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Tabu search approaches for solving the two-group classification problem

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  • Saïd Hanafi
  • Nicola Yanev

Abstract

The two-group classification problem consists in constructing a classifier that can distinguish between the two groups. In this paper, we consider the two-group classification problem which consists in determining a hyperplane that minimizes the number of misclassified points. We assume that the data set is numeric and with no missing data. We develop a tabu search (TS) heuristic for solving this NP-hard problem. The TS approach is based on a more convenient equivalent formulation of the classification problem. We also propose supplementary new intensification phases based on surrogate constraints. The results of the conducted computational experiments show that our TS algorithms produce solutions very close to the optimum and require significantly lower computational effort, so it is a valuable alternative to the MIP approaches. Moreover the tabu search procedures showed in this paper can be extended in a natural way to the general classification problem, which consists of generating more than one separating hyperplanes. Copyright Springer Science+Business Media, LLC 2011

Suggested Citation

  • Saïd Hanafi & Nicola Yanev, 2011. "Tabu search approaches for solving the two-group classification problem," Annals of Operations Research, Springer, vol. 183(1), pages 25-46, March.
    • Handle: RePEc:spr:annopr:v:183:y:2011:i:1:p:25-46:10.1007/s10479-009-0581-9
    DOI: 10.1007/s10479-009-0581-9
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    References listed on IDEAS

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    1. Blue, Jennifer A. & Bennett, Kristin P., 1998. "Hybrid extreme point tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 676-688, April.
    2. Yanev, N. & Balev, S., 1999. "A combinatorial approach to the classification problem," European Journal of Operational Research, Elsevier, vol. 115(2), pages 339-350, June.
    3. P. S. Bradley & Usama M. Fayyad & O. L. Mangasarian, 1999. "Mathematical Programming for Data Mining: Formulations and Challenges," INFORMS Journal on Computing, INFORMS, vol. 11(3), pages 217-238, August.
    4. Freed, Ned & Glover, Fred, 1981. "Simple but powerful goal programming models for discriminant problems," European Journal of Operational Research, Elsevier, vol. 7(1), pages 44-60, May.
    5. Abad, P. L. & Banks, W. J., 1993. "New LP based heuristics for the classification problem," European Journal of Operational Research, Elsevier, vol. 67(1), pages 88-100, May.
    6. Fred Glover, 1990. "Tabu Search—Part II," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 4-32, February.
    7. Antonie Stam & Cliff T. Ragsdale, 1992. "On the classification gap in mathematical programming‐based approaches to the discriminant problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(4), pages 545-559, June.
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    Cited by:

    1. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.

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