Abstract
In this paper, we address the Single Source Capacitated Facility Location Problem (SSCFLP) which considers a set of possible locations for opening facilities and a set of clients whose demand must be satisfied. The objective is to minimize the cost of assigning the clients to the facilities, ensuring that all clients are served by only one facility without exceeding the capacity of the facilities. We propose a Relaxation Adaptive Memory Programming (RAMP) heuristic for solving the SSCFLP to efficiently explore the relation between the primal and the dual sides of this combinatorial optimisation problem. Computational experiments demonstrated that the proposed heuristic is very effective in terms of solution quality with reasonable computing times.
Similar content being viewed by others
References
Farahani, R., Hekmatfar, M.: Facility location: concepts, models, algorithms and case studies. Physica-Verlag. (2009). https://doi.org/10.1007/978-3-7908-2151-2
Rego, C.: RAMP: a new metaheuristic framework for combinatorial optimization. In: Rego, C., Alidaee, B. (eds.) Metaheuristic Optimization Via Memory and Evolution, pp. 441–460. Kluwer Academic Publishers (2005). https://doi.org/10.1007/0-387-23667-8_20
Riley, C., Rego, C., Li, H.: A simple dual-RAMP algorithm for resource constraint project scheduling. In: Proceedings of the 48th Annual Southeast Regional Conference on - ACM SE ‘10. p. 1. ACM Press, New York, New York, USA (2010). https://doi.org/10.1145/1900008.1900097
Gamboa, D.: Adaptive Memory Algorithms for the Solution of Large Scale Combinatorial Optimization Problems, PhD Thesis (in Portuguese), Instituto Superior Técnico, Universidade Técnica de Lisboa, (2008)
Rego, C., Mathew, F., Glover, F.: RAMP for the capacitated minimum spanning tree problem. Ann. Oper. Res. 181, 661–681 (2010). https://doi.org/10.1007/s10479-010-0800-4
Matos, T., Gamboa, D.: Dual-RAMP for the Capacitated Single Allocation Hub Location Problem. In: Gervasi, O., Murgante, B., Misra, S., Borruso, G., Torre, C.M., Rocha, A.M.A.C., Taniar, D., Apduhan, B.O., Stankova, E., and Cuzzocrea, A. (eds.) Computational Science and Its Applications -- ICCSA 2017: 17th International Conference, Trieste, Italy, July 3–6, 2017, Proceedings, Part II. pp. 696–708. Springer International Publishing (2017). https://doi.org/10.1007/978-3-319-62395-5_48
Matos, T., Maia, F., Gamboa, D.: Improving Traditional Dual Ascent Algorithm for the Uncapacitated Multiple Allocation Hub Location Problem: A RAMP Approach. In: The Fourth International Conference on Machine Learning, Optimization, and Data Science – September 13–16, 2018 – Volterra, Tuscany, Italy. pp. 243–253. Springer, Italy (2019). https://doi.org/10.1007/978-3-030-13709-0_20
Glover, F.: Tabu Search—Part I. ORSA J. Comput. 1, 190–206 (1989). https://doi.org/10.1287/ijoc.1.3.190
Glover, F.: Tabu Search—Part II. Tabu Search—Part II. ORSA J. Comput. 2, 4–32 (1990). https://doi.org/10.1287/ijoc.2.1.4
Oliveira, Ó., Matos, T., Gamboa, D.: A RAMP Algorithm for Large-Scale Single Source Capacitated Facility Location Problems. In: Matsatsinis, N.F., Marinakis, Y., and Pardalos, P. (eds.) Learning and Intelligent Optimization. LION 2019. pp. 171–183 (2020). https://doi.org/10.1007/978-3-030-38629-0_14
Garey, M.R., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco (1979). https://doi.org/10.2307/2273574, Michael R. ΠGarey and David S. Johnson. Computers and intractability. A guide to the theory of NP-completeness. W. H. Freeman and Company, San Francisco1979, x + 338 pp
Neebe, A.W., Rao, M.R.: An algorithm for the fixed-charge assigning users to sources problem. J. Oper. Res. Soc. 34, 1107–1113 (1983). https://doi.org/10.1057/jors.1983.242
Barceló, J., Casanovas, J.: A heuristic Lagrangean algorithm for the capacitated plant location problem. Eur. J. Oper. Res. 15, 212–226 (1984)
Klincewicz, J.G., Luss, H.: A Lagrangian relaxation heuristic for capacitated facility location with single-source constraints. J. Oper. Res. Soc. 37, 495–500 (1986). https://doi.org/10.1057/jors.1986.84
Erlenkotter, D.: A dual-based procedure for Uncapacitated facility location. Oper. Res. 26, 992–1009 (1978). https://doi.org/10.1287/opre.26.6.992
Sridharan, R.: A Lagrangian heuristic for the capacitated plant location problem with side constraints. J. Oper. Res. Soc. 66, 579–585 (1991). https://doi.org/10.1057/jors.1991.117
Pirkul, H.: Efficient algorithms for the capacitated concentrator location problem. Comput. Oper. Res. 14, 197–208 (1987). https://doi.org/10.1016/0305-0548(87)90022-0
