Machine Learning Algorithms for Improving Exact Classical Solvers in Mixed Integer Continuous Optimization

TL;DR

This survey explores how machine learning techniques can enhance exact classical solvers for mixed-integer nonlinear programming, improving efficiency without losing optimality.

Contribution

It introduces a unified branch-and-bound framework embedding learning strategies and provides a taxonomy of learning methods for solver enhancement.

Findings

Learning-based strategies accelerate convergence.

Classical algorithms are augmented with ML models.

Framework maintains correctness while improving performance.

Abstract

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.