A hybrid metaheuristic algorithm to solve the Capacitated m-Ring Star Problem Antonio Mauttone, Universidad de la Rep´ ublica, Uruguay Sergio Nesmachnow, Universidad de la Rep´ ublica, Uruguay Alfredo Olivera, Universidad de la Rep´ ublica, Uruguay Franco Robledo, Universidad de la Rep´ ublica, Uruguay Email: {mauttone, sergion, aolivera, frobledo}@fing.edu.uy Keywords: metaheuristics; network design; survivability. 1. Introduction This work presents a metaheuristic approach to solve the Capacitated m-Ring Star Problem (CmRSP), a problem introduced by Baldacci et al. [1] which models the design of telecommunication networks with survivability properties. The CmRSP consists of finding a set of m cycles (rings), each of them including the central depot (the central telephone office), a subset of customers, and a set of optional nodes (secondary stations) used to diminish the costs of the network design. The rings must be node-disjoint (except for the central depot) in order to provide survivability to the network when node failure occurs. Customers that are not part of the rings must be directly connected to nodes in the rings. An additional constraint is that no ring (the cycle itself and pendants) can have more than Q customers, being Q a prefixed parameter (the ring capacity). The objective is to minimize the sum of routing and connection costs. The CmRSP is a NP-Hard problem, since it generalizes the Traveling Salesman Problem. System survivability is the ability to provide service despite failures on some components [5]. Survivability is an important goal in the design of communication network backbones, to ensure that the topology is able to resist node malfunctions as well as connection lines failures. In this sense, telecommunication companies have particular interest in problems like the CmRSP, which may help to design large metropolitan optical fiber networks at minimum cost. Baldacci et al. [1] introduced the CmRSP, proposing a branch-and-cut exact algorithm using inequalities from two integer programming formulations as cutting planes. The branch-and-cut algorithm was able to achieve highly accurate results on small and medium-size CmRSP instances. However, numerical results degrade when solving bigger scenarios, even employing up to two hours of execution time. Other similar problems have been previously proposed in the literature. A well-known particular case of the CmRSP is the Ring Star Problem (RSP) [7, 2], which consists of building a simple cycle to minimize the sum of routing and assignment costs. The Steiner Ring Star Problem (SRSP) is a variant of the RSP, where the goal is to find a minimum cost cycle considering only optional nodes (Steiner nodes) and the customers must be connected to exactly one node on the cycle. The Median Cycle Problem (MCP) [8, 9] consists of finding a simple cycle that minimizes the routing cost, while the assignment costs are bounded by a prefixed value. Other location models have also been used, where instead of a ring, a topology such as a path or a tree must be designed and the customers not integrated to this topology must be linked to it [6]. All these related problems have been widely solved using several algorithms, including metaheuristic approaches. However, due to its recent formulation, there have not been attempts to solve the CmRSP using metaheuristic algorithms. This article proposes the application of a combined GRASP and Tabu Search algorithm for solving the CmRSP, which was able to find accurate results in moderate execution times. The rest of the paper is organized as follows. Next section presents the CmRSP formalization. The combined GRASP-Tabu Search algorithm to solve the CmRSP is described Section 3. Section 4 presents the discussion on the empirical analysis on applying the algorithm on a set of CmRSP benchmark instances, and summarizes the numerical results. Finally, the last section formulates the conclusions as well as main lines for future work.