T-自适应段路由的字典序极小极大负载均衡

中文摘要 AI 辅助

我们引入了T-自适应段路由（T-Adaptive Segment Routing），这是一个多周期优化问题，出现在涉及计划维护操作的核心IP/MPLS网络的流量工程中。该问题寻求一系列段路由（Segment Routing, SR）配置，这些配置能够适应多周期的计划维护，同时允许在连续时间步之间进行有限数量的路径重配置。我们不仅限于最小化经典的最大链路利用率（Maximum Link Utilization, MLU）标准，而是提出了一种更精细的字典序目标，该目标最小化链路负载的排序向量整体，从而在所有链路上实现更高效的资源利用。为了解决这个问题，我们开发了三种精确公式来求解由此产生的字典序优化问题。其中，Stela和Carla公式为基于轨迹的优化提供了最有利的计算基础。因此，我们为这些公式开发了一种轨迹列生成方案，使用从启发式到精确的定价预言（pricing oracles）。精确定价给出了轨迹主问题的线性规划松弛的精确解，但它本身并不提供整数最优性的证书：在根节点生成的列上求解整数主问题仅能证明在生成的列池内的最优性。为了克服这一差距，我们将轨迹列生成纳入分支定价（Branch-and-Price）框架。分支规则作用于表示段使用情况的聚合变量，这些变量对应于原始紧凑路由变量。因此，分支定价保证了每个Stela和Carla秩的全局整数最优性，并且当所有秩都被精确求解时，它保证了最终解的字典序最优性。

英文摘要

We introduce the T-Adaptive Segment Routing, a multi-period optimization problem that emerges in the traffic engineering of core IP/MPLS networks when scheduled maintenance operations are involved. The problem seeks a sequence of Segment Routing (SR) configurations that can adapt to a multi-period scheduled maintenance, while allowing limited number of path reconfigurations between successive time steps. Instead of only minimizing the classical Maximum Link Utilization (MLU) criteria, we propose a more refined lexicographic objective that minimizes the sorted vector of link loads in its entirety, thereby enabling a more efficient resource utilization across all links. To tackle this problem, we develop three exact formulations for solving the resulting lexicographic optimization problem. Among these, the Stela and Carla formulations provide the most favorable computational basis for trajectory-based optimization. We thus develop a trajectory column-generation scheme for these formulations, using pricing oracles that vary from heuristic to exact. Exact pricing gives an exact solution of the LP relaxation of the trajectory master, but it does not itself give a certificate of integer optimality: solving the integer master over the columns generated at the root node only certifies optimality within the generated column pool. To overcome this gap, we incorporate trajectory column generation into a Branch-and-Price framework. The branching rule operates on aggregate variables representing segment usage, which correspond to the original compact routing variables. Thus, Branch-and-Price guarantees global integer optimality for every Stela and Carla rank, and when all ranks are solved to exactness, it guarantees lexicographic optimality of the final solution.

发表机构

• École polytechnique（巴黎综合理工学院）
• Institut Polytechnique de Paris（巴黎理工学院）

机构由 AI 辅助整理，请以论文原文为准。

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69 pages