Integer Programming for Telecommunications

  • Eva K. Lee
  • David P. Lewis


This chapter presents an overview of integer programming in the field of telecommunications. Various integer programming models are described, and computational strategies for solving the integer programming instances are summarized. Techniques such as branching variable selection and node selection schemes are discussed; and the concepts of problem preprocessing and reformulation, heuristics, and continuous reduced-cost fixing are outlined. These latter techniques have been shown to be very effective when embedded within a branch-and-bound algorithm. The use of an interior point method as a subproblem solver is also described. Finally, Lagrangian relaxation in the context of solving specific telecommunication instances is analyzed as an alternative relaxation for use within the branch-and-bound tree search environment.


Integer programming preprocessing heuristics branching reduced-cost fixing branch-and-bound interior point methods Lagrangian relaxation Benders’ decomposition column generation branch-and-cut 


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  1. D. Alevras, M. Grötschel, P. Jonas, U. Paul, and R. Wessäly. Survivable mobile phone network architectures: models and solution methods. IEEE Communications Magazine, 36(3):88–93, 1998a.CrossRefGoogle Scholar
  2. D. Alevras, M. Grötschel, and R. Wessaly. Cost-efficient network synthesis from leased lines. Annals of Operations Research, 76:1–20, 1998b.zbMATHCrossRefGoogle Scholar
  3. A. Amiri. A system for the design of packet-switched communication networks with economic tradeoffs. Computer Communications, 21(18): 1670–1680, 1998.CrossRefGoogle Scholar
  4. A. Amiri and H. Pirkul. Primary and secondary route selection in backbone communication networks. European Journal of Operational Research, 93(1):98–109, 1996.zbMATHCrossRefGoogle Scholar
  5. E. D. Andersen, J. Gondzio, C. Mészáros, and X. Xu. Implementation of interior point methods for large scale linear programming. In T. Terlaky, editor, Interior Point Methods in Mathematical Programming, chapter 6. Kluwer Academic Publishers, 1996.Google Scholar
  6. D. Applegate, R.E. Bixby, V. Chvátal, and W. Cook. Finding cuts in the TSP (a preliminary report). Technical Report 95-05, DIMACS, Rutgers University, New Brunswick, NJ 08903, 1995.Google Scholar
  7. A. Balakrishnan and K. Altinkemer. Using a hop-constrained model to generate alternative communication network design. ORSA Journal on Computing, 4(2): 192–205, 1992.zbMATHGoogle Scholar
  8. A. Balakrishnan, T.L. Magnanti, and P. Mirchandani. A dual-based algorithm for multi-level network design. Management Science, 40(5):567–581, 1994.zbMATHCrossRefGoogle Scholar
  9. A. Balakrishnan, T.L. Magnanti, J.S. Sokol, and W. Yi. Spare-capacity assignment for line restoration using a single-facility type. Operations Research, 50(4):2120, 2002.CrossRefGoogle Scholar
  10. A. Balakrishnan, T.L. Magnanti, and R.T. Wong. A decomposition algorithm for local access telecommunications network expansion planning. Operations Research, 43(1):58–76, 1995.zbMATHCrossRefGoogle Scholar
  11. E. Balas and C.H. Martin. Pivot and complement-a heuristic for 0/1 programming. Management Science, 26:86–96, 1980.MathSciNetzbMATHCrossRefGoogle Scholar
  12. R. Baldick. A randomized heuristic for inequality-constrained mixed-integer programming. Technical report, Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, 1992.Google Scholar
  13. J. Barbas and A. Marin. Maximal covering code multiplexing access telecommunication networks. European Journal of Operational Research, 159(1):219–238, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  14. C. Barnhart, C.A. Hane, and P.H. Vance. Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Operations Research, 48(2):318–326, 2000.CrossRefGoogle Scholar
  15. C. Barnhart, E.L. Johnson, G.L. Nemhauser, M.W.P. Savelsbergh, and P.H. Vance. Branch and price: column generation for solving huge integer programs. Operations Research, 46:316–329, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  16. E.M.L. Beale. Branch and bound methods for mathematical programming systems. Annals of Discrete Mathematics, 5:201–219, 1979.MathSciNetzbMATHCrossRefGoogle Scholar
