This manuscript describes the notions of blocker and interdiction applied to well-known optimization problems. The main interest of these two concepts is the capability to analyze the existence of a combinatorial structure after some modifications. We focus on graph modification, like removing vertices or links in a network. In the interdiction version, we have a budget for modification to reduce as much as possible the size of a given combinatorial structure. Whereas, for the blocker version, we minimize the number of modifications such that the network does not contain a given combinatorial structure. Blocker and interdiction problems have some similarities and can be applied to well-known optimization problems. We consider matching, connectivity, shortest path, max flow, and clique problems. For these problems, we analyze either the blocker version or the interdiction one. Applying the concept of blocker or interdiction to well-known optimization problems can change their complexities. Some optimization problems become harder when one of these two notions is applied. For this reason, we propose some complexity analysis to show when an optimization problem, or the associated decision problem, becomes harder. Another fundamental aspect developed in the manuscript is the use of exact methods to tackle these optimization problems. The main way to solve these problems is to use integer linear programming to model them. An interesting aspect of integer linear programming is the possibility to analyze theoretically the strength of these models, using cutting planes. For most of the problems studied in this manuscript, a polyhedral analysis is performed to prove the strength of inequalities or describe new families of inequalities. The exact algorithms proposed are based on Branch-and-Cut or Branch-and-Price algorithm, where dedicated separation and pricing algorithms are proposed.

翻译：本文阐述了应用于经典优化问题的阻塞与阻断概念。这两个概念的核心价值在于能够分析网络经过特定修改后组合结构的存在性。我们重点关注图结构修改，例如移除网络中的顶点或连接边。在阻断问题中，我们通过给定预算的修改操作来最大程度缩减特定组合结构的规模；而在阻塞问题中，我们则寻求最小化修改次数，使得网络中不再包含给定组合结构。阻塞与阻断问题具有相似性，可应用于多种经典优化问题。本文研究匹配、连通性、最短路径、最大流以及团问题，并分别分析其阻塞或阻断版本。将阻塞或阻断概念应用于经典优化问题可能改变其计算复杂度——部分优化问题在应用这些概念后会变得更加困难。为此，我们通过复杂度分析来揭示优化问题及其对应判定问题何时会转变为更难解问题。本文另一核心内容是研究解决此类优化问题的精确算法。主要方法采用整数线性规划进行建模，其理论优势在于可通过割平面分析模型强度。针对本文研究的大部分问题，我们通过多面体分析证明了不等式的强度或提出了新的不等式族。所提出的精确算法基于分支切割法或分支定价法，并设计了专用的分离算法与定价算法。