In this article, we introduce the Generalized [Formula: see text]-Survivable Network Design Problem ([Formula: see text]-GSNDP) which has applications in the design of backbone networks. Different mixed integer linear programming formulations are derived by combining previous results obtained for the related [Formula: see text]-GSNDP and Generalized Network Design Problems. An extensive computa...

ii The Abstract This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a well-known optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear equalities and inequalities. The state of the art in solvers for this problem is th...

We address a generic Mixed-Integer Bilevel Linear Program (MIBLP), i.e., a bilevel optimization problem where all objective functions and constraints are linear, and some/all variables are required to take integer values. Rather than proposing an ad-hoc method applicable only to specific cases, we describe a general-purpose MIBLP approach. We first propose necessary modifications needed to turn...

In this work we present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further we show how to use odd hole inequalities and additional inequalities to ...

Penalty cuts provide a new class of cutting planes for GUB-constrained (and ordinary) mixed integer programs, which are easy to generate by exploiting standard penalty calculations employed in branch-and-bound. The Penalty cuts are created by reference to a selected GUB set and a foundation hyperplane that is typically dual feasible relative to a current linear programming basis. As a special c...

In this paper we consider the k-node-connected subgraph problem. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We introduce further classes of valid inequalities and discuss their facial aspect. We also devise separation routines, investigate the structural properties of the linear relaxation and discuss some reduction operations t...

We study the design of capacitated survivable networks using directed p-cycles. A p-cycle is a cycle with at least three arcs, used for rerouting disrupted flow during edge failures. Survivability of the network is accomplished by reserving sufficient slack on directed p-cycles so that if an edge fails, its flow can be rerouted along the p-cycles. We describe a model for designing capacitated s...