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Handbook of Optimization in Telecommunications pp 67–102Cite as

Integer Programming for Telecommunications

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Abstract

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.

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Bibliography

  • 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.

    Article  Google Scholar 

  • D. Alevras, M. Grötschel, and R. Wessaly. Cost-efficient network synthesis from leased lines. Annals of Operations Research, 76:1–20, 1998b.

    Article  MATH  Google Scholar 

  • A. Amiri. A system for the design of packet-switched communication networks with economic tradeoffs. Computer Communications, 21(18): 1670–1680, 1998.

    Article  Google Scholar 

  • A. Amiri and H. Pirkul. Primary and secondary route selection in backbone communication networks. European Journal of Operational Research, 93(1):98–109, 1996.

    Article  MATH  Google Scholar 

  • 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 

  • 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 

  • 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.

    MATH  Google Scholar 

  • A. Balakrishnan, T.L. Magnanti, and P. Mirchandani. A dual-based algorithm for multi-level network design. Management Science, 40(5):567–581, 1994.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • E. Balas and C.H. Martin. Pivot and complement-a heuristic for 0/1 programming. Management Science, 26:86–96, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • J. Barbas and A. Marin. Maximal covering code multiplexing access telecommunication networks. European Journal of Operational Research, 159(1):219–238, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • E.M.L. Beale. Branch and bound methods for mathematical programming systems. Annals of Discrete Mathematics, 5:201–219, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • J.E. Beasley and P.C. Chu. A genetic algorithm for the set covering problem. European Journal of Operations Research, 194:392–404, 1996.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • J.F. Benders. Partitioning procedures for solving mixed-variable programming problems. Numerische Mathematik, 4:238–252, 1962.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • R.E. Bixby and D.K. Wagner. A note on detecting simple redundancies in linear systems. Operations Research Letters, 6:15–18, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • R. Bordoefer. Aspects of set packing, partitioning, and covering. Technical report, Technischen Universitäte, Berlin, Germany, 1997.

    Google Scholar 

  • G.H. Bradley, PL. Hammer, and L. Wolsey. Coefficient reduction in 0-1 variables. Mathematical Programming, 7:263–282, 1975.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • R. Breu and C.A. Burdet. Branch and bound experiments in zero-one programming. Mathematical Programming, 2:1–50, 1974.

    MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • H. Crowder, E.L. Johnson, and M. Padberg. Solving large-scale zero-one linear programming problem. Operations Research, 31:803–834, 1983.

    Article  MATH  Google Scholar 

  • 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 

  • G. Dahl, A. Martin, and M. Stoer. Routing through virtual paths in layered telecommunication networks. Operations Research, 47(5):693–702, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  • R.J. Dakin. A tree search algorithm for mixed integer programming problems. Computer Journal, 8:250–255, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  • G.B. Dantzig and P. Wolfe. Decomposition principle for linear programs. Operations Research, 8:101–111, 1960.

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • J. Desrosiers, F. Soumis, and M. Desrochers. Routing with time windows by column generation. Networks, 14:545–565, 1984.

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • N.J. Driebeek. An algorithm for the solution of mixed integer programming problems. Management Science, 21:576–587, 1966.

    Article  Google Scholar 

  • A. Dutta. Capacity planning of private networks using DCS under multibusy-hour traffic. IEEE Transactions on Communications, 42(7):2371–2374, 1994.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • D. Erlenkotter. A dual-based procedure for uncapacitated facility location. Operations Research, 26:992–1009, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Fenelon. Branching strategies for MIP. CPLEX, 1991.

    Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • M.L. Fisher. The Lagrangian relaxation method for solving integer programming problems. Management Science, 27(1):1–18, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  • L.R. Ford and D.R. Fulkerson. A suggested computation for maximal multicommodity network flows. Management Science, 5:97–101, 1958.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • B. Fortz, M. Labbe, and F. Maffioli. Solving the two-connected network with bounded meshes problem. Operations Research, 48(6):866–877, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  • L.F Frantzeskaskis and H. Luss. The network redesign problem for access telecommunications networks. Naval Research Logistics, 46(5):487–506, 1999.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • J.M. Gauthier and G. Ribiere. Experiments in mixed integer programming using pseudo-costs. Mathematical Programming, 12:26–47, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • A.M. Geoffrion. Lagrangian relaxation and its uses in integer programming. Mathematical Programming, 2:82–114, 1974.

    Google Scholar 

  • A.M. Geoffrion and R. McBride. Lagrangian relaxation applied to capacitated facility location problems. AIIE Transaction, 10:40–47, 1978.

    Google Scholar 

  • P.C. Gilmore and R.E. Gomory. A linear programming approach to the cutting-stock problem. Operations Research, 9:849–859, 1961.

    Article  MathSciNet  MATH  Google Scholar 

  • P.C. Gilmore and R.E. Gomory. A linear programming approach to the cutting-stock problem-part ii. Operations Research, 11:863–888, 1963.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • J.L. Goffin. On the convergence rates of subgradient optimization methods. Mathematical Programming, 13:329–347, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  • D.E. Goldberg. Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, 1989.

    Google Scholar 

  • R.E. Gomory. Outline of an algorithm for integer solution to linear programs. Bulletin American Mathematical Society, 64:275–278, 1958.

    Article  MathSciNet  MATH  Google Scholar 

  • L. Gouveia. Multicommodity flow models for spanning trees with hop constraints. European Journal of Operational Research, 95(1): 178–190, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • W.D. Grover and J. Doucette. Topological design of survivable mesh-based transport networks. Annals of Operations Research, 106:79–125, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Guignard and K. Spielberg. Logical reduction methods in zero-one programming. Operations Research, 29:49–74, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  • J. Hardin, J. Lee, and J. Leung. On the boolean-quadric packing uncapacitated facility-location polytope. Annals of Operations Research, 83:77–94, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Held and R.M. Karp. The traveling salesman problem and minimum spanning trees. Operations Research, 18:1138–1162, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Held, P. Wolfe, and H.D. Crowder. Validation of subgradient optimization. Mathematical Programming, 6:61–88, 1974.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • K. Holmberg and D. Yuan. A Lagrangian approach to network design problems. International Transactions in Operational Research, 5(6):529–539, 1998.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • K. Holmberg and D. Yuan. Optimization of internet protocol network design and routing. Networks, 43(1):39–53, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • B. Jæger and D. Tipper. Prioritized traffic restoration in connection oriented QoS based networks. Computer Communications, 26(18):2025–2036, 2003.

    Article  Google Scholar 

  • P. Jaillet, G. Song, and G. Yu. Airline network design and hub location problems. Location Science, 4(3): 195–211, 1996.

    Article  MATH  Google Scholar 

  • 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 

  • J. Kang, K. Park, and S. Park. ATM VP-based network design. European Journal of Operational Research, 158(3):555–569, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  • R. Kawatra. A multiperiod degree constrained minimal spanning tree problem. European Journal of Operational Research, 143(1):43–53, 2002.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • J.G. Klincewicz. A dual algorithm for the uncapacitated hub location problem. Location Science, 4(3): 173–184, 1996.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • P. Laborczi and T. Cinkler. IP over WDM configuration with shared protection. Optical Networks Magazine, 3(5):21–33, 2002.

    Google Scholar 

  • A.H. Land and A.G. Doig. An automatic method for solving discrete programming problems. Econometrica, 28:497–520, 1960.

    Article  MathSciNet  MATH  Google Scholar 

  • A.H. Land and S. Powell. Computer codes for problems of integer programming. Annals of Discrete Mathematics, 5:221–269, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • D. Li, Z. Sun, X. Jia, and K. Makki. Traffic grooming on general topology WDM networks. IEE Proceedings-Communications, 150(3):197–201, 2003.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Y. Luo and N. Ansari. Restoration with wavelength conversion in WDM networks. Electronics Letters, 38(16):900–901, 2002.

