Journal of Heuristics

, 15:259 | Cite as

Algorithms for the non-bifurcated network design problem

  • Enrico BartoliniEmail author
  • Aristide Mingozzi


In this paper we consider the non-bifurcated network design problem where a given set of cities must be connected by installing on a given set of links integer multiples of some base capacity so that a set of commodity demands can be routed. Each commodity flow is constrained to run through a single path along the network. The objective is to minimize the sum of capacity installation and routing costs. We present an exact algorithm and four new heuristics. The first heuristic generates an initial feasible solution, then it improves it until a necessary condition for optimality is satisfied. Two heuristics are partial enumeration methods and the last one iteratively applies a tabu search method to different initial feasible solutions. Computational results over a set of test problems from the literature show the effectiveness of the proposed algorithms.


Network design Integer programming Heuristic algorithms Partial enumeration 


  1. Agarwal, K.: Design of capacitated multicommodity networks with multiple facilities. Oper. Res. 50, 333–344 (2002) CrossRefMathSciNetzbMATHGoogle Scholar
  2. Atamtürk, A., Rajan, D.: On splittable and unsplittable flow capacitated network design arc-set polyhedra. Math. Program. 92, 315–333 (2002) zbMATHCrossRefMathSciNetGoogle Scholar
  3. Barahona, F.: Network design using cut inequalities. SIAM J. Optim. 6, 823–837 (1996) zbMATHCrossRefMathSciNetGoogle Scholar
  4. Barahona, F.: On the k-cut problem. Oper. Res. Lett. 26, 99–105 (2000) zbMATHCrossRefMathSciNetGoogle Scholar
  5. Barnhart, C., Hane, C.A., Vance, P.H.: Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Oper. Res. 48, 318–326 (2000) CrossRefGoogle Scholar
  6. Bienstock, D., Günlük, O.: Capacitated network design—polyhedral structure and computation. ORSA J. Comput. 8, 243–260 (1996) zbMATHGoogle Scholar
  7. Bienstock, D., Chopra, S., Günlük, O., Tsai, C.-Y.: Minimum cost capacity installation for multicommodity network flows. Math. Program. 81, 177–199 (1998) Google Scholar
  8. Brockmüller, B., Günlük, O., Wolsey, L.A.: Designing private line networks—Polyhedral analysis and computation. Discussion Paper 9647, Center for Operations Research and Econometrics, October 1996 Google Scholar
  9. Brockmüller, B., Günlük, O., Wolsey, L.A.: Designing private line networks—Polyhedral analysis and computation. Discussion Paper 9647 revised, Center for Operations Research and Econometrics, March 1998 Google Scholar
  10. CPLEX: ILOG CPLEX 10.1 callable library. ILOG (2007) Google Scholar
  11. Crainic, T.G., Gendreau, M., Farvolden, J.M.: A simplex-based tabu search method for capacitated network design. INFORMS J. Comput. 12, 223–236 (2000) zbMATHCrossRefMathSciNetGoogle Scholar
  12. Dongarra, J.J.: Performance of various computers using standard linear equations software. Technical Report CS-89-85, Computer Science Department, University of Tennessee, Knoxville, TN (2007) Google Scholar
  13. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979) zbMATHGoogle Scholar
  14. Gavish, B., Altinkemer, K.: Backbone network design tools with economic tradeoffs. ORSA J. Comput. 2, 236–252 (1990) zbMATHGoogle Scholar
  15. Ghamlouche, I., Crainic, T.G., Gendreau, M.: Cycle-based neighbourhoods for fixed-charge capacitated multicommodity network design. Oper. Res. 51, 655–667 (2003) CrossRefMathSciNetzbMATHGoogle Scholar
  16. Ghamlouche, I., Crainic, T.G., Gendreau, M.: Path relinking, cycle-based neighbourhoods and capacitated multicommodity network design. Ann. Oper. Res. 131, 109–133 (2004) zbMATHCrossRefMathSciNetGoogle Scholar
  17. Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Boston (1997) zbMATHGoogle Scholar
  18. Höller, H., Voß, S.: A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks. Eur. J. Oper. Res. 171, 787–796 (2006) zbMATHCrossRefGoogle Scholar
  19. Höller, H., Melian, B., Voß, S.: Applying the pilot method to improve VNS and GRASP metaheuristics for the design of SDH/WDM networks. Eur. J. Oper. Res. 191, 691–704 (2008) zbMATHCrossRefGoogle Scholar
  20. Holmberg, K., Yuan, D.: A Lagrangean heuristic based branch-and-bound approach for the capacitated network design problem. Oper. Res. 48, 461–481 (2000) zbMATHCrossRefMathSciNetGoogle Scholar
  21. Kousik, I., Ghosh, D., Murthy, I.: A heuristic procedure for leasing channels in telecommunications networks. J. Oper. Res. Soc. 44, 659–672 (1993) zbMATHCrossRefGoogle Scholar
  22. Magnanti, T.L., Wong, R.T.: Network design and transportation planning: Models and algorithms. Transp. Sci. 18, 1–55 (1986) CrossRefGoogle Scholar
  23. Magnanti, T.L., Mirchandani, P., Vachani, R.: The convex hull of two core capacitated network design problems. Math. Program. 60, 233–250 (1993) CrossRefMathSciNetGoogle Scholar
  24. Magnanti, T.L., Mirchandani, P., Vachani, R.: Modeling and solving the two-facility capacitated network loading problem. Oper. Res. 43, 142–157 (1995) zbMATHCrossRefMathSciNetGoogle Scholar
  25. Minoux, M.: Network synthesis and optimum network design problems: Models, solution methods and applications. Networks 19, 313–360 (1989) zbMATHCrossRefMathSciNetGoogle Scholar
  26. van Hoesel, S.P.M., Koster, A.M.C.A., de Leensel, R.L.M.J., Savelsbergh, M.W.P.: Polyhedral results for the edge capacity polytope. Math. Program. 92, 335–358 (2002) zbMATHCrossRefMathSciNetGoogle Scholar
  27. van Hoesel, S.P.M., Koster, A.M.C.A., de Leensel, R.L.M.J., Savelsbergh, M.W.P.: Bidirected and unidirected capacity installation in telecommunication networks. Discrete Appl. Math. 133, 103–121 (2004) Google Scholar
  28. Wolsey, L.A.: Integer Programming. Wiley, New York (1998) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BolognaBolognaItaly
  2. 2.Department of MathematicsUniversity of BolognaBolognaItaly

Personalised recommendations