12. Ji, J., Yang, C., Liu, J., Liu, J., Yin, B.: A comparative study on swarm intelligence for structure learning of Bayesian networks. Soft Comput. 21(22), 6713–6738 (2017)

    Article  Google Scholar 

  13. Kabli, R., Herrmann, F., McCall, J.: A chain-model genetic algorithm for Bayesian network structure learning. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp. 1264–1271. ACM (2007)

    Google Scholar 

  14. Koller, D., Friedman, N.: Probabilistic Graphical Models Principles and Techniques. MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  15. Kuo, S.-C., Wang, H.-J.., Wei, H.-Y., Chen, C.-C., Li, S.-T.: Applying MDL in PSO for learning Bayesian networks. In: 2011 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1587–1592. IEEE (2011)

    Google Scholar 

  16. Lang, S.: Algebra, vol. 211. Springer, Heidelberg (2002). https://doi.org/10.1007/978-1-4613-0041-0

    Book  MATH  Google Scholar 

  17. Larrañaga, P., Kuijpers, C.M.H., Murga, R.H., Inza, I., Dizdarevic, S.: Genetic algorithms for the travelling salesman problem: a review of representations and operators. Artif. Intell. Rev. 13(2), 129–170 (1999)

    Article  Google Scholar 

  18. Larrañaga, P., Poza, M., Yurramendi, Y., Murga, R.H., Kuijpers, C.M.H.: Structure learning of Bayesian network by genetic algorithms: a performance analysis of control parameters. IEEE Trans. Pattern Anal. Mach. Intell. 18(9), 912–926 (1996)

    Article  Google Scholar 

  19. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Heidelberg (2005). https://doi.org/10.1007/3-540-31306-0

    Book  MATH  Google Scholar 

  20. Santucci, V., Baioletti, M., Milani, A.: An algebraic differential evolution for the linear ordering problem. In: Proceedings of the Companion Publication of the 2015 Annual Conference on Genetic and Evolutionary Computation (GECCO 2015), pp. 1479–1480. ACM, New York (2015). https://doi.org/10.1145/2739482.2764693

  21. Santucci, V., Baioletti, M., Milani, A.: Algebraic differential evolution algorithm for the permutation flowshop scheduling problem with total flowtime criterion. IEEE Trans. Evol. Comput. 20(5), 682–694 (2016). https://doi.org/10.1109/TEVC.2015.2507785

    Article  MATH  Google Scholar 

  22. Santucci, V., Baioletti, M., Milani, A.: Solving permutation flowshop scheduling problems with a discrete differential evolution algorithm. AI Commun. 29(2), 269–286 (2016). https://doi.org/10.3233/AIC-150695

    Article  MathSciNet  MATH  Google Scholar 

  23. Scutari, M.: Learning Bayesian networks with the bnlearn R package. J. Stat. Softw. 35(3), 1–22 (2010)

    Article  Google Scholar 

  24. Tsamardinos, I., Brown, L.E., Aliferis, C.F.: The max-min hill-climbing Bayesian network structure learning algorithm. Mach. Learn. 65(1), 31–78 (2006)

    Article  Google Scholar 

  25. van Dijk, S., van der Gaag, L.C., Thierens, D.: A skeleton-based approach to learning Bayesian networks from data. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) PKDD 2003. LNCS (LNAI), vol. 2838, pp. 132–143. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-39804-2_14

    Chapter  Google Scholar 

  26. Wu, Y., McCall, J.A.W., Corne, D.W.: Two novel ant colony optimization approaches for Bayesian network structure learning. In: IEEE Congress on Evolutionary Computation, pp. 1–7 (2010)

    Google Scholar 

  27. Xing-Chen, H., Zheng, Q., Lei, T., Li-Ping, S.: Learning Bayesian networks structures with discrete particle swarm optimization algorithm. In: 2007 IEEE Symposium on Foundations of Computational Intelligence, pp. 47–52 (2007)

    Google Scholar 

  28. Yang, C., Ji, J., Liu, J., Liu, J., Yin, B.: Structural learning of Bayesian networks by bacterial foraging optimization. Int. J. Approx. Reason. 69, 147–167 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Marco Baioletti & Alfredo Milani

  2. Department of Social and Human Sciences, University for Foreigners of Perugia, Perugia, Italy

    Valentino Santucci

  3. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China

    Alfredo Milani

Authors
  1. Marco Baioletti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alfredo Milani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Valentino Santucci
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marco Baioletti .

Editor information

Editors and Affiliations

  1. Inria Saclay, Palaiseau, France

    Anne Auger

  2. University of Coimbra, Coimbra, Portugal

    Carlos M. Fonseca

  3. University of Coimbra, Coimbra, Portugal

    Nuno Lourenço

  4. University of Coimbra, Coimbra, Portugal

    Penousal Machado

  5. University of Coimbra, Coimbra, Portugal

    Luís Paquete

  6. Colorado State University, Fort Collins, Colorado, USA

    Darrell Whitley

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Baioletti, M., Milani, A., Santucci, V. (2018). Learning Bayesian Networks with Algebraic Differential Evolution. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11102. Springer, Cham. https://doi.org/10.1007/978-3-319-99259-4_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99259-4_35

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99258-7

  • Online ISBN: 978-3-319-99259-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation