Randomized Heuristics for the Regenerator Location Problem

Telecommunication systems make use of optical signals to transmit information. The strength of a signal in an optical network deteriorates and loses power as it gets farther from the source, mainly due to attenuation. Therefore, to enable the signal to arrive at its intended destination with good quality, it is necessary to regenerate it periodically using regenerators. These components are relatively expensive and therefore it is desirable to deploy in the network as few of them as possible. In the regenerator location problem, we are given an undirected graph, positive edge lengths, and a parameter specifying the maximum length that a signal can travel before its quality deteriorates and regeneration is needed. The problem consists in determining paths that connect all pairs of nodes in the graph and, if necessary, locating single regenerators in some of those nodes such that the signal never travels more than the maximum allowed distance without traversing a regenerator node. In this paper we present a GRASP and a biased random-key genetic algorithm for the regenerator location problem. Computational experiments comparing the proposed solution procedure with other heuristics described in the literature illustrate the efficiency and effectiveness of our methods.