Learning explicit binary warm starts for mixed-integer programming

In this paper we propose a lightweight neural network architecture that is able to learn the binary components of the optimal solution of a class of multiparametric mixed-integer quadratic programming (MIQP) problems, such as those that arise from hybrid model predictive control formulations. The predictor provides a binary warm-start to a specifically designed branch and bound (B&B) algorithm to quickly discover an integer-feasible solution of the given MIQP, with the aim of reducing the overall solution time required to find the global optimal solution on line.