用机器学习提升经典优化算法效率，不牺牲解的精确性。
Machine Learning Algorithms for Improving Exact Classical Solvers in Mixed Integer Continuous Optimization
- 将学习策略融入分支定界法的分支、剪枝等环节
- 通过监督与强化学习加速收敛，保持全局最优
- 适合需要精确解的物流、能源调度场景
整数与混合整数非线性规划（INLP、MINLP）在物流、能源和排班等领域至关重要，但计算仍具挑战。本文综述机器学习与强化学习如何增强精确优化方法，特别是分支定界法（BB），在不牺牲全局最优性的前提下提升性能。涵盖离散、连续及混合整数建模，重点应用包括车辆路径规划、水电调度和乘务排班。提出统一的BB框架，将基于学习的策略嵌入分支、割平面选择、节点排序与参数控制中。通过监督、模仿与强化学习模型对经典算法进行增强，实现加速收敛的同时保证正确性。最后构建按求解器类别与学习范式分类的体系，指出泛化能力、混合架构与智能求解器扩展性等开放问题。
原文摘要 · Abstract (English)
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.
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