Abstract
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.
Similar content being viewed by others
References
Agarwal, K.: Design of capacitated multicommodity networks with multiple facilities. Oper. Res. 50, 333–344 (2002)
Atamtürk, A., Rajan, D.: On splittable and unsplittable flow capacitated network design arc-set polyhedra. Math. Program. 92, 315–333 (2002)
Barahona, F.: Network design using cut inequalities. SIAM J. Optim. 6, 823–837 (1996)
Barahona, F.: On the k-cut problem. Oper. Res. Lett. 26, 99–105 (2000)
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)
Bienstock, D., Günlük, O.: Capacitated network design—polyhedral structure and computation. ORSA J. Comput. 8, 243–260 (1996)
Bienstock, D., Chopra, S., Günlük, O., Tsai, C.-Y.: Minimum cost capacity installation for multicommodity network flows. Math. Program. 81, 177–199 (1998)
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
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
CPLEX: ILOG CPLEX 10.1 callable library. ILOG (2007)
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)
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)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Gavish, B., Altinkemer, K.: Backbone network design tools with economic tradeoffs. ORSA J. Comput. 2, 236–252 (1990)
Ghamlouche, I., Crainic, T.G., Gendreau, M.: Cycle-based neighbourhoods for fixed-charge capacitated multicommodity network design. Oper. Res. 51, 655–667 (2003)
Ghamlouche, I., Crainic, T.G., Gendreau, M.: Path relinking, cycle-based neighbourhoods and capacitated multicommodity network design. Ann. Oper. Res. 131, 109–133 (2004)
Glover, F., Laguna, M.: Tabu Search. Kluwer Academic, Boston (1997)
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)
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)
Holmberg, K., Yuan, D.: A Lagrangean heuristic based branch-and-bound approach for the capacitated network design problem. Oper. Res. 48, 461–481 (2000)
Kousik, I., Ghosh, D., Murthy, I.: A heuristic procedure for leasing channels in telecommunications networks. J. Oper. Res. Soc. 44, 659–672 (1993)
Magnanti, T.L., Wong, R.T.: Network design and transportation planning: Models and algorithms. Transp. Sci. 18, 1–55 (1986)
Magnanti, T.L., Mirchandani, P., Vachani, R.: The convex hull of two core capacitated network design problems. Math. Program. 60, 233–250 (1993)
Magnanti, T.L., Mirchandani, P., Vachani, R.: Modeling and solving the two-facility capacitated network loading problem. Oper. Res. 43, 142–157 (1995)
Minoux, M.: Network synthesis and optimum network design problems: Models, solution methods and applications. Networks 19, 313–360 (1989)
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)
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)
Wolsey, L.A.: Integer Programming. Wiley, New York (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bartolini, E., Mingozzi, A. Algorithms for the non-bifurcated network design problem. J Heuristics 15, 259–281 (2009). https://doi.org/10.1007/s10732-008-9091-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-008-9091-1