  17. E.M.L. Beale and J.A. Tomlin. Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables. Proceedings of the Fifth International Conference on Operations Research, J. Lawerence, ed., Tavistock Publications, pages 447–454, 1970.Google Scholar
  18. J.E. Beasley and P.C. Chu. A genetic algorithm for the set covering problem. European Journal of Operations Research, 194:392–404, 1996.CrossRefGoogle Scholar
  19. G. Belvaux, N. Boissin, A. Sutter, and L.A. Wolsey. Optimal placement of add/drop multiplexers: static and dynamic models. European Journal of Operational Research, 108(1):26–35, 1998.zbMATHCrossRefGoogle Scholar
  20. J.F. Benders. Partitioning procedures for solving mixed-variable programming problems. Numerische Mathematik, 4:238–252, 1962.MathSciNetzbMATHCrossRefGoogle Scholar
  21. M. Benichou, J.M. Gauthier, P. Girodet, G. Hehntges, G. Ribiere, and O. Vincent. Experiments in mixed integer linear programming. Mathematical Programming, 1: 76–94, 1971.MathSciNetzbMATHCrossRefGoogle Scholar
  22. M. Benichou, J.M. Gauthier, G. Hehntges, and G. Ribiere. The efficient solution of large-scale linear programming problems-some algorithmic techniques and computational results. Mathematical Programming, 13:280–322, 1977.MathSciNetzbMATHCrossRefGoogle Scholar
  23. A. Bianco, M. Guido, and E. Leonardi. Incremental scheduling algorithms for WDM/TDM networks with arbitrary tuning latencies. IEEE Transactions on Communications, 51(3):464–475, 2003.CrossRefGoogle Scholar
  24. D. Bienstock, S. Chopra, O. Günlük, and C.-Y. Tsai. Minimum cost capacity installation for multicommodity network flows. Mathematical Programming, 81(2): 177–199, 1998.MathSciNetCrossRefGoogle Scholar
  25. R.E. Bixby, W. Cook, A. Cox, and E. K. Lee. Parallel mixed integer programming. Technical Report CRPC-TR95554, Center for Research on Parallel Computation, Rice University, Houston, Texas, 1995. Revised paper appeared in Annals of Operations Research, Special Issue on Parallel Optimization, 1997.Google Scholar
  26. R.E. Bixby, W. Cook, A. Cox, and E. K. Lee. Computational experience with parallel mixed integer programming in a distributed environment. Annals of Operations Research, 90:19–43, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  27. R.E. Bixby and E.K. Lee. Solving a truck dispatching scheduling problem using branch-and-cut. Technical Report TR93-37, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, 1993. Companion paper appeared in Operations Research 46 (3) (1998), 355–367.Google Scholar
  28. R.E. Bixby and D.K. Wagner. A note on detecting simple redundancies in linear systems. Operations Research Letters, 6:15–18, 1987.MathSciNetzbMATHCrossRefGoogle Scholar
  29. B. Borchers and J.E. Mitchell. Using an interior point method in a branch and bound algorithm for integer programming. Technical Report 195, Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, March 1991. Revised July 7, 1992.Google Scholar
  30. R. Bordoefer. Aspects of set packing, partitioning, and covering. Technical report, Technischen Universitäte, Berlin, Germany, 1997.Google Scholar
  31. G.H. Bradley, PL. Hammer, and L. Wolsey. Coefficient reduction in 0-1 variables. Mathematical Programming, 7:263–282, 1975.MathSciNetCrossRefGoogle Scholar
  32. A.L. Brearley, G. Mitre, and H. P. Williams. Analysis of mathematical programming problems prior to applying the simplex method. Mathematical Programming, 5: 54–83, 1975.CrossRefGoogle Scholar
  33. R. Breu and C.A. Burdet. Branch and bound experiments in zero-one programming. Mathematical Programming, 2:1–50, 1974.MathSciNetGoogle Scholar
  34. L. Brunetta, M. Conforti, and M. Fischetti. A polyhedral approach to an integer multicommodity flow problem. Discrete Applied Mathematics, 101(1–3): 13–36, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  35. X. Cao, V. Anand, X. Yizhi, and Q. Chunming. A study of waveband switching with multilayer multigranular optical cross-connects. IEEE Journal on Selected Areas in Communications, 21(7): 1081–1095, 2003.CrossRefGoogle Scholar
  36. P. Chardaire, J.L. Lutton, and A. Sutter. Upper and lower bounds for the two-level simple plant location problem. Annals of Operations Research, 86:117–140, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  37. G. Corneujols, M.L. Fisher, and G.L. Nemhauser. Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms. Management Science, 23:789–810, 1977.CrossRefGoogle Scholar
  38. H. Crowder, E.L. Johnson, and M. Padberg. Solving large-scale zero-one linear programming problem. Operations Research, 31:803–834, 1983.zbMATHCrossRefGoogle Scholar
  39. V. Chvátal D. Applegate, R. E. Bixby and W. Cook. On the solution of traveling salesman problems. Documenta Mathematica Journal der Deutschen Mathematiker-Vereinigung ICM III, pages 645–656, 1998.Google Scholar
  40. G. Dahl, A. Martin, and M. Stoer. Routing through virtual paths in layered telecommunication networks. Operations Research, 47(5):693–702, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  41. R.J. Dakin. A tree search algorithm for mixed integer programming problems. Computer Journal, 8:250–255, 1965.MathSciNetzbMATHCrossRefGoogle Scholar
  42. G.B. Dantzig and P. Wolfe. Decomposition principle for linear programs. Operations Research, 8:101–111, 1960.zbMATHCrossRefGoogle Scholar
  43. A. de Silva and D. Abramson. A parallel interior point method and its application to facility location problems. Computational Optimization and Applications, 9:249–273, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  44. J. Desrosiers, F. Soumis, and M. Desrochers. Routing with time windows by column generation. Networks, 14:545–565, 1984.zbMATHCrossRefGoogle Scholar
  45. B. Dietrich and L. Escudero. Coefficient reduction for knapsack-like constraints in 0/1 programs with variable upper bounds. Operations Research Letters, 9:9–14, 1990.MathSciNetzbMATHCrossRefGoogle Scholar
  46. J. Doucette and W.D. Grover. Influence of modularity and economy-of-scale effects on design of mesh-restorable DWDM networks. IEEE Journal on Selected Areas in Communications, 18(10): 1912–1923, 2000.CrossRefGoogle Scholar
  47. N.J. Driebeek. An algorithm for the solution of mixed integer programming problems. Management Science, 21:576–587, 1966.CrossRefGoogle Scholar
  48. A. Dutta. Capacity planning of private networks using DCS under multibusy-hour traffic. IEEE Transactions on Communications, 42(7):2371–2374, 1994.CrossRefGoogle Scholar
  49. G. Cornuéjols E. Balas, S. Ceria. Mixed 0-1 programming by lift-and-project in a branch-and-cut framework. Management Science, 42(9):1229–1246, Sept. 1996.zbMATHCrossRefGoogle Scholar
  50. D. Erlenkotter. A dual-based procedure for uncapacitated facility location. Operations Research, 26:992–1009, 1978.MathSciNetzbMATHCrossRefGoogle Scholar
  51. M. Fenelon. Branching strategies for MIP. CPLEX, 1991.Google Scholar
  52. C. Feremans, M. Labbe, and G. Laporte. The generalized minimum spanning tree problem:polyhedral analysis and branch-and-cut algorithm. Networks, 43(2):71–86, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  53. M.L. Fisher. The Lagrangian relaxation method for solving integer programming problems. Management Science, 27(1):1–18, 1981.MathSciNetzbMATHCrossRefGoogle Scholar
  54. L.R. Ford and D.R. Fulkerson. A suggested computation for maximal multicommodity network flows. Management Science, 5:97–101, 1958.MathSciNetzbMATHCrossRefGoogle Scholar
  55. J.J. Forrest, J.P.H. Hirst, and J.A. Tomlin. Practical solution of large mixed integer programming problems with umpire. Management Science, 20:736–773, 1974.MathSciNetzbMATHCrossRefGoogle Scholar
  56. B. Fortz, M. Labbe, and F. Maffioli. Solving the two-connected network with bounded meshes problem. Operations Research, 48(6):866–877, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  57. L.F Frantzeskaskis and H. Luss. The network redesign problem for access telecommunications networks. Naval Research Logistics, 46(5):487–506, 1999.MathSciNetCrossRefGoogle Scholar
  58. A. Fumagalli, I. Cerutti, and M. Tacca. Optimal design of survivable mesh networks based on line switched WDM self-healing rings. IEEE/ACM Transactions on Networking, 11(3):501–512, 2003.CrossRefGoogle Scholar
