发表机构
Università di Pisa; Alma Mater Studiorum Università di Bologna; Università di Trento（比萨大学; 博洛尼亚大学; 特伦托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对IP网络中的时延约束路由问题，提出一种无求解器的嵌套Benders-Lagrange双重分解方法，结合定制空间分支定界与分段凸割，在竞争性时间内获得紧的上下界。
AI 中文摘要
我们研究了IP计算机网络中出现的时延约束路由（DCR）问题，该问题旨在支持高带宽应用。目标是在满足服务质量约束（特别是最坏情况时延的界限）的前提下，将IP数据包从源路由到目的地，同时最小化网络中分配的总带宽。DCR问题可以表述为一个混合整数二阶锥规划，并使用标准求解器进行求解；虽然通常效率较高，但这依赖于现成的工具，并且无法扩展到大规模实例。我们设计了一种无求解器的定制方法，采用嵌套的Benders-Lagrange分解，即利用问题特殊结构的双重分解方法。具体而言，我们使用问题的非凸非线性表述，这导致了一个非凸的Benders值函数，我们通过一种定制的空间分支定界方法，使用自定义的分段凸割来处理该函数的优化。我们证明了我们的方法在与先前最先进方法相比具有竞争力的运行时间内，提供了非常紧的上下界。
英文摘要
We study the Delay Constrained Routing (DCR) problem arising in IP computer networks to support high bandwidth applications. The goal is to route IP packets, from source to destination, subject to quality of service constraints -- in particular, bounding the worst case delay -- while minimizing the total allocated bandwidth in the network. DCR can be formulated as a Mixed-Integer Second-Order Cone Program, and solved using standard solvers; while generally efficient, this hinges on off-the-shelf tools and does not scale to large instances. We devise a solver-free bespoke approach that uses nested Benders-Lagrange, namely, a double decomposition approach that exploits the special structure of the problem. In particular, we use a nonconvex nonlinear formulation of the problem, that results in a nonconvex Benders value function whose optimization we tackle with a bespoke Spatial Branch-and-Bound approach using custom piecewise-convex cuts. We show that our approach provides very tight upper and lower bounds in competitive running times w.r.t. previous state-of-the-art approaches.
Comments31 pages, 5 figures
