Abstract
This work deals with the Two-architecture Network Problem, which consists in satisfying growing traffic demand by superimposing rings on an existing meshed network. The goal of this work is to solve the proposed mathematical model via column generation techniques. Firstly a complete model is proposed, then it is simplified to become more manageable. A branch-and-price approach is presented with all its problem-dependent issues. The numerical experience reported consists of two cases, one of 7 nodes and 11 edges, the other with 10 nodes and 36 edges, both drawn from real European telecommunications networks.
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References
Sutter, A. and F. Vanderbeck, L. W.: 1998, `Optimal Placement of Add/Drop Multiplexers: Heuristic and Exact Algorithms’. Operations Research 46 (5), 719–728.
Barnhart, C., E. L. Johnson, G. L. Nemhauser, M. W. P. Savelsbergh, and P. H. Vance: 1998, `Branch-and-price: Column Generation for Solving Huge Integer Programs’. Operations Research 46, 316–329.
Brito, J. A. M.: 1999, `Um Modelo de Otimizaçâo para Dimensionamento de uma Rede de Telecomunicaçóes’. Tese de mestrado, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil.
Campello, R. E. and N. Maculan: 1994, Algoritmos e HeurÃsticas: Desenvolvimento e Avaliaçâo de Performance. Niterói, Brasil: EDUFF.
Chvâtal, V.: 1983, Linear programming. New York/San Francisco: W. H. Freeman and Company.
Dantzig, G. and P. Wolfe: 1960, `Decomposition principle for linear programming’. Operations Research 8, 101–111.
Dantzig, G. B.: 1963, Linear programming and extensions. New Jersey, USA: Princeton University Press.
Gilmore, P. and R. Gomory: 1961, `A Linear Programming Approach to the Cutting Stock Problem’. Operations Research 9, 849–859.
Gilmore, P. and R. Gomory: 1963, `A linear programming approach to the cutting stock problem–part II’. Operations Research 11, 863–888.
Glover, F., J. P. Kelly, and M. Laguna: 1995, `Genetic Algorithms and Tabu Search: Hybrids for Optimization’. Computers e4 Operations Research 22, 111–134.
Hochbaum, D. S. (ed.): 1997, Approximation algorithms for NP-hard problems. PWS Publishing Company.
Lasdon, L. S.: 1970, Optimization Theory for Large Systems. New York, USA: Macmillan.
Lisser, A., N. Maculan, and M. Passini: 1996a, `A Mathematical Model for Solving Design Problems of Telecommunication Networks’. In: INFORMS. Atlanta, USA.
Lisser, A., N. Maculan, and M. Passini: 1996b, `Modelling and Solving Design Problems of Telecommunication Network Using Two Different Architectures’. In: Conférence Internationale en Recherche Opérationnelle. Marrakech, Maroc.
Lisser, A., R. Sarkassian, and J.-P. Vial: 1995, `Survivability in Transmission Telecommunication Networks’. Technical report, NT/PAA/ATR/ORI, CNET, France Télécorn. To appear in Investigación Operativa.
Maculan, N., M. Fampa, and P. Michelon: 1999, Programaçâo Linear e Inteira’. Notes - COPPE/Universidade Federal do Rio de Janeiro.
Maculan, N., M. Passini, and I. Loiseau: 1998a, `Column-Generation in Integer Linear Programming’. Technical report, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil.
Maculan, N., M. Passini, and A. Silvério: 1998b, `Caracterizaçâo de um Emaranhado de Anéis em uma Rede de Telecomunicaçóes’. Technical report, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil.
Minoux, M.: 1987, `Network Synthesis and Dynamic Network Optimization’. Annals of Discrete Mathematics 31, 283–324.
Passini, M. M.: 1996, `Um Modelo de Otimizaçâo Combinatória para o Dimensionamento de uma Rede Urbana de Telecomunicaçóes’. Master’s thesis, COPPE, Universidade Federal do Rio de Janeiro.
Savelsbergh, M.: 1997, `A Branch-and-price Algorithm for the Generalized Assignment Problem’. Operations Research 46, 831–841.
Szwarcfiter, J. and P. Lauer: 1975, `A Search Strategy for the Elementary Cycles of a Directed Graph’. BIT 16, 192–204.
Vachani, R., A. Shulman, and P. Kubat: 1996, `Multicommodity Flows in Ring Networks’. INFORMS Journal on Computing 8, 235–242.
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Maculan, N., Passini, M.M., Brito, J.A.M., Lisser, A. (2002). Column Generation Method for Network Design. In: Gendreau, M., Marcotte, P. (eds) Transportation and Network Analysis: Current Trends. Applied Optimization, vol 63. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6871-8_11
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DOI: https://doi.org/10.1007/978-1-4757-6871-8_11
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