Abstract
The Connected Facility Location problem combining facility location and Steiner trees has recently gained stronger scientific interest as it can be used to model the extension of last mile communication networks in so-called fiber-to-the-curb scenarios. We consider a generalization of this problem which considers capacity constraints on potential facilities and aims at maximizing the resulting profit by potentially supplying only a subset of all customers. In this work, we discuss two metaheuristic approaches for this problem based on variable neighborhood search and greedy randomized adaptive search. Computational results show that both approaches allow for computing high quality solutions in relatively short time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahuja, R.K., Orlin, J.B., Pallottino, S., Scaparra, M.P., Scutella, M.G.: A multi-exchange heuristic for the single-source capacitated facility location problem. Management Science 50(6), 749–760 (2004)
Ahuja, R.K., Orlin, J.B., Sharma, D.: Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem. Mathematical Programming 91(1), 71–97 (2001)
Bardossy, M.G., Raghavan, S.: Dual-based local search for the connected facility location and related problems. INFORMS Journal on Computing 22(4), 584–602 (2010)
Contreras, I.A., Diaz, J.A.: Scatter search for the single source capacitated facility location problem. Annals of Operations Research 157(1), 73–89 (2008)
Cornuejols, G., Nemhauser, G.L., Wolsey, L.A.: The uncapacitated facility location problem. In: Mirchandani, P.B., Francis, R.L. (eds.) Discrete Location Theory, pp. 119–171. Wiley, Chichester (1990)
Eisenbrand, F., Grandoni, F., Rothvoß, T., Schäfer, G.: Connected facility location via random facility sampling and core detouring. Journal of Computer and System Sciences 76(8), 709–726 (2010)
Feo, T., Resende, M.: Greedy randomized adaptive search procedures. Journal of Global Optimization 6(2), 109–133 (1995)
Gollowitzer, S., Ljubić, I.: MIP models for connected facility location: A theoretical and computational study. Computers & Operations Research 38(2), 435–449 (2011)
Gupta, A., Kleinberg, J., Kumar, A., Rastogi, R., Yener, B.: Provisioning a virtual private network: a network design problem for multicommodity flow. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 389–398 (2001)
Hansen, P., Mladenovic, N.: An introduction to variable neighborhood search. In: Voss, S., Martello, S., Osman, I.H., Roucairol, C. (eds.) Meta-heuristics, Advances and trends in local search paradigms for optimization, pp. 433–458. Kluwer Academic Publishers, Dordrecht (1999)
Hansen, P., Mladenović, N.: Variable neighborhood search: Principles and applications. European Journal of Operational Research 130(3), 449–467 (2001)
Hasan, M.K., Jung, H., Chwa, K.: Approximation algorithms for connected facility location problems. Journal of Combinatorial Optimization 16(2), 155–172 (2008)
Karger, D.R., Minkoff, M.: Building Steiner trees with incomplete global knowledge. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp. 613–623. IEEE Computer Society, Los Alamitos (2000)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Leitner, M., Raidl, G.R.: Variable neighborhood search for a prize collecting capacity constrained connected facility location problem. In: Proceedings of the 2008 International Symposium on Applications and the Internet, pp. 233–236. IEEE Computer Society, Los Alamitos (2008)
Leitner, M., Raidl, G.R.: A Lagrangian decomposition based heuristic for capacitated connected facility location. In: Voß, S., Caserta, M. (eds.) Proceedings of the 8th Metaheuristic International Conference (MIC 2009), Hamburg, Germany (2009)
Leitner, M., Raidl, G.R.: Branch-and-cut-and-price for capacitated connected facility location. Journal of Mathematical Modelling and Algorithms (2011), http://dx.doi.org/10.1007/s10852-011-9153-5
Leitner, M., Raidl, G.R.: Combining Lagrangian decomposition with very large scale neighborhoood search for capacitated connected facility location. In: Post-Conference Book of the Eight Metaheuristics International Conference – MIC (2009) (to appear)
Ljubić, I.: A hybrid VNS for connected facility location. In: Bartz-Beielstein, T., Blesa Aguilera, M.J., Blum, C., Naujoks, B., Roli, A., Rudolph, G., Sampels, M. (eds.) HM 2007. LNCS, vol. 4771, pp. 157–169. Springer, Heidelberg (2007)
Ljubić, I., Gollowitzer, S.: Hop constrained connected facility location. Tech. Rep. 2009–09, University of Vienna (2009)
Ljubić, I., Gollowitzer, S.: Layered graph approaches to the hop constrained connected facility location problem. Tech. Rep. 2010-08, University of Vienna (2010) (submitted)
Ljubić, I., Gollowitzer, S.: Modelling the hop constrained connected facility location problem on layered graphs. In: International Symposium on Combinatorial Optimization (ISCO 2010), Hammamet, Tunisia. Electronic Notes in Discrete Mathematics, vol. 36, pp. 207–214 (2010)
Martello, S., Pisinger, D., Toth, P.: Dynamic programming and strong bounds for the 0–1 knapsack problem. Management Science 45(3), 414–424 (1999)
Raghavan, S., Bardossy, M.G.: Dual based heuristics for the connected facility location problem. In: Scutellà, M.G., et al. (eds.) Proceedings of the International Network Optimization Conference 2009 (2009)
Swamy, C., Kumar, A.: Primal-dual algorithms for connected facility location problems. Algorithmica 40(4), 245–269 (2004)
Thompson, P.M., Orlin, J.B.: The theory of cyclic transfers. Tech. Rep. OR 200-89, Massachusetts Institute of Technology, Operations Research Center (1989)
Tomazic, A., Ljubić, I.: A GRASP algorithm for the connected facility location problem. In: Proceedings of the 2008 International Symposium on Applications and the Internet, pp. 257–260. IEEE Computer Society Press, Los Alamitos (2008)
Voß, S.: Steiner’s problem in graphs: heuristic methods. Discrete Applied Mathematics 40, 45–72 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Leitner, M., Raidl, G.R. (2012). Variable Neighborhood and Greedy Randomized Adaptive Search for Capacitated Connected Facility Location. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27549-4_38
Download citation
DOI: https://doi.org/10.1007/978-3-642-27549-4_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27548-7
Online ISBN: 978-3-642-27549-4
eBook Packages: Computer ScienceComputer Science (R0)