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This article considers resilience of service networks that are composed of service and control nodes to node‐targeted attacks. Two complementary problems of selecting attacked nodes and placing control nodes reflect the interaction between the network operator and the network attacker. This interaction can be analyzed within the framework of game theory. Considering the limited performance of the previously introduced iterative solution algorithms based on non‐compact problem models, new compact integer programming formulations of the node attack optimization problem are proposed, which are based on the notion of pseudo‐components and on a bilevel model. The efficiency of the new formulations is illustrated by the numerical study that uses two reference networks (medium‐size and large‐size), and a wide range of the sizes of attacks and controllers placements. [ABSTRACT FROM AUTHOR]

We study the relation between the linear programming relaxation of two classes of models for the Steiner tree problem with hop constraints. One class is characterized by having hop‐indexed arc variables. Although such models have proved to have a very strong linear programming bound, they are not easy to use because of the huge number of variables. This has motivated some studies with models involving fewer variables that use, instead of the hop‐indexed arc variables, hop‐indexed node variables. In this article, we contextualize the linear programming relaxation of these node‐based models in terms of the linear programming relaxation of known arc‐based models. We show that the linear programming relaxation of a general node‐based model is implied by the linear programming relaxation of a straightforward arc‐based model. [ABSTRACT FROM AUTHOR]

During the planning of communication networks, the routing decision process (distributed and online) often remains decoupled from the network design process, that is, resource installation and allocation-planning process (centralized and offline). To reconcile both processes and take into account demand variability, we generalize the capacitated multicommodity fixed charge network design class of problems by including different types of fixed costs (installation and maintenance costs) and variable costs (routing costs) but also variable traffic demands over multiple periods. However, conventional integer programming methods can typically solve only small to medium size instances of this problem. Two major difficulties are encountered when using commercial solvers to solve the associated mixed integer programs: (i) problems are large scale and even solving the linear relaxation of the problem can be challenging; and (ii) the solver hardly find good feasible solutions for medium to large scale instances. As an alternative, we propose a Lagrangian approach for computing a lower bound by relaxing the flow conservation constraints such that the Lagrangian subproblem itself decomposes by node. Though this approach yields one subproblem per network node, solving the Lagrangian dual by means of the bundle method remains a complex computational tasks. However, it always provides a lower bound on the optimal solution. Moreover, based on this relaxation, we propose a Lagrangian heuristic that makes the approach more robust than a black-box usage of a Mixed Integer Programming (MIP) solver. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 110-123 2017 [ABSTRACT FROM AUTHOR]