Reload cost trees and network design

Abstract

In this article, we consider the notion of "reload costs" in network design. Reload costs occur naturally in many different settings including telecommunication networks using diverse technologies. However, reload costs have not been studied extensively in the literature. Given that reload costs occur naturally in many settings, we are motivated by the desire to develop "good" models for network design problems involving reload costs. In this article, and as a first step in this direction, we propose and discuss the reload cost spanning tree problem (RCSTP). We show that the RCSTP is NP-complete. We discuss several ways of modeling network design problems with reload costs. These involve models that expand the original graph significantly-to a directed line graph and a colored graph-to model reload costs. We show that the different modeling approaches lead to models with the same linear programming bound. We then discuss several variations of reload cost spanning tree and network design problems, and discuss both their complexity and models for these variations. To assess the effectiveness of the proposed models to solve RCSTP instances, we present results taken from instances with up to 50 nodes, 300 edges, and nine technologies for several variations of the problem.

On minimum reload cost paths, tours, and flows

“…The network problems where the reload cost model most naturally applies have objective functions dealing with paths. The objective function of concern in [2, 7] is the reload cost of the diameter of a spanning tree, whereas in [3] it is the sum of the reload costs of all paths between pairs of nodes in a spanning tree. Despite the obvious applicability of the reload cost concept, these were the only references in the literature until very recently.…”

A swarm intelligence approach to the minimum reload cost spanning tree problem

“…The goal is to build a spanning tree that has the smallest possible diameter with respect to the reload cost. In [3], the authors have developed a node-color graph model for the reload cost tree problem. Their computational experiment focuses on the strength of the LP relaxation of the reload cost tree problem.…”

Polyhedral results, branch‐and‐cut and Lagrangian relaxation algorithms for the adjacent only quadratic minimum spanning tree problem

“…A problem that closely relates to the application outlined above and, as such, to the AQMSTP, is the reload cost spanning tree problem (RCSTP) [6]. For this problem, edges in the telecommunication network may employ different technologies or belong to different service providers.…”

“…In addition to the usual routing costs, the RCSTP involves the so called reload costs, costs incurred when packages are routed through paths involving edges of different colors. Several variants of the RCSTP, involving different cost structures as well as capacity, hop, and diameter constraints were discussed in [6]. In the general RCSTP case, the reload costs depend on the amount of flow being routed.…”

“…That means reload costs do not depend on the amount of data being shipped but only on the colors of the links in the paths and the FRCSTP becomes the AQMSTP. Gamvros et al [6] proposed integer programming models for the RCSTP and many of its variations, including the FRCSTP. Nevertheless, no computational investigation for the FRCSTP was carried out in that reference.…”