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引用次数: 0
摘要
对社会具有重要意义的领域中的业务经常被模拟为混合整数线性规划（MILP）问题。虽然 MILP 问题具有组合复杂性，但拉格朗日松弛法（Lagrangian Relaxation）一直是通过分解来解决相关难题的希望之光。由于拉格朗日对偶函数的非光滑性质，该方法的协调性面临严峻挑战。本文介绍了几个重要的历史里程碑（从 1967 年 Polyak 的开创性工作开始），旨在通过改进非光滑函数的优化来改善拉格朗日松弛协调。最后，本文介绍了拉格朗日松弛法在快速解决 MILP 问题方面的最新进展。本文还简要讨论了拉格朗日松弛法在当前所能提供的机遇。
Survey on Lagrangian relaxation for MILP: importance, challenges, historical review, recent advancements, and opportunities
Operations in areas of importance to society are frequently modeled as mixed-integer linear programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak’s pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time.
期刊介绍：
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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