Random Mixed Integer Programs for Classification

Classification is a fundamental task in data science and statistics. Although a wide range of statistical and machine learning methods has been extensively studied, optimization-based classification methods remain an active research direction in operations research. In this paper, we propose a mixed-integer programming (MIP) framework for binary classification based on grouping same-class observations into linearly separable regions. We then embed this formulation into a bagging-based ensemble, called Random MIPs, in which several smaller MIP classifiers are trained on bootstrap samples and combined by majority voting. The proposed framework is intended to combine the modeling flexibility and interpretability of integer programming with the variance-reduction effect of ensemble learning. Preliminary computational experiments indicate that the approach can be competitive with standard classifiers on small and medium-sized benchmark datasets, while also highlighting the need for careful tuning and scalability analysis.