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A system of techniques is presented for optimizing open shortest path first (OSPF) or intermediate system-intermediate system (IS-IS) weights for intradomain routing in a changing world, the goal being to avoid overloaded links. We address predicted periodic changes in traffic as well as problems arising from link failures and emerging hot spots. Index Terms-Combinatorial optimization, intermediate system-intermediate system (IS-IS), local search, open shortest path first (OSPF), shortest path first, traffic engineering, traffic management.

Traffic engineering involves adapting the routing of traffic to the network conditions, with the joint goals of good user performance and efficient use of network resources. In this paper, we describe an approach to intradomain traffic engineering that works within the existing deployed base of Interior Gateway Protocols (IGPs), such as Open Shortest Path First (OSPF) and Intermediate System-Intermediate System (IS-IS). We explain how to adapt the configuration of link weights, based on a network-wide view of the traffic and topology within a domain. In addition, we summarize the results of several studies of techniques for optimizing OSPF/IS-IS weights to the prevailing traffic. The paper argues that traditional shortest-path routing protocols are surprisingly effective for engineering the flow of traffic in large IP networks.

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Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia (1998), we present a formulation for the problem valid for any K, L ≥ 1. We use a Benders decomposition method to efficiently handle the big number of variables and constraints. We show that our Benders cuts contain the constraints used by Huygens et al. to formulate the problem for L = 2,3,4, as well as new inequalities when L ≥ 5. While some recent works on Benders decomposition study the impact of the normalization constraint in the dual subproblem, we focus here on when to generate the Benders cuts. We present a thorough computational study of various branch-and-cut algorithms on a large set of instances including the real based instances from SNDlib. Our best branch-and-cut algorithm combined with an efficient heuristic is able to solve the instances significantly faster than CPLEX 12 on the extended formulation.

We study the problem of designing at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a “mesh”) does not exceed a given length K. This problem arises in the design of fiber-optic-based backbone telecommunication networks. A Branch-and-Cut approach to this problem is presented for which we introduce several families of valid inequalities and discuss the corresponding separation algorithms. Because the size of the problems solvable to optimality by this approach is too small, we also develop some heuristics. The computational performances of these exact and approximate methods are then thoroughly assessed both on randomly generated instances as well as instances suggested by real applications.

Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bi-layer networks, comparing with Knippel's previous results.

In this paper, we analyze different mathematical formulations for general Stackelberg games (GSGs) and Stackelberg security games (SSGs). We consider GSGs in which a single leader commits to a utility maximizing strategy knowing that p possible followers optimize their own utility taking the leader's strategy into account. SSGs are a type of GSG that arise in security applications where the strategies of the leader consist of protecting a subset of targets and the strategies of the p followers consist of attacking a single target. We compare existing mixed integer linear programming (MILP) formulations for GSGs, ranking them according to the tightness of their linear programming (LP) relaxations. We show that SSG formulations are projections of GSG formulations and exploit this link to derive a new SSG MILP formulation that i) has the tightest LP relaxation known among SSG MILP formulations and ii) has an LP relaxation that coincides with the convex hull of feasible solutions in the case of a single follower. We present computational experiments empirically comparing the difficulty of solving the formulations in the general and security settings. The new SSG MILP formulation remains computationally efficient as problem size increases.