强化学习如何赋能运筹学：一篇技术综述与实践路线图

Reinforcement Learning in Operational Research: A Technical Review and Practical Roadmap

The growing demand for real-time, data-driven decision-making in complex and dynamic systems is placing increasing pressure on traditional Operational Research (OR) methodologies. Reinforcement learning (RL) has emerged as a complementary approach, offering strong learning and computational capabilities for sequential decision-making in dynamic and uncertain environments. Recent research shows an increasing interest in integrating RL with OR to address dynamic decision-making problems, enhance heuristic and exact methods for combinatorial optimization, and support the development of digital replicas of operational systems. The overarching goal across these efforts is to leverage the learning capabilities of RL to strengthen traditional OR algorithms, improving solution quality, computational efficiency, and robustness. Given the diversity of integration approaches and application settings, there is a clear need for a systematic and technically detailed review of how RL empowers OR methods. To address this gap, this paper presents a structured review of three key roles that RL plays in empowering OR: (i) solving sequential decision-making problems in dynamic environments, (ii) serving as an end-to-end solution method or as a component integrated within heuristic and exact OR methods for combinatorial optimization problems, and (iii) facilitating extended reality analysis through integration with digital twin systems. We critically synthesize recent advances across these roles, highlighting their advantages, implementation requirements, limitations, and challenges. Finally, based on these insights, we outline a roadmap for future research to further advance the methodological and practical integration of RL and OR.