A branch-and-cut algorithm for two-level survivable network design problems

Abstract

This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through access networks (second network level). We consider two survivable structures in both network levels. One structure is a two-edge connected network, and the other structure is a ring. There is a limit on the number of nodes in each access network, and there are fixed costs associated with the hubs and the access and backbone links. The aim of the problem is to minimize the total cost. We give integer programming formulations and valid inequalities for the different versions of the problem, solve them using a branch-and-cut algorithm, and discuss computational results. Some of the new inequalities can be used also to solve other problems in the literature, like the plant cycle location problem and the hub location routing problem. © 2015 Elsevier Ltd. All rights reserved

The ring/κ‐rings network design problem: Model and branch‐and‐cut algorithm

“…We tested the algorithm on two data sets used in consisting of 36 instances each, with a number of nodes ranging from 15 to 40. In the Class I instances, edge costs are randomly generated in .…”

“…Two of these problems are ring/two‐edge connected network design and ring/ring network design problems. However, the ring/ring problem in differs from the ring/1‐ring problem studied here (i.e., the ring/ ‐rings where ) since in the former not all nodes must be necessarily on an access network, giving rise to optimal solutions with hubs without any adjacent access network. Carroll and McGarraghy propose to decompose the problems of designing the rings in different levels.…”

“…Let be the feasible set of model (2)–(18). In this section, we propose several families of valid inequalities for that generalize other inequalities given in Rodríguez‐Martín et al for the ring/ring network design problem.…”

“…We follow the same idea to devise exact separation procedures for inequalities (11) and (12). The detailed algorithms are given in .…”

“…Our approach to the ring/1‐ring network design problem tackles the two steps simultaneously, as an integrated problem, although without considering savings in the objective function. Rodríguez‐Martín et al propose a branch‐and‐cut algorithm for several two‐level network design problems with survivability requirements in both levels. Two of these problems are ring/two‐edge connected network design and ring/ring network design problems.…”