  59. V. Gabrel, A. Knippel, and M. Minoux. Exact solution of multicommodity network optimization problems with general step cost functions. Operations Research Letters, 25(1):15–23, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  60. M.R. Garey and D.S. Johnson. Computers and Intractability-A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, Oxford, England, 1979.zbMATHGoogle Scholar
  61. J.M. Gauthier and G. Ribiere. Experiments in mixed integer programming using pseudo-costs. Mathematical Programming, 12:26–47, 1977.MathSciNetzbMATHCrossRefGoogle Scholar
  62. A. Gençata and B. Mukherjee. Virtual-topology adaptation for WDM mesh networks under dynamic traffic. IEEE/ACM Transactions on Networking, 11(2):236–247, 2003.CrossRefGoogle Scholar
  63. A.M. Geoffrion. Lagrangian relaxation and its uses in integer programming. Mathematical Programming, 2:82–114, 1974.Google Scholar
  64. A.M. Geoffrion and R. McBride. Lagrangian relaxation applied to capacitated facility location problems. AIIE Transaction, 10:40–47, 1978.Google Scholar
  65. P.C. Gilmore and R.E. Gomory. A linear programming approach to the cutting-stock problem. Operations Research, 9:849–859, 1961.MathSciNetzbMATHCrossRefGoogle Scholar
  66. P.C. Gilmore and R.E. Gomory. A linear programming approach to the cutting-stock problem-part ii. Operations Research, 11:863–888, 1963.zbMATHCrossRefGoogle Scholar
  67. A.I. Giortzis, L.F. Turner, and J.A. Barria. Decomposition technique for fixed channel assignment problems in mobile radio networks. IEE Proceedings: Communications, 147(3):187–194, 2000.CrossRefGoogle Scholar
  68. J.L. Goffin. On the convergence rates of subgradient optimization methods. Mathematical Programming, 13:329–347, 1977.MathSciNetzbMATHCrossRefGoogle Scholar
  69. D.E. Goldberg. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, 1989.Google Scholar
  70. R.E. Gomory. Outline of an algorithm for integer solution to linear programs. Bulletin American Mathematical Society, 64:275–278, 1958.MathSciNetzbMATHCrossRefGoogle Scholar
  71. L. Gouveia. Multicommodity flow models for spanning trees with hop constraints. European Journal of Operational Research, 95(1): 178–190, 1996.MathSciNetzbMATHCrossRefGoogle Scholar
  72. M. Grötschel, C.L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309–330, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  73. M. Grötschel, C.L. Monma, and M. Stoer. Polyhedral and computational investigations for designing communication networks with high survivability requirements. Operations Research, 43(6): 1012–1024, 1995.MathSciNetzbMATHCrossRefGoogle Scholar
  74. W.D. Grover and J. Doucette. Topological design of survivable mesh-based transport networks. Annals of Operations Research, 106:79–125, 2001.MathSciNetzbMATHCrossRefGoogle Scholar
  75. M. Guignard and K. Spielberg. Logical reduction methods in zero-one programming. Operations Research, 29:49–74, 1981.MathSciNetzbMATHCrossRefGoogle Scholar
  76. J. Hardin, J. Lee, and J. Leung. On the boolean-quadric packing uncapacitated facility-location polytope. Annals of Operations Research, 83:77–94, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  77. M. Held and R.M. Karp. The traveling salesman problem and minimum spanning trees. Operations Research, 18:1138–1162, 1970.MathSciNetzbMATHCrossRefGoogle Scholar
  78. M. Held, P. Wolfe, and H.D. Crowder. Validation of subgradient optimization. Mathematical Programming, 6:61–88, 1974.MathSciNetCrossRefGoogle Scholar
  79. P.-H. Ho, H.T. Mouftah, and J. Wu. A scalable design of multigranularity optical cross-connects for the next-generation optical internet. IEEE Journal on Selected Areas in Communications, 21(7):1133–1142, 2003.CrossRefGoogle Scholar
  80. K.L. Hoffman and M. Padberg. Improving LP-representations of zero-one linear programs for branch-and-cut. ORSA Journal on Computing, 3:121–134, 1991.zbMATHGoogle Scholar
  81. K. Holmberg, M. Rönnqvist, and D. Yuan. An exact algorithm for the capacitated facility location problems with single sourcing. European Journal of Operational Research, 113(3):544–559, 1999.zbMATHCrossRefGoogle Scholar
