Skip to main content

Hybrid ant colony optimization for capacitated multiple-allocation cluster hub location problem

  • Mohammad Mirabi (a1) and Parya Seddighi (a2)

The hub location problems involve locating facilities and designing hub networks to minimize the total cost of transportation (as a function of distance) between hubs, establishing facilities and demand management. In this paper, we consider the capacitated cluster hub location problem because of its wide range of applications in real-world cases, especially in transportation and telecommunication networks. In this regard, a mathematical model is presented to address this problem under capacity constraints imposed on hubs and transportation lines. Then, a new hybrid algorithm based on simulated annealing and ant colony optimization is proposed to solve the presented problem. Finally, the computational experiments demonstrate that the proposed heuristic algorithm is both effective and efficient.

Corresponding author
Reprint requests to: Mohammad Mirabi, Industrial Engineering Group, Department of Engineering, Ayatollah Haeri University of Meybod, Meybod, Iran. E-mail:
Hide All
Abdinnour-Helm, S. (1998). A hybrid heuristic for the un-capacitated hub location problem. European Journal of Operational Research 106(2–3), 489499.
Abdinnour-Helm, S., & Venkataramanan, M.A. (1998). Solution approaches to hub location problems. Annals of Operations Research 78, 3150.
Alumur, S., & Kara, B.Y. (2008). Network hub location problems: the state of the art. European Journal of Operational Research 190, 121.
Bailey, A., Ornbuki-Berrnan, B., & Asobiela, S. (2013). Discrete PSO for the uncapacitated single allocation hub location problem. Proc IEEE Workshop on Computational Intelligence in Production and Logistics Systems, CIPLS, pp. 9298, Singapore, April 16–19.
Blum, C. (2005). Ant colony optimization: introduction and recent trends. Physics of Life Reviews 2, 353373.
Calık, H., Alumur, S.A., Kara, B.Y., & Karasan, O.E. (2009). A tabu-search based heuristic for the hub covering problem over incomplete hub networks. Computers and Operations Research 36(12), 30883096.
Campbell, J.F. (1992). Location and allocation for distribution systems with transshipments and transportation economies of scale. Annals of Operations Research 40, 7799.
Campbell, J.F., Ernst, A.T., & Krishnamoorthy, M. (2002). Hub location problems. In Facility Location: Applications and Theory (Drezner, Z., & Hamacher, H.W., Eds.), pp. 373408. New York: Springer.
Chen, J.F. (2007). A hybrid heuristic for the un-capacitated single allocation hub location problem. Omega 35, 211220.
Chen, J.F. (2013). Heuristics for hub location problems with alternative capacity levels and allocation constraints. In Intelligent Computing Theories (Huang, D.-S., Bevilacqua, V., Figueroa, J.C., & Premaratne, P., Eds.), LNCS Vol. 7995, pp. 207216. Berlin: Springer.
Contreras, I., Cordeau, J.-F., & Laporte, G. (2012). Exact solution of large-scale hub location problems with multiple capacity levels. Transportation Science 46(4), 439459.
Contreras, I., Díaz, J.A., & Fernández, E. (2011). Branch and price for large-scale capacitated hub location problems with single assignment. INFORMS Journal on Computing 23(1), 4155.
Correia, I., Nickel, S., & Saldanha-da-Gama, F. (2010). The capacitated single-allocation hub location problem revisited: a note on a classical formulation. European Journal of Operational Research 207(1), 9296.
Correia, I., Nickel, S., & Saldanha-da-Gama, F. (2014). Multi-product capacitated single-allocation hub location problems: Formulations and inequalities. Networks and Spatial Economics 14(1), 125.
Cunha, C.B., & Silva, M.R. (2007). A genetic algorithm for the problem of configuring a hub-and-spoke network for a LTL trucking company in Brazil. European Journal of Operational Research 179, 747758.
Damgacioglu, H., Dinler, D., Ozdemirel, N.E., & Iyigun, C. (2015). A genetic algorithm for the uncapacitated single allocation planar hub location problem. Computers & Operations Research 62, 224236.
Dorigo, M., Di Caro, G., & Gambardella, L.M. (1999). Ant algorithms for discrete optimization. Artificial Life 5(2), 137172.
Dorigo, M., & Gambardella, L.M. (1997). Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 5366.
Dorigo, M., & Stützle, T. (2004). Ant Colony Optimization. Cambridge, MA: MIT Press.
Ernst, A.T., & Krishnamoorthy, M. (1998). Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem. European Journal of Operational Research 104, 100112.
Ernst, A.T., & Krishnamoorthy, M. (1999). Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research 86, 141159.
Farahani, R.Z., Hekmatfar, M., Arabani, A.B., & Nikbakhsh, E. (2013). Hub location problems: a review of models, classification, solution techniques, and applications. Computers & Industrial Engineering 64(4), 10961109.
Gelareh, S. (2008). Hub location models in public transport planning . PhD Thesis. University of Kaiserslautern.
Geramianfar, R., Pakzad, M., Golhashem, H., & Moghaddam, R. (2013). A multi-objective hub covering location problem under congestion using simulated annealing algorithm. Uncertain Supply Chain Management 1(3), 153164.
Goldman, A.J. (1969). Optimal location for centers in a network. Transportation Science 3, 352360.
Granville, V., Krivánek, M., & Rasson, J.P. (1994). Simulated annealing: a proof of convergence. IEEE Transactions on Pattern Analysis and Machine Intelligence 16(6), 652656.
He, Y., Wu, T., Zhang, C., & Liang, Z. (2015). An improved MIP heuristic for the intermodal hub location problem. Omega 57, 203211.
Henderson, D., Jacobson, S.H., & Johnson, A.W. (2003). The theory and practice of simulated annealing. In Handbook of Metaheuristics (Glover, F., & Kochenberger, G.A., Eds.), pp. 287319. Dordrecht: Kluwer Academic.
Holland, J.H. (1992). Adaptation in Natural and Artificial Systems. Cambridge, MA: MIT Press.
Jabalameli, M.S., Barzinpour, F., Saboury, A., & Ghaffari-Nasab, N. (2012). A simulated annealing-based heuristic for the single allocation maximal covering hub location problem. International Journal of Metaheuristics 2(1), 1537.
Kara, B.Y. (1999). Modeling and analysis of issues in hub location problems. PhD thesis. Bilkent University.
Kirkpatrick, S., Gelatt, C.D., & Vecchi, M.P. (1983). Optimization by simulated annealing. Science 220(4598), 671680.
Klincewicz, J.G. (1992). Avoiding local optima in the p-hub location problem using tabu search and grasp. Annals of Operations Research 40, 283302.
Ma, K., & Thing, C. (2008). An ant colony optimization algorithm for solving the un-capacitated multiple allocation p-hub median. Proc. 9th Asia Pasific Industrial Engineering & Management Systems Conf., pp. 6171, Bali, Indonesia, December 3–5.
Marić, M., Stanimirović, Z., & Stanojević, P. (2013). An efficient memetic algorithm for the uncapacitated single allocation hub location problem. Soft Computing 17(3), 445466.
Marin, A. (2005). Formulating and solving splittable capacitated multiple allocation hub location problems. Computers & Operations Research 32, 30933109.
Naeem, M., & Ombuki-Berman, B. (2010). An efficient genetic algorithm for the uncapacitated single allocation hub location problem. Proc. IEEE Congr. Evolutionary Computation, CEC, pp. 18, Barcelona, July 18–23.
O'Kelly, M.E. (1986a). The location of interacting hub facilities. Transportation Science 20(2), 92105.
O'Kelly, M.E. (1986b). Activity levels at hub facilities in interacting networks. Geographical Analysis 18(4), 343356.
O'Kelly, M.E. (1987). A quadratic integer program for the location of interacting hub facilities. European Journal of Operational Research 32, 393404.
Parvaresh, F., Hashemi Golpayegany, S.A., Moattar Husseini, S.M., & Karimi, B. (2013). Solving the p-hub median problem under intentional disruptions using simulated annealing. Networks and Spatial Economics 13(4), 445470.
Puerto, J., Ramos, A.B., & Rodríguez-Chía, A.M. (2013). A specialized branch & bound & cut for single-allocation ordered median hub location problems. Discrete Applied Mathematics 161(16–17), 26242646.
Randall, M. (2008). Solution approaches for the capacitated single allocation hub location problem using ant colony optimization. Computational Optimization and Applications 39, 239261.
Rasoulinejad, Z., Bashiri, M., & Mehrbanfar, M. (2013). A clustering based simulated annealing approach for solving an un-capacitated single allocation p-hub location problem. Proc. 5th Int. Conf. Modeling, Simulation and Applied Optimization, ICMSAO, pp. 16, Hammamet, Tunisia, April 28–30.
Reeves, C. (2003). Genetic algorithms. In Handbook of Metaheuristics (Glover, F., & Kochenberger, G.A., Eds.), pp. 5582. Dordrecht: Kluwer Academic.
Saboury, A., Ghaffari-Nasab, N., Barzinpour, F., & Jabalameli, M.S. (2013). Applying two efficient hybrid heuristics for hub location problem with fully interconnected backbone and access networks. Computers & Operations Research 40(10), 24932507.
Sender, J., & Clausen, U. (2013). Heuristics for solving a capacitated multiple allocation hub location problem with application in German wagonload traffic. Electronic Notes in Discrete Mathematics 41, 1320.
Skorin-Kapov, D., & Skorin-Kapov, J. (1994). On tabu search for the location of interacting hub facilities. European Journal of Operational Research 73, 502509.
Stanimirovic, Z. (2010). A genetic algorithm approach for the capacitated single allocation p-hub median problem. Computing and Informatics 29, 117132.
Sun, J. (2011). An ant colony optimization algorithm for the capacitated hub location problem. Proc. 2011 New Orleans Int. Academic Conf., pp. 721732, New Orleans, March 14–16.
Sung, C.S., & Jin, H.W. (2001). Dual-based approach for a hub network design problem under non-restrictive policy. European Journal of Operational Research 132, 88105.
Topcuoglu, H., Corut, F., Ermis, M., & Yilmaz, G. (2005). Solving the un-capacitated hub location problem using genetic algorithms. Computers & Operations Research 32(4), 967984.
Wagner, B. (2007). An exact solution procedure for a cluster hub location problem. European Journal of Operational Research 178, 391401.
Xu, L., Hu, D., Xuan, D., & Lin, H. (2009). A tabu search algorithm to logistics network design for multiple hub location routing problem. In Logistics: The Emerging Frontiers of Transportation and Development in China (Liu, R., Zhang, J., & Guan, C., Eds.), pp. 889896. New York: American Society of Civil Engineers.
Yaman, H. (2005). Polyhedral analysis for the uncapacitated hub location problem with modular arc capacities. SIAM Journal on Discrete Mathematics 19(2), 501522.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0890-0604
  • EISSN: 1469-1760
  • URL: /core/journals/ai-edam
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 1
Total number of PDF views: 26 *
Loading metrics...

Abstract views

Total abstract views: 249 *
Loading metrics...

* Views captured on Cambridge Core between 14th August 2017 - 19th March 2018. This data will be updated every 24 hours.