    Article  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • S. Melkote and M.S. Daskin. Capacitated facility location/network design problems. European Journal of Operational Research, 129(3):481–495, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  • G. Mitra. Investigations of some branch and bound strategies for the solution of mixed integer linear programs. Mathematical Programming, 4:155–170, 1973.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Y.-S. Myung, H.-J. Kim, and D.-W. Tcha. Design of communication networks with survivability constraints. Management Science, 45(2):238–252, 1999.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • G.L. Nemhauser and L.A. Wolsey. Integer and Combinatorial Optimization. Wiley, New York, 1988.

    MATH  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • A.E. Ozdaglar and D.P. Bertsekas. Routing and wavelength assignment in optical networks. IEEE/ACM Transactions on Networking, 11(2):259–272, 2003.

    Article  Google Scholar 

  • M. Padberg and G. Rinaldi. Optimization of a 537-city tsp by branch-and-cut. OR letters, 6:1–8, 1987.

    MathSciNet  MATH  Google Scholar 

  • M. Padberg and G. Rinaldi. A branch-and-cut approach to a traveling salesman problem with side constraints. Management Science, 35:1393–1412, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • K. Park, S. Kang, and S. Park. An integer programming approach to the bandwidth packing problem. Management Science, 42(9):1277–1291, 1996.

    Article  MATH  Google Scholar 

  • R.G. Parker and R.L. Rardin. Discrete Optimization. Academic Press, San Diego, 1988.

    MATH  Google Scholar 

  • M. Prytz and A. Forsgren. Dimensioning multicast-enabled communications networks. Networks, 39(4):216–231, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • M. Riis and K.A. Andersen. Capacitated network design with uncertain demand. INFORMS Journal on Computing, 14(3):247–260, 2002.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • M.B. Rosenwein and R.T. Wong. A constrained steiner tree problem. European Journal of Operational Research, 81(2):430–439, 1995.

    Article  MATH  Google Scholar 

  • M.W.P. Savelsbergh. Preprocessing and probing for mixed integer programming problems. ORSA Journal on Computing, 6:445–454, 1994.

    MathSciNet  MATH  Google Scholar 

  • A. Schrijver. Theory of Linear and Integer Programming. Wiley, New York, 1986.

    MATH  Google Scholar 

  • J.F. Shapiro. A survey of Lagrangian techniques for discrete optimization. Annals of Operations Research, 5:113–138, 1979.

    MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • H.D. Sherali and T. Park. Discrete equal-capacity p-median problem. Naval Research Logistics, 47(2): 166–183, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • M. Stoer and G. Dahl. A polyhedral approach to multicommodity survivable network design. Numerische Mathematik, 68(1): 149–167, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • A. Sutter, F. Vanderbeck, and L. Wolsey. Optimal placement of add/drop multiplexers: heuristic and exact algorithms. Operations Research, 46(5):719–728, 1998.

    Article  MATH  Google Scholar 

  • J.A. Tomlin. An improved branch and bound method for integer programming. Operations Research, 19:1070–1075, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • C. Wynants. Network Synthesis Problems. Kluwer Academic Publishers, 2001.

    Google Scholar 

  • Y. Xiong. Optimal design of restorable ATM mesh networks. IEEE ATM Workshop, Proceedings, pages 394–399, 1998.

    Google Scholar 

  • 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.

    MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Eva K. Lee & David P. Lewis

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  1. Eva K. Lee
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  1. AT&T Labs Research, Florham Park, New Jersey

    Mauricio G. C. Resende

  2. University of Florida, Gainesville, Florida

    Panos M. Pardalos

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Lee, E.K., Lewis, D.P. (2006). Integer Programming for Telecommunications. In: Resende, M.G.C., Pardalos, P.M. (eds) Handbook of Optimization in Telecommunications. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30165-5_3

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