Single-Layer Cuts for Multi-Layer Network Design Problems (original) (raw)

Two-layer network design by branch-and-cut featuring MIP-based heuristics

2006

This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.

Branch-and-Cut Techniques for Solving Realistic Two-Layer Network Design Problems

Texts in Theoretical Computer Science. An EATCS Series, 2009

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A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems

INFORMS Journal on Computing, 1998

We present a cutting plane algorithm for solving the following telecommunications network design problem: given point-to-point traffic demands in a network, specified survivability requirements and a discrete cost/capacity function for each link, find minimum cost capacity expansions satisfying the given demands. This algorithm is based on the polyhedral study described in . In this paper we describe the underlying problem, the model and the main ingredients in our algorithm. This includes: initial formulation, feasibility test, separation for strong cutting planes and primal heuristics. Computational results for a set of real-world problems are reported.

Capacitated Multi-Layer Network Design with Unsplittable Demands: Polyhedra and Branch-and-Cut

Discrete Optimization, 2019

We consider the Capacitated Multi-Layer Network Design with Unsplittable demands (CMLND-U) problem. Given a two-layer network and a set of traffic demands, this problem consists in installing minimum cost capacities on the upper layer so that each demand is routed along a unique "virtual" path (even using a unique capacity on each link) in this layer, and each installed capacity is in turn associated a "physical" path in the lower layer. This particular hierarchical and unsplittable requirement for routing arises in the design of optical networks, including optical OFDM based networks. In this paper, we give an ILP formulation to the CMLND-U problem and we take advantage of its sub-problems to provide a partial characterization of the CMLND-U polytope including several families of facets. Based on this polyhedral study, we develop a Branch-and-Cut algorithm for the problem and show its effectiveness though a set of experiments, conducted on SNDlib-derived instances and also on real instances.

A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks

European Journal of Operational Research, 2006

The paper deals with a multi-layer network design problem for a high-speed telecommunication network based on Synchronous Digital Hierarchy (SDH) and Wavelength Division Multiplex (WDM) technology. The network has to carry a certain set of demands with the objective of minimizing the investment in the equipment. The different layers are the fiber-layer, 2.5 Gbit/s-, 10 Gbit/s-and WDM-systems. Several variations of the problem including pathprotected demands and specific types of cross-connect equipment are considered. The problem is described as a mixed integer linear programming model and some results for small networks are presented. Two greedy heuristics, a random start heuristic and a GRASP-like approach are implemented to solve large real world problems.

A branch-and-cut approach for minimum cost multi-level network design

Discrete Mathematics, 2002

Network design models with more than one facility type have many applications in communication and distribution problems. Due to their complexity, previous studies have focused on ÿnding good heuristic solutions. In this study, we develop algorithms that solve the multi-level network design problem to optimality. In our approach, the problem is converted to a Steiner tree problem and is solved by a branch-and-cut approach. Our computational study shows that the approach outperforms a dual ascent approach in the literature (Mirchandani, INFORMS J. Comput. 8 (3) (1996) 202) not only on solution times but also on the quality of the solutions.

A Branch-and-Cut algorithm for the Capacitated Multi-Failure Survivable Network Design problem

Computers & Industrial Engineering, 2018

Telecommunication networks can be seen as the stacking of several layers like, for instance, IP-over-Optical networks. This infrastructure should have sufficient capacities to route some demands between their origindestination nodes. In this paper we consider the Capacitated Multi-Failure Survivable Network Design problem. We study two variants of this problem with simple and multiple capacities. We give two multicommodity flow formulations for each variant of this problem and describe some valid inequalities. In particular, we characterize valid inequalities obtained using Chvatal-Gomory procedure from the well known Cutset inequalities. We show that some of these inequalities are facet defining. We discuss separation routines for all the valid inequalities. Using these results, we develop a Branch-and-Cut algorithm and a Branch-and-Cut-and-Price algorithm for each variant and present extensive computational results.

A packing integer program arising in two-layer network design

2009

In this paper we study a certain cardinality constrained packing integer program which is motivated by the problem of dimensioning a cut in a two-layer network. We prove N P-hardness and consider the facial structure of the corresponding polytope. We provide a complete description for the smallest nontrivial case and develop two general classes of facet-defining inequalities. This approach extends the notion of the well known cutset inequalities to two network layers.

A Near-Optimal Solution Approach for the Multi-hop Traffic Grooming Problem

Journal of Optical Communications and Networking, 2011

In this paper we consider a capacity sizing and routing problem in synchronous digital hierarchy/wavelength division multiplexing networks with nodes having switching capabilities. This problem is well known in the literature as the multi-hop traffic grooming problem and is generally formulated as an integer linear program, which is especially hard to solve when the demand channels are unsplittable and nonuniform. To overcome this difficulty we develop a branching strategy, using a lower bound that is close to the optimal solution. We also devise a reformulation which accelerates branch-and-bound-based solvers. The computational results clearly show that our method is effective in reducing execution time as well as memory consumption, in comparison to traditional methods based on branch-and-bound.