Efficient Greedy Randomized Adaptive Search Procedure for the Generalized Regenerator Location Problem

Over the years, there has been an evolution in the manner in which we perform traditional tasks. Nowadays, almost every simple action that we can think about involves the connection among two or more devices. It is desirable to have a high quality connection among devices, by using electronic or optical signals. Therefore, it is really important to have a reliable connection among terminals in the network. However, the transmission of the signal deteriorates when increasing the distance among devices. There exists a special piece of equipment that we can deploy in a network, called regenerator, which is able to restore the signal transmitted through it, in order to maintain its quality. Deploying a regenerator in a network is generally expensive, so it is important to minimize the number of regenerators used. In this paper we focus on the Generalized Regenerator Location Problem (GRLP), which tries to find the minimum number of regenerators that must be deployed in a network in order to have a reliable communication without loss of quality. We present a GRASP metaheuristic in order to find good solutions for the GRLP. The results obtained by the proposal are compared with the best previous methods for this problem. We conduct an extensive computational experience with 60 large and challenging instances, emerging the proposed method as the best performing one. This fact is finally supported by non-parametric statistical tests.