Swarm Intelligence

, Volume 11, Issue 3–4, pp 317–346 | Cite as

PolyACO+: a multi-level polygon-based ant colony optimisation classifier

  • Morten Goodwin
  • Torry Tufteland
  • Guro Ødesneltvedt
  • Anis YazidiEmail author


Ant colony optimisation (ACO) for classification has mostly been limited to rule-based approaches where artificial ants walk on datasets in order to extract rules from the trends in the data, and hybrid approaches which attempt to boost the performance of existing classifiers through guided feature reductions or parameter optimisations. A recent notable example that is distinct from the mainstream approaches is PolyACO, which is a proof-of-concept polygon-based classifier that resorts to ACO as a technique to create multi-edged polygons as class separators. Despite possessing some promise, PolyACO has some significant limitations, most notably, the fact of supporting classification of only two classes, including two features per class. This paper introduces PolyACO+, which is an extension of PolyACO in three significant ways: (1) PolyACO+ supports classifying multiple classes, (2) PolyACO+ supports polygons in multiple dimensions enabling classification with more than two features, and (3) PolyACO+ substantially reduces the training time compared to PolyACO by using the concept of multi-levelling. This paper empirically demonstrates that these updates improve the algorithm to such a degree that it becomes comparable to state-of-the-art techniques such as SVM, neural networks, and AntMiner+.


Ant colony optimisation Classification Polygon Multi-levelling 



The authors would like to thank the editor and anonymous referees for their unusually meticulous review and valuable comments to improve the quality of this paper.