Beasley, J.E.: Lagrangean heuristics for location problems. Eur. J. Oper. Res. 65, 383–399 (1993). https://doi.org/10.1016/0377-2217(93)90118-7
Delmaire, H., Díaz, J.A., Fernández, E., Ortega, M.: Comparing new heuristics for the pure integer capacitated plant location problem. Investig. Oper. 8, 217–242 (1997)
Delmaire, H., Díaz, J.A., Fernández, E., Ortega, M.: Reactive Grasp and Tabu search based heuristics for the single source capacitated plant location problem. INFOR Inf. Syst. Oper. Res. 37, 194–225 (1999). https://doi.org/10.1080/03155986.1999.11732381
Rönnqvist, M., Tragantalerngsak, S., Holt, J.: A repeated matching heuristic for the single-source capacitated facility location problem. Eur. J. Oper. Res. 116, 51–68 (1999). https://doi.org/10.1016/S0377-2217(98)00045-9
Holmberg, K., Rönnqvist, M., Yuan, D.: An exact algorithm for the capacitated facility location problems with single sourcing. Eur. J. Oper. Res. 113, 544–559 (1999). https://doi.org/10.1016/S0377-2217(98)00008-3
Hindi, K.S., Pieńkosz, K.: Efficient solution of large scale, single-source, capacitated plant location problems. J. Oper. Res. Soc. 50, 268–274 (1999). https://doi.org/10.1057/palgrave.jors.2600698
Ahuja, R.K., Orlin, J.B., Pallottino, S., Scaparra, M.P., Scutellà, M.G.: A multi-exchange heuristic for the single-source capacitated facility location problem. Manag. Sci. 50, 749–760 (2004). https://doi.org/10.1287/mnsc.1030.0193
Cortinhal, M.J., Captivo, M.E.: Upper and lower bounds for the single source capacitated location problem. Eur. J. Oper. Res. 151, 333–351 (2003). https://doi.org/10.1016/S0377-2217(02)00829-9
Contreras, I.A., Díaz, J.A.: Scatter search for the single source capacitated facility location problem. Ann. Oper. Res. 157, 73–89 (2007). https://doi.org/10.1007/s10479-007-0193-1
Laguna, M., Martí, R., Marti, R.: Scatter search. Oper. Res. Comput. Sci. Interfaces Ser. 24, 1–283 (2003). https://doi.org/10.1007/978-1-4615-0337-8
Kumweang, K., Kawtummachai, R.: Solving a SSCFLP in a supply chain with ACO. Suranaree J. Sci. 12, 28–38 (2005)
Chen, C.-H., Ting, C.-J.: Combining Lagrangian heuristic and ant Colony system to solve the single source capacitated facility location problem. Transp. Res. Part E Logist. Transp. Rev. 44, 1099–1122 (2008). https://doi.org/10.1007/11839088_55
Lina, Y., Xu, S., Tianhe, C.: A Hybrid Ant Colony Optimization Algorithm with Local Search Strategies to Solve Single Source Capacitated Facility Location Problem. In: 2012 International Conference on Industrial Control and Electronics Engineering. pp. 83–85. IEEE (2012). https://doi.org/10.1109/ICICEE.2012.30
Yang, Z., Chu, F., Chen, H.: A cut-and-solve based algorithm for the single-source capacitated facility location problem. Eur. J. Oper. Res. 221, 521–532 (2012). https://doi.org/10.1016/j.ejor.2012.03.047
Climer, S., Zhang, W.: Cut-and-solve: an iterative search strategy for combinatorial optimization problems. Artif. Intell. 170, 714–738 (2006). https://doi.org/10.1016/j.artint.2006.02.005
Ho, S.C.: An iterated tabu search heuristic for the single source capacitated facility location problem. Appl. Soft Comput. 27, 169–178 (2015). https://doi.org/10.1016/j.asoc.2014.11.004
Guastaroba, G., Speranza, M.G.: A heuristic for BILP problems: the single source capacitated facility location problem. Eur. J. Oper. Res. 238, 438–450 (2014). https://doi.org/10.1016/j.ejor.2014.04.007
Tran, T.H., Scaparra, M.P., O’Hanley, J.R.: A hypergraph multi-exchange heuristic for the single-source capacitated facility location problem. Eur. J. Oper. Res. 263, 173–187 (2017). https://doi.org/10.1016/j.ejor.2017.04.032
Martello, S., Pisinger, D., Toth, P.: Dynamic programming and strong bounds for the 0-1 knapsack problem. Manag. Sci. 45, 414–425 (1999). https://doi.org/10.1287/mnsc.45.3.414
Avella, P., Boccia, M.: A cutting plane algorithm for the capacitated facility location problem. Comput. Optim. Appl. 43, 39–65 (2009). https://doi.org/10.1007/s10589-007-9125-x
Acknowledgements
This work has been supported by national funds through FCT – Fundação para a Ciência e Tecnologia through project UIDB/04728/2020.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Oliveira, Ó., Matos, T. & Gamboa, D. A dual RAMP algorithm for single source capacitated facility location problems. Ann Math Artif Intell 89, 815–834 (2021). https://doi.org/10.1007/s10472-021-09756-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10472-021-09756-0