  82. K. Holmberg and D. Yuan. A Lagrangian approach to network design problems. International Transactions in Operational Research, 5(6):529–539, 1998.CrossRefGoogle Scholar
  83. K. Holmberg and D. Yuan. A Lagrangian heuristic based branch-and-bound approach for the capacitated network design problem. Operations Research, 48(3):461–481, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  84. K. Holmberg and D. Yuan. A multicommodity network-flow problem with side constraints on paths solved by column generation. INFORMS Journal on Computing, 15(1):42–57, 2003.MathSciNetCrossRefGoogle Scholar
  85. K. Holmberg and D. Yuan. Optimization of internet protocol network design and routing. Networks, 43(1):39–53, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  86. J.-Q. Hu. Traffic grooming in wavelength-division-multiplexing ring networks: a linear programming solution. Journal of Optical Networking, 1(11):397–408, 2002.Google Scholar
  87. R.R Iraschko and W.D. Grover. A highly efficient path-restoration protocol for management of optical network transport integrity. IEEE Journal on Selected Areas in Communications, 18(5):779–794, 2000.CrossRefGoogle Scholar
  88. R.R. Iraschko, M.H. MacGregor, and W.D. Grover. Optimal capacity placement for path restoration in STM or ATM mesh-survivable networks. IEEE/ACM Transactions on Networking, 6(3):325–336, 1998.CrossRefGoogle Scholar
  89. B. Jæger and D. Tipper. Prioritized traffic restoration in connection oriented QoS based networks. Computer Communications, 26(18):2025–2036, 2003.CrossRefGoogle Scholar
  90. P. Jaillet, G. Song, and G. Yu. Airline network design and hub location problems. Location Science, 4(3): 195–211, 1996.zbMATHCrossRefGoogle Scholar
  91. E.L. Johnson. Modeling and strong linear programs for mixed integer programming. In S.W. Wallace, editor, Algorithms and Model Formulations in Mathematical Programming, pages 1–41. NATO ASI Series 51, 1989.Google Scholar
  92. J. Kang, K. Park, and S. Park. ATM VP-based network design. European Journal of Operational Research, 158(3):555–569, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  93. R. Kawatra. A multiperiod degree constrained minimal spanning tree problem. European Journal of Operational Research, 143(1):43–53, 2002.MathSciNetCrossRefGoogle Scholar
  94. R. Kawatra and D. Bricker. A multiperiod planning model for the capacitated minimal spanning tree problem. European Journal of Operational Research, 121(2):412–419, 2000.zbMATHCrossRefGoogle Scholar
  95. R. Kawatra and D. Bricker. Design of a degree-constrained minimal spanning tree with unreliable links and node outage costs. European Journal of Operational Research, 156(1):73–82, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  96. H. Kerivin and A.R. Mahjoub. Separation of partition inequalities for the (1,2)-survivable network design problem. Operations Research Letters, 30:265–268, 2002.MathSciNetzbMATHCrossRefGoogle Scholar
  97. H.-J. Kim, S.-H. Chung, and D.-W. Tcha. Optimal design of the two-level distributed network with dual homing local connections. IIE Transactions, 27(5):555–563, 1995.CrossRefGoogle Scholar
  98. G. Raghu Kiran and C. Siva Ram Murthy. QoS based survivable logical topology design in WDM optical networks. Photonic Network Communications, 7(2): 193–206, 2004.CrossRefGoogle Scholar
  99. J.G. Klincewicz. A dual algorithm for the uncapacitated hub location problem. Location Science, 4(3): 173–184, 1996.zbMATHCrossRefGoogle Scholar
  100. A. Kumar, R. Rastogi, A. Silberschatz, and B. Yener. Algorithms for provisioning virtual private networks in the hose model. IEEE/ACM Transactions on Networking, 10(4):565–578, 2002.CrossRefGoogle Scholar
  101. M.S. Kumar and P.S. Kumar. Static lightpath establishment in WDM networks-new ILP formulations and heuristic algorithms. Computer Communications, 25(1):109–114, 2002.CrossRefGoogle Scholar
  102. P. Laborczi and T. Cinkler. IP over WDM configuration with shared protection. Optical Networks Magazine, 3(5):21–33, 2002.Google Scholar
  103. A.H. Land and A.G. Doig. An automatic method for solving discrete programming problems. Econometrica, 28:497–520, 1960.MathSciNetzbMATHCrossRefGoogle Scholar
