Abstract
We define the Balanced Disjoint Rings (BDR) problem as developing a method to partition of the nodes in a network to form a given number of disjoint rings of minimum total link length in such a way that there is almost the same number of nodes in each ring. The BDR problem has potential applications in the design of survivable network structures in telecommunications as well as in the identification of local distribution/collection routes in logistics. The BDR problem can also be considered a generalization of the traveling salesman problem since we are interested in multiple tours instead of a single tour. We develop an efficient heuristic solution methodology that involves various GRASP-based randomized solution construction routines that allow a multi-start framework and a n effective combination of cyclic-exchange and single-move neighborhoods in a local search improvement procedure. The algorithms perform very well in our numerical studies, providing encouraging optimality and lower bound gaps with very reasonable runtimes.
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Ahuja, R.K., Orlin, J.B., Sharma, D.: Multi-exchange neighborhood search algorithms for the capacitated minimum spanning tree problem. Math. Program. 91, 71–97 (2001)
Ahuja, R.K., Orlin, J.B., Sharma, D.: A composite very large-scale neighborhood structure for the capacitated minimum spanning tree problem. Oper. Res. Lett. 31, 185–194 (2003)
Altinkemer, K.: Topological design of ring networks. Comput. Oper. Res. 21, 421–431 (1994)
Bellmore, M., Hong, S.: Transformation of multisalesmen problem to standard traveling salesman problem. J. Assoc. Comput. Mach. 21, 500–504 (1974)
Branco, I.M., Coelho, J.D.: The Hamiltonian p-median problem. Eur. J. Oper. Res. 47, 86–95 (1990)
Christofides, N.: Worst-case analysis for a new heuristic for the traveling-salesman problem. Technical Report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976)
Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. Wiley, New York (1998)
Cosares, S., Deutsch, D.N., Saniee, I., Wasem, O.J.: SONET Toolkit: A decision support system for designing robust and cost-effective fiber-optic networks. Interfaces 25(1), 20–40 (1995)
Daskin, M.S.: Network and Discrete Location: Models, Aplications and Algorithms. Wiley, New York (1995)
Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)
Fisher, M.L.: Vehicle routing. In: Ball, M.O., Magnanti, T.L., Monma, C.L., Nemhauser, G.L. (eds.) Network Routing. Handbooks in Operations Research and Management Science, vol. 8. Elsevier Science, Amsterdam (1995)
Gawande, M., Klincewicz, J.G., Luss, H.: Design of SONET ring networks for local access. Adv. Perform. Anal. 2(2), 159–173 (1999). Also see US Patent No. 6061335 at http://patft.uspto.gov/netahtml/PTO/srchnum.htm, given in 2000
Glaab, H., Pott, A.: The Hamiltonian p-median problem. Electron. J. Comb. 7, R-42 (2000)
Jonker, R., Volgenat, T.: An improved transformation of the symmetric multiple traveling salesman problem. Oper. Res. 34(5), 698–717 (1986)
Laporte, G., Nobert, Y.: Generalized traveling salesman problem through n sets of nodes: An integer programming approach. INFOR 21(1), 61–75 (1983)
Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling salesman problem. Oper. Res. 21, 498–516 (1973)
Luss, H., Rosenwein, M.B., Wong, R.T.: Topological network design for SONET ring structure. IEEE Trans. Syst. Man Cybern.-Part A: Syst. Hum. 28(6), 780–790 (1998)
Perl, J., Daskin, M.S.: A warehouse location problem. Transp. Res. Q. Part B—Methodol. 19, 381–396 (1983)
Renaud, J., Boctor, F.F.: An efficient composite heuristic for the symmetric generalized traveling salesman problem. Eur. J. Oper. Res. 108, 571–584 (1998)
Resende, M.G.C., Riberio, C.C.: Greedy randomized adaptive search procedures. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp. 219–249. Kluwer Academic, Norwell (2003)
Shi, J., Fonseka, J.P.: Hierarchical self-healing rings. IEEE/ACM Trans. Netw. 3(6), 690–697 (1995)
Soriano, P., Wynants, C., Séguin, R., Labbé, M., Gendreau, M., Fortz, B.: Design and dimensioning of survivable SDH/SONET networks. In: Sansò, B., Soriano, P. (eds.) Telecommunications Network Planning, pp. 571–584. Center for Research on Transportation, University of Montreal, Montreal (1998)
Thomadsen, T., Stidsen, T.: Hierarchical ring network design using branch-and-price. Telecommun. Syst. 29(1), 61–76 (2005)
Thompson, P.M., Orlin, J.B.: The theory of cyclic transfers. Technical Report OR200-89, MIT Operations Research Center (1989)
Thompson, P.M., Psaraftis, H.N.: Cyclic transfer algorithms for multi-vehicle routing and scheduling problems. Oper. Res. 41, 935–946 (1993)
Tietz, M.B., Bart, P.: Heuristic methods for estimating the generalized vertex median of a weighted graph. Oper. Res. 16, 955–961 (1968)
Wu, T.H.: Emerging technologies for fiber network survivability. IEEE Commun. Mag. 33, 58–74 (1995)
Wu, T., Low, C., Bai, J.: Heuristic solutions to multi-depot location-routing problem. Comput. Oper. Res. 29, 1393–1415 (2002)
Xu, J., Chiu, S.Y., Glover, F.: Optimizing a ring-based private line telecommunication network using tabu search. Manag. Sci. 45(3), 330–345 (1999)
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Üster, H., Kumar, S.K.S. Algorithms for the design of network topologies with balanced disjoint rings. J Heuristics 16, 37–63 (2010). https://doi.org/10.1007/s10732-008-9085-z
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DOI: https://doi.org/10.1007/s10732-008-9085-z