  1. Abadeh, M. S., Habibi, J., Soroush, E. (2008). Induction of fuzzy classification systems via evolutionary ACO-based algorithms. In First Asia international conference on modelling & simulation, 2007. AMS’07. (pp. 346–351). IEEE.Google Scholar
  2. Albinati, J., Oliveira, S. E., Otero, F. E., & Pappa, G. L. (2015). An ant colony-based semi-supervised approach for learning classification rules. Swarm Intelligence, 9(4), 315–341.CrossRefGoogle Scholar
  3. Aribarg, T., Supratid, S., & Lursinsap, C. (2012). Optimizing the modified fuzzy ant-miner for efficient medical diagnosis. Applied Intelligence, 37(3), 357–376.CrossRefGoogle Scholar
  4. Berger, M. J., & Colella, P. (1989). Local adaptive mesh refinement for shock hydrodynamics. Journal of Computational Physics, 82(1), 64–84.CrossRefzbMATHGoogle Scholar
  5. Caruana, R., Karampatziakis, N., & Yessenalina, A. (2008) An empirical evaluation of supervised learning in high dimensions. In W. Cohen, A. McCallum & S. Roweis (Eds.), Proceedings of the 25th international conference on machine learning (pp. 96–193). ACM.Google Scholar
  6. Daly, R., Shen, Q., et al. (2009). Learning Bayesian network equivalence classes with ant colony optimization. Journal of Artificial Intelligence Research, 35(1), 391.MathSciNetzbMATHGoogle Scholar
  7. Daly, R., Shen, Q., & Aitken, S. (2011). Learning Bayesian networks: Approaches and issues. The Knowledge Engineering Review, 26(02), 99–157.CrossRefGoogle Scholar
  8. De Campos, L. M., Puerta, J., et al. (2008). Learning Bayesian networks by ant colony optimisation: Searching in two different spaces. Mathware & Soft Computing, 9(3), 251–268.MathSciNetzbMATHGoogle Scholar
  9. Goodwin, M., & Yazidi, A. (2016). Ant colony optimisation-based classification using two-dimensional polygons. In M. Dorigo, M. Birattari, X. Li, M. Lòpez-Ibáñez, K. Ohkura, C. Pinciroli & T. Stüzle (Eds.), International conference on swarm intelligence (Proceedings ANTS-2016), Lecture notes in computers science (Vol. 9882, pp. 53–64). Springer.Google Scholar
  10. Goodwin, M., Yazidi, A., & Møller, T. (2016). Distributed learning automata for solving a classification task. In 2016 IEEE congress on evolutionary computation (CEC) (pp. 3999–4006). IEEE.Google Scholar
  11. Jun-Zhong, J., Zhang, H. X., Ren-Bing, H., & Chun-Nian, L. (2009). A Bayesian network learning algorithm based on independence test and ant colony optimization. Acta Automatica Sinica, 35(3), 281–288.Google Scholar
  12. Klein, R. I. (1999). Star formation with 3-D adaptive mesh refinement: The collapse and fragmentation of molecular clouds. Journal of Computational and Applied Mathematics, 109(1), 123–152.CrossRefzbMATHGoogle Scholar
  13. Lian, T. A., Llave, M. R., Goodwin, M., & Bouhmala, N. (2015). Towards multilevel ant colony optimisation for the Euclidean symmetric traveling salesman problem. In M. Ali , Y. Kwon, C. H. Lee, J. Kim, & Y. Kim (Eds.), Current approaches in applied artificial intelligence (Proceedings IEA/AIE 2015), Lecture notes in computer science (Vol. 9101, pp. 222–231). Springer.Google Scholar
  14. Lichman, M. (2013). UCI machine learning repository. Accessed 11 Nov 2017.
  15. Liu, B., Abbas, H., & McKay, B. (2003). Classification rule discovery with ant colony optimization. In IEEE/WIC international conference on intelligent agent technology, 2003. IAT 2003 (pp. 83–88). IEEE.Google Scholar
  16. Madjarov, G., Kocev, D., Gjorgjevikj, D., & Džeroski, S. (2012). An extensive experimental comparison of methods for multi-label learning. Pattern Recognition, 45(9), 3084–3104.CrossRefGoogle Scholar
  17. Martens, D., Backer, M. D., Haesen, R., Vanthienen, J., Snoeck, M., & Baesens, B. (2007). Classification with ant colony optimization. IEEE Transactions on Evolutionary Computation, 11(5), 651–665.CrossRefGoogle Scholar
  18. Martens, D., Baesens, B., & Fawcett, T. (2011). Editorial survey: Swarm intelligence for data mining. Machine Learning, 82(1), 1–42.MathSciNetCrossRefGoogle Scholar
  19. Parpinelli, R., Lopes, H., & Freitas, A. (2002). Data mining with an ant colony optimization algorithm. IEEE Transactions on Evolutionary Computation, 6(4), 321–332.CrossRefzbMATHGoogle Scholar
  20. Ryoo, S., Rodrigues, C. I., Baghsorkhi, S. S., Stone, S. S., Kirk, D. B., & Hwu, W. W. (2008). Optimization principles and application performance evaluation of a multithreaded GPU using CUDA. In Proceedings of the 13th ACM SIGPLAN symposium on principles and practice of parallel programming (pp. 73–82). ACM.Google Scholar
  21. Salama, K. M., & Abdelbar, A. M. (2015). Learning neural network structures with ant colony algorithms. Swarm Intelligence, 9(4), 229–265.CrossRefGoogle Scholar
  22. Salama, K. M., & Abdelbar, A. M. (2016). Using Ant Colony Optimization to build cluster-based classification systems. In M. Dorigo, M. Birattari, X. Li, M. Lòpez-Ibáñez, K. Ohkura, C. Pinciroli & T. Stüzle (Eds.), International conference on swarm intelligence (Proceedings ANTS-2016), Lecture notes in computers science (Vol. 9882, pp. 210–222). Springer.Google Scholar
  23. Sapin, E., Keedwell, E., & Frayling, T. (2015). Ant colony optimisation of decision tree and contingency table models for the discovery of gene interactions. IET Systems Biology, 9(6), 218–225.CrossRefGoogle Scholar
  24. Sharma, S., Ghosh, S., Anantharaman, N., & Jayaraman, V. K. (2012). Simultaneous informative gene extraction and cancer classification using ACO-AntMiner and ACO-Random forests. In S. C. Satapathy, P. S. Avadhani, & A. Abraham (Eds.), Proceedings of the international conference on information systems design and intelligent applications 2012 (INDIA 2012) Advances in Intelligent and Soft Computing (Vol. 132, pp. 755–761). Springer.Google Scholar
  25. Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing, 14(3), 199–222.MathSciNetCrossRefGoogle Scholar
  26. Stützle, T., & Hoos, H. H. (2000). MAX–MIN ant system. Future Generation Computer Systems, 16(8), 889–914.CrossRefzbMATHGoogle Scholar
  27. Tripathy, S., Hota, S., & Satapathy, P. (2013). MTACO-Miner: Modified threshold ant colony optimization miner for classification rule mining. In: N. R. Shetty, N. H. Prasad, & N. Nalini (Eds.), International conference on emerging research in computing, information, communication and applications (pp. 529–534). Elsevier.Google Scholar
  28. Tufteland, T., Desneltvedt, G., & Goodwin, M. (2016). Optimizing PolyACO training with GPU-based parallelization. In: M. Dorigo, M. Birattari, X. Li, M. Lòpez-Ibáñez, K. Ohkura, C. Pinciroli, & T. Stüzle (Eds.), International conference on swarm intelligence (Proceedings ANTS-2016), Lecture notes in computers science (Vol. 9882, pp. 233–240). Springer.Google Scholar
  29. Van Der Maaten, L. (2014). Accelerating t-SNE using tree-based algorithms. Journal of Machine Learning research, 15(1), 3221–3245.MathSciNetzbMATHGoogle Scholar
  30. Varma, P. R. K., Kumari, V. V., & Kumar, S. S. (2015). A novel rough set attribute reduction based on ant colony optimisation. International Journal of Intelligent Systems Technologies and Applications, 14(3–4), 330–353.CrossRefGoogle Scholar
  31. Walshaw, C. (2004). Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research, 131(1–4), 325–372.MathSciNetCrossRefzbMATHGoogle Scholar
  32. Xue, B., Zhang, M., & Browne, W. N. (2014). Particle swarm optimisation for feature selection in classification: Novel initialisation and updating mechanisms. Applied Soft Computing, 18, 261–276.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Morten Goodwin
    • 1
  • Torry Tufteland
    • 1
  • Guro Ødesneltvedt
    • 1
  • Anis Yazidi
    • 2
    Email author
  1. 1.Department of Computer ScienceUniversity of AgderGrimstadNorway
  2. 2.Department of Computer ScienceOslo and Akershus University College of Applied SciencesOsloNorway

Personalised recommendations