  104. A.H. Land and S. Powell. Computer codes for problems of integer programming. Annals of Discrete Mathematics, 5:221–269, 1979.MathSciNetzbMATHCrossRefGoogle Scholar
  105. C.-M. Lee, C.-C. R. Hui, F. F.-K. Tong, and P. T.-S. Yum. Network dimensioning in WDM-based all-optical networks. Photonic Network Communications, 2(3):215–225, 2000a.CrossRefGoogle Scholar
  106. E. K. Lee. Generating cutting planes for mixed integer programming problems in a parallel computing environment. INFORMS Journal on Computing, 16(1):3–26, Winter 2004.MathSciNetCrossRefGoogle Scholar
  107. E.K. Lee and J.E. Mitchell. Computational experience in nonlinear mixed integer programming. In The Operations Research Proceedings 1996, pages 95–100. Springer-Verlag, 1996.Google Scholar
  108. E.K. Lee and J.E. Mitchell. Computational experience of an interior-point SQP algorithm in a parallel branch-and-bound framework. In Proceedings of High Performance Optimization Techniques 1997. Springer-Verlag, 1997.Google Scholar
  109. K. Lee, K. Park, S. Park, and H. Lee. Economic spare capacity planning for DCS mesh-restorable networks. European Journal of Operational Research, 110(1):63–75, 1998.zbMATHCrossRefGoogle Scholar
  110. M. Lee, J. Yu, Y. Kim, C.-H. Kang, and J. Park. Design of hierarchical crossconnect WDM networks employing a two-stage multiplexing scheme of waveband and wavelength. IEEE Journal on Selected Areas in Communications, 20(1): 166–171, 2002.CrossRefGoogle Scholar
  111. T. Lee, K. Lee, and S. Park. Optimal routing and wavelength assignment in WDM ring networks. IEEE Journal on Selected Areas in Communications, 18(10):2146–2154, 2000b.MathSciNetCrossRefGoogle Scholar
  112. T. Lee and S. Park. An integer programming approach to the time slot assignment problem in SS/TDMA systems with intersatellite links. European Journal of Operational Research, 135(1):57–66, 2001.zbMATHCrossRefGoogle Scholar
  113. Y. Lee, J. Han, and K. Kang. A fiber routing problem in designing optical transport networks with wavelength division multiplexed systems. Photonic Network Communications, 5(3):247–258, 2003a.CrossRefGoogle Scholar
  114. Y. Lee, S. Kim, S. Lee, and K. Kang. A location-routing problem in designing optical internet access with WDM systems. Photonic Network Communications, 6(2): 151–160, 2003b.zbMATHCrossRefGoogle Scholar
  115. D. Li, Z. Sun, X. Jia, and K. Makki. Traffic grooming on general topology WDM networks. IEE Proceedings-Communications, 150(3):197–201, 2003.CrossRefGoogle Scholar
  116. C.-C. Lo and B.-W. Chuang. A novel approach of backup path reservation for survivable high-speed networks. IEEE Communications Magazine, 41(3): 146–152, 2003.CrossRefGoogle Scholar
  117. C.-C. Lo and A. Kershenbaum. A two-phase algorithm and performance bounds for the star-star concentrator location problem. IEEE Transactions on Communications, 37(11): 1151–1163, 1989.MathSciNetCrossRefGoogle Scholar
  118. Y. Luo and N. Ansari. Restoration with wavelength conversion in WDM networks. Electronics Letters, 38(16):900–901, 2002.CrossRefGoogle Scholar
  119. I. J. Lustig, R. E. Marsten, and D. F. Shanno. Interior point methods for linear programming: Computational state of the art. ORSA Journal on Computing, 6(1): 1–14, 1994.MathSciNetzbMATHGoogle Scholar
  120. M.H. MacGregor, W.D. Grover, and K. Ryhorchuk. Optimal spare capacity preconfiguration for faster restoration of mesh networks. Journal of Network and Systems Management, 5(2):159–171, 1997.CrossRefGoogle Scholar
  121. T.L. Magnanti, P. Mirchandani, and R. Vachani. Modeling and solving the two-facility capacitated network loading problem. Operations Research, 43(1): 142–157, 1995.MathSciNetzbMATHCrossRefGoogle Scholar
  122. R. Mathar and M. Schmeink. Optimal base station positioning and channel assignment for 3G mobile networks by integer programming. Annals of Operations Research, 107:225–236, 2001.MathSciNetzbMATHCrossRefGoogle Scholar
  123. F.F. Mazzini, G.R. Mateus, and J.M. Smith. Lagrangean based methods for solving large-scale cellular networks design problems. Wireless Networks, 9(6):659–672, 2003.CrossRefGoogle Scholar
