Solving a Ring Star Problem Generalization

The Capacitated m-Ring Star Problem (CmRSP) consists of finding a set of m rings, each of them including the central depot, a subset of customers, and a set of optional nodes used to diminish the costs of the network design. The rings must be node-disjoint (except for the central depot) in order to provide node-survivability to the network. Customers that are not part of the rings must be directly connected to nodes in the rings (as pendants). An additional constraint is that no ring (the cycle itself and pendants) can have more than Q customers. The objective is to minimize the sum of routing and connection costs. The CmRSP is NP-Hard and has important applications in the metropolitan optical fiber network planning. This work presents a metaheuristic approach to solve the CmRSP. The algorithm was tested over a set of 90 benchmark instances accomplishing in all cases optimal or near-optimal solutions.

[1]  Inmaculada Rodríguez Martín,et al.  Locating median cycles in networks , 2005, Eur. J. Oper. Res..

[2]  Ali Ridha Mahjoub,et al.  Design of Survivable Networks: A survey , 2005, Networks.

[3]  Paolo Toth,et al.  The Granular Tabu Search and Its Application to the Vehicle-Routing Problem , 2003, INFORMS J. Comput..

[4]  Yves Rochat,et al.  Probabilistic diversification and intensification in local search for vehicle routing , 1995, J. Heuristics.

[5]  Mauro Dell'Amico,et al.  The Capacitated m-Ring-Star Problem , 2007, Oper. Res..

[6]  Celso C. Ribeiro,et al.  Greedy Randomized Adaptive Search Procedures , 2003, Handbook of Metaheuristics.

[7]  Cid C. de Souza,et al.  Column Generation Algorithms for the Capacitated m-Ring-Star Problem , 2008, CTW.

[8]  Gilbert Laporte,et al.  Path, Tree and Cycle Location , 1998 .

[9]  Celso C. Ribeiro,et al.  Parallel Greedy Randomized Adaptive Search Procedures , 2005 .

[10]  Celso C. Ribeiro,et al.  GRASP and path-relinking : Recent advances and applications , 2003 .

[11]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[12]  Fred W. Glover,et al.  Tabu Search , 1997, Handbook of Heuristics.

[13]  Lucídio dos Anjos Formiga Cabral,et al.  An Efficient Heuristic for the Ring Star Problem , 2006, WEA.

[14]  Gilbert Laporte,et al.  New Insertion and Postoptimization Procedures for the Traveling Salesman Problem , 1992, Oper. Res..

[15]  Inmaculada Rodríguez Martín,et al.  Variable neighborhood tabu search and its application to the median cycle problem , 2003, Eur. J. Oper. Res..

[16]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[17]  Inmaculada Rodríguez Martín,et al.  The Ring Star Problem: Polyhedral analysis and exact algorithm , 2004, Networks.