GripNews➤ 整數線性規劃的實用進展與未來展望
✤ https://inria.hal.science/hal-04776866v1
本文回顧了過去五十年整數線性規劃 (MILP) 的發展，重點關注近年來在實用效能方面的進展。MILP 已成為運營研究的基石，得益於現代求解器的效率提升，如今能在短時間內為十年前難以解決的問題找到全局最佳解。這些求解器的多功能性使其在運輸、物流、供應鏈管理、收益管理、金融、電信和製造等領域得到成功應用。儘管已取得了顯著的成功，但仍存在許多挑戰，MILP 仍然是一個活躍的研究領域。本文概述了推動 MILP 解決方法進展的最重要成果，著重於計算方面和最近的實用效能改進，並強調報告計算實驗的研究。本文將研究分為三個主要部分，分別探討分支定割法、丹錫格-沃爾夫分解和 Bender 分解。文章最後強調了 MILP 研究中持續的挑戰和未來機會。
+ 這篇文章很好地總結了整數線性規劃領域的發展，對於研究者和從業者來說都很有價值。
+ 瞭解 MILP 近年來的進展對於應用這些技術解決實際問題非常有幫
#運營研究 #數學規劃 #計算機科學
Last fifty years of integer linear programming: a focus on recent practical advances
<div><p>Mixed-integer linear programming (MILP) has become a cornerstone of operations research. This is driven by the enhanced efficiency of modern solvers, which can today find globally optimal solutions within seconds for problems that were out of reach a decade ago. The versatility of these solvers allowed successful applications in many areas, such as transportation, logistics, supply chain management, revenue management, finance, telecommunications, and manufacturing. Despite the impressive success already obtained, many challenges remain, and MILP is still a very active field.</p><p>This article provides an overview of the most significant results achieved in advancing the MILP solution methods. Given the immense literature on this topic, we made deliberate choices to focus on computational aspects and recent practical performance improvements, emphasizing research that reports computational experiments. We organize our survey into three main parts, dedicated to branch-and-cut methods, Dantzig-Wolfe decomposition, and Benders decomposition. The paper concludes by highlighting ongoing challenges and future opportunities in MILP research.</p></div>