  124. S. Melkote and M.S. Daskin. Capacitated facility location/network design problems. European Journal of Operational Research, 129(3):481–495, 2001.MathSciNetzbMATHCrossRefGoogle Scholar
  125. G. Mitra. Investigations of some branch and bound strategies for the solution of mixed integer linear programs. Mathematical Programming, 4:155–170, 1973.MathSciNetzbMATHCrossRefGoogle Scholar
  126. Y. Miyao and H. Saito. Optimal design and evaluation of survivable WDM transport networks. IEEE Journal on Selected Areas in Communications, 16(7):1190–1198, 1998.CrossRefGoogle Scholar
  127. R. Montemanni, D.H. Smith, and S.M. Allen. An improved algorithm to determine lower bounds for the fixed spectrum frequency assignment problem. European Journal of Operational Research, 156(3):736–751, 2004.zbMATHCrossRefGoogle Scholar
  128. Y.-S. Myung and H.-J. Kim. A cutting plane algorithm for computing k-edge survivability of a network. European Journal of Operational Research, 156(3):579–589, 2004.MathSciNetzbMATHCrossRefGoogle Scholar
  129. Y.-S. Myung, H.-J. Kim, and D.-W. Tcha. Design of communication networks with survivability constraints. Management Science, 45(2):238–252, 1999.CrossRefGoogle Scholar
  130. A.W. Neebe and M.R. Rao. An algorithm for the fixed charge assignment of users to sources problem. Journal of the Operational Research Society, 34:1107–1115, 1983.zbMATHCrossRefGoogle Scholar
  131. G.L. Nemhauser and L.A. Wolsey. Integer and Combinatorial Optimization. Wiley, New York, 1988.zbMATHGoogle Scholar
  132. D. Orincsay, B. Szviatovszki, and G. Böhm. Prompt partial path optimization in mpls networks. Computer Networks: The International Journal of Computer and Telecommunications Networking, 43(5):557–572, 2003.zbMATHGoogle Scholar
  133. A.E. Ozdaglar and D.P. Bertsekas. Routing and wavelength assignment in optical networks. IEEE/ACM Transactions on Networking, 11(2):259–272, 2003.CrossRefGoogle Scholar
  134. M. Padberg and G. Rinaldi. Optimization of a 537-city tsp by branch-and-cut. OR letters, 6:1–8, 1987.MathSciNetzbMATHGoogle Scholar
  135. M. Padberg and G. Rinaldi. A branch-and-cut approach to a traveling salesman problem with side constraints. Management Science, 35:1393–1412, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  136. M. Padberg and G. Rinaldi. A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Review, 33:60–100, 1991.MathSciNetzbMATHCrossRefGoogle Scholar
  137. K. Park, S. Kang, and S. Park. An integer programming approach to the bandwidth packing problem. Management Science, 42(9):1277–1291, 1996.zbMATHCrossRefGoogle Scholar
  138. R.G. Parker and R.L. Rardin. Discrete Optimization. Academic Press, San Diego, 1988.zbMATHGoogle Scholar
  139. M. Prytz and A. Forsgren. Dimensioning multicast-enabled communications networks. Networks, 39(4):216–231, 2002.MathSciNetzbMATHCrossRefGoogle Scholar
  140. N. Puech, J. Kuri, and M. Gagnaire. Topological design and lightpath routing in WDM mesh networks: a combined approach. Photonic Network Communications, 4(3–4): 443–456, 2002.CrossRefGoogle Scholar
  141. R. Ramaswami and K.N. Sivarajan. Design of logical topologies for wavelength-routed optical networks. IEEE Journal on Selected Areas in Communications, 14(5):840–851, 1996.CrossRefGoogle Scholar
  142. C.D. Randazzo and H.P.L. Luna. A comparison of optimal methods for local access uncapacitated network design. Annals of Operations Research, 106:263–286, 2001.MathSciNetzbMATHCrossRefGoogle Scholar
  143. M. Riis and K.A. Andersen. Capacitated network design with uncertain demand. INFORMS Journal on Computing, 14(3):247–260, 2002.MathSciNetCrossRefGoogle Scholar
  144. M. Riis and J. Lodahl. A bicriteria stochastic programming model for capacity expansion in telecommunications. Mathematical Methods of Operations Research, 56(1): 83–100, 2002.MathSciNetzbMATHCrossRefGoogle Scholar
  145. M.B. Rosenwein and R.T. Wong. A constrained steiner tree problem. European Journal of Operational Research, 81(2):430–439, 1995.zbMATHCrossRefGoogle Scholar
  146. M.W.P. Savelsbergh. Preprocessing and probing for mixed integer programming problems. ORSA Journal on Computing, 6:445–454, 1994.MathSciNetzbMATHGoogle Scholar
