A tabu search with an oscillation strategy for the discriminant analysis problem

Authors:
Arnaud Fréville;Saïd Hanafi;Frédéric Semet;Nicolas Yanev
Affiliations:
LAMIH, UMR CNRS 8530, Université de Valenciennes, Le Mont-Houy, 59313 Valenciennes Cedex 9, France;LAMIH, UMR CNRS 8530, Université de Valenciennes, Le Mont-Houy, 59313 Valenciennes Cedex 9, France;LAMIH, UMR CNRS 8530, Université de Valenciennes, Le Mont-Houy, 59313 Valenciennes Cedex 9, France and LAGIS, UMR CNRS 8146, Ecole Centrale de Lille, Cité Scientifique, BP 48, 59651 Vill ...;Faculty of Mathematics and Computer Science, University of Sofia, 5, J. Bouchier str., 1126 Sofia, Bulgaria
Venue:
Computers and Operations Research
Year:
2010

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Abstract

This article proposes a tabu search approach to solve a mathematical programming formulation of the linear classification problem, which consists of determining an hyperplane that separates two groups of points as well as possible in @?^m. The tabu search approach proposed is based on a non-standard formulation using linear system infeasibility. The search space is the set of bases defined on the matrix that describes the linear system. The moves are performed by pivoting on a specified row and column. On real machine learning databases, our approach compares favorably with implementations based on parametric programming and irreducible infeasible constraint sets. Additional computational results for randomly generated instances confirm that our method provides a suitable alternative to the mixed integer programming formulation that is solved by a commercial code when the number of attributes m increases.