Machine Learning Algorithms for Improving Exact Classical Solvers in Mixed Integer Continuous Optimization
This is an incremental survey paper that organizes existing research on integrating machine learning into classical optimization solvers for domains like logistics and energy.
This survey examines how machine learning and reinforcement learning can enhance exact optimization methods like branch-and-bound for integer and mixed-integer nonlinear programming, covering applications in logistics and scheduling while maintaining global optimality.
Integer and mixed-integer nonlinear programming (INLP, MINLP) are central to logistics, energy, and scheduling, but remain computationally challenging. This survey examines how machine learning and reinforcement learning can enhance exact optimization methods-particularly branch-and-bound (BB)-without compromising global optimality. We cover discrete, continuous, and mixed-integer formulations, and highlight applications such as vehicle routing, hydropower planning, and crew scheduling. We introduce a unified BB framework that embeds learning-based strategies into branching, cut selection, node ordering, and parameter control. Classical algorithms are augmented using supervised, imitation, and reinforcement learning models to accelerate convergence while maintaining correctness. We conclude with a taxonomy of learning methods by solver class and learning paradigm, and outline open challenges in generalization, hybridization, and scaling intelligent solvers.