In this paper, we concentrate on generating cutting planes for the unsplittable capacitated network design problem. We use flow arc-set polyhedron of considered problem as a substructure and generate by solving separation over it. To relieve computational burden, show that, in some special cases, closed form can be derived. For general case, brute-force algorithm, called exact is employed such ...

We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem. The restricted master problem solved at each column generation iteration is obtained directly from the compact arc-based model by considering only a subset of the commodity flow variables. The pricing subproblem corresponds to a Lagrangian rela...

We describe the first multilevel cooperative tabu search for the capacitated multicommodity network design problem. Main design challenges are associated to the specification of the problem instance addressed at each level in cooperation, as well as to the definition of the cooperation operators. The paper proposes a first approach to address these challenges and tests it on a set of well-known...

The fixed charge capacitated multicommodity network design problem is a well-known problem, of both practical and theoretical significance. This paper presents an efficient procedure to determine tight upper bounds on the optimal solution of realistically sized problem instances. Feasible solutions are obtained by using a tabu search framework that explores the space of the continuous flow vari...

We improve the mixed-integer programming formulation of the multicommodity capacitated fixed-charge network design problem by incorporating valid inequalities into a cutting-plane algorithm. We use five classes of valid inequalities: the strong, cover, minimum cardinality, flow cover, and flow pack inequalities, the last four being expressed in terms of cutsets of the network. We develop effici...

In this paper we address branch-and-price algorithms for the unsplittable multicommodity flow problem. This problem is defined over a capacitated network in which we intend to route a set of commodities, each one with a given origin, destination and demand, at minimal cost, without exceeding the arc capacities. Furthermore, the flow of each commodity must be routed using a single path. Formulat...

This paper addresses the multicommodity capacitated fixed-charge network design problem with nonbifurcated flows and hop constraints. We present and compare mathematical programming formulations for this problem and we study different relaxations: linear programming relaxations, Lagrangean relaxations and partial relaxations of the integrality constraints. In particular, for the hop-indexed for...