GRASP heuristics for a generalized capacitated ring tree problem

Abstract

This paper introduces a new mathematical optimization problem, inspired in the evolution of fiber optics communication. Real-life implementations must address a cost-robustness tradeoff. Typically, real topologies are hierarchically organized in backbone and access networks. The backbone is two-node-connected, while the access network usually considers either leaf nodes or elementary paths, directly connected to the backbone. We define the Capacitated Two-Node Survivable Tree Problem (CTNSTP for short). The backbone consists of at most m two-node-connected structures with a perfect depot as a common node. The access network consists of trees directly connected to the backbone. The CTNSTP belongs to the NP-Complete computational class. A GRASP heuristic enriched with a Variable Neighborhood Descent (VND) is provided. Certain neighborhoods of our VND include exact models based on Integer Linear Programming formulations. The comparison among recent works in the field confirm remarkable savings with the novel proposal.