  147. A. Schrijver. Theory of Linear and Integer Programming. Wiley, New York, 1986.zbMATHGoogle Scholar
  148. J.F. Shapiro. A survey of Lagrangian techniques for discrete optimization. Annals of Operations Research, 5:113–138, 1979.zbMATHGoogle Scholar
  149. H.D. Sherali, Y. Lee, and T. Park. New modeling approaches for the design of local access transport area networks. European Journal of Operational Research, 127(1): 94–108, 2000.zbMATHCrossRefGoogle Scholar
  150. H.D. Sherali and T. Park. Discrete equal-capacity p-median problem. Naval Research Logistics, 47(2): 166–183, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  151. J.C. Smith. Algorithms for distributing telecommunication traffic on a multiple-ring sonet-based network. European Journal of Operational Research, 154(3):659–672, 2004.zbMATHCrossRefGoogle Scholar
  152. V. Sridhar and J.S. Park. Benders-and-cut algorithm for fixed-charge capacitated network design problem. European Journal of Operational Research, 125(3):622–632, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  153. M. Sridharan, M.V. Salapaka, and A.K. Somani. A practical approach to operating survivable WDM networks. IEEE Journal on Selected Areas in Communications, 20(1):34–46, 2002.CrossRefGoogle Scholar
  154. M. Stoer and G. Dahl. A polyhedral approach to multicommodity survivable network design. Numerische Mathematik, 68(1): 149–167, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  155. C.S. Sung and H.W. Jin. Dual-based approach for a hub network design problem under non-restrictive policy. European Journal of Operational Research, 132(1):88–105, 2001.MathSciNetzbMATHCrossRefGoogle Scholar
  156. A. Sutter, F. Vanderbeck, and L. Wolsey. Optimal placement of add/drop multiplexers: heuristic and exact algorithms. Operations Research, 46(5):719–728, 1998.zbMATHCrossRefGoogle Scholar
  157. J.A. Tomlin. An improved branch and bound method for integer programming. Operations Research, 19:1070–1075, 1971.MathSciNetzbMATHCrossRefGoogle Scholar
  158. F. Tong, T.-S. Yum, and C.-C. Hui. Supervisory management and lightpath restoration for wavelength routing networks. Journal of Lightwave Technology, 18(9):1181–1186, 2000.CrossRefGoogle Scholar
  159. S. Tragantalerngsak, J. Holt, and M. Rönnqvist. An exact method for the two-echelon, single-source, capacitated facility location problem. European Journal of Operational Research, 123(3):473–489, 2000.MathSciNetzbMATHCrossRefGoogle Scholar
  160. S.P.M. van Hoesel, A.M.C.A. Koster, R.L.M.J. van de Leensel, and M.W.P. Savelsbergh. Polyhedral results for the edge capacity polytope. Mathematical Programming, Ser. A 92:335–358, 2002.MathSciNetzbMATHCrossRefGoogle Scholar
  161. B. Van Caenegem, W. Van Parys, F. De Turck, and P.M. Demeester. Dimensioning of survivable WDM networks. IEEE Journal on Selected Areas in Communications, 16(7): 1146–1157, 1998.CrossRefGoogle Scholar
  162. C. Wynants. Network Synthesis Problems. Kluwer Academic Publishers, 2001.Google Scholar
  163. Y. Xiong. Optimal design of restorable ATM mesh networks. IEEE ATM Workshop, Proceedings, pages 394–399, 1998.Google Scholar
  164. S. Yan, J.S. Deogun, and M. Ali. Routing in sparse splitting optical networks with multicast traffic. Computer Networks: The International Journal of Computer and Telecommunications Networking, 41(1):89–113, 2003.zbMATHGoogle Scholar
  165. Y. Zhang, R. Tapia, and J. Dennis Jr. On the superlinear and quadratic convergence of primal-dual interior-point linear programming algorithms. SIAM Journal on Optimization, 2:304–324, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  166. Y. Zheng, W.D. Grover, and M.H. MacGregor. Dependence of network capacity requirements on the allowable flow convergence overloads in ATM backup VP restoration. Electronics Letters, 33(5):362–363, 1997.CrossRefGoogle Scholar
  167. K. Zhu and B. Mukherjee. Traffic grooming in an optical WDM mesh network. IEEE Journal on Selected Areas in Communications, 20(1):122–133, 2002.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Eva K. Lee
    • 1
  • David P. Lewis
    • 1
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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