Integration of machine constraint learning methods within optimization models

One important aspect of the connection between optimization models and machine learning is “constraint learning”, which involves deriving mathematical expressions for the objective function and constraints of optimization models, particularly when explicit expressions for these components are unavailable. In such situation, objective function or constraints can be learned from a labeled dataset using machine learning algorithms and then incorporated into the optimization model. To the best of our knowledge, support vector machine with RBF kernel, linear and nonlinear twin support vector machine and K-nearest-neighbors approaches have not yet been applied for constraint learning. To address this research gap, we focus on embedding functions learned through these approaches into optimization models, and discuss the necessary linearization techniques. Moreover, as the K-nearest-neighbors approach leads to a large-scale optimization model, a heuristic algorithm is proposed to solve it efficiently. The performance of the proposed approaches are evaluated on two real-world applications in the context of optimizing food basket compositions and scholarship allocation.