Tabu search approaches for solving the two‐group classification problem

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.