Skip to main content
SpringerLink
Log in

RAMP algorithms for the capacitated facility location problem

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

In this paper, we address the Capacitated Facility Location Problem (CFLP) in which the assignment of facilities to customers must ensure enough facility capacity and all the customers must be served. We propose both sequential and parallel Relaxation Adaptive Memory Programming approaches for the CFLP, combining a Lagrangean subgradient search with an improvement method to explore primal-dual relationships to create advanced memory structures that integrate information from both primal and dual solution spaces. Computational experiments of the effectiveness of this approach are presented and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lewis, H.R., ΠGarey, M.R., Johnson, D.S.: Computers and intractability. A guide to the theory of NP-completeness. W. H. Freeman and Company, San Francisco 1979, x + 338 pp. J. Symb. Log. 48, 498–500 (1983)

    Article  Google Scholar 

  2. Rego, C.: RAMP: A new metaheuristic framework for combinatorial optimization. In: Rego, C. and Alidaee, B. (eds.) Metaheuristic Optimization via Memory and Evolution: Tabu Search and Scatter Search. pp. 441–460. Kluwer Academic Publishers (2005)

  3. Rego, C., Mathew, F., Glover, F.: RAMP for the capacitated minimum spanning tree problem. Ann. Oper. Res. 181, 661–681 (2010)

    Article  MathSciNet  Google Scholar 

  4. Gamboa, D.: Adaptive memory algorithms for the solution of large scale combinatorial optimization problems, PhD Thesis (in Portuguese), (2008)

  5. Matos, T., Gamboa, D.: Dual-RAMP for the capacitated single allocation hub location problem. In: 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)

  6. 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)

  7. Matos, T., Maia, F., Gamboa, D.: A simple dual-RAMP Algorithm for the Uncapacitated Multiple Allocation Hub Location Problem. In: Advances in Intelligent Systems and Computing. pp. 331–339. , Valencia, Spain (2020)

  8. Matos, T., Oliveira, Ó., Gamboa, D.: A simple dual-RAMP Algorithm for the Capacitated Facility Location Problem. In: Learning and Intelligent Optimization. pp. 1–13 (2020)

  9. Jacobsen, S.K.: Heuristics for the capacitated plant location model. Eur. J. Oper. Res. 12, 253–261 (1983)

    Article  Google Scholar 

  10. Kuehn, A., Hamburger, M.: A heuristic program for locating warehouses. Manag. Sci. 9, 643–666 (1963)

    Article  Google Scholar 

  11. Cornuéjols, G., Sridharan, R., Thizy, J.: A comparison of heuristics and relaxations for the capacitated plant location problem. Eur. J. Oper. Res. 50, 280–297 (1991)

    Article  Google Scholar 

  12. Guignard, M., Spielberg, K.: A direct dual method for the mixed plant location problem with some side constraints. Math. Program. 17, 198–228 (1979)

    Article  MathSciNet  Google Scholar 

  13. Bilde, O., Krarup, J.: Sharp lower bounds and efficient algorithms for the simple plant location problem. In: Annals of Discrete Mathematics. pp. 79–97 (1977)

  14. Erlenkotter, D.: A dual-based procedure for uncapacitated facility location. Oper. Res. 26, 992–1009 (1978)

    Article  MathSciNet  Google Scholar 

  15. Avella, P., Boccia, M., Sforza, A., Vasil’ev, I., Vasil’ev, I.: An effective heuristic for large-scale capacitated facility location problems. J. Heuristics. 15, 597–615 (2008)

    Article  Google Scholar 

  16. Lorena, L., Senne, E.: Improving traditional subgradient scheme for Lagrangean relaxation: an application to location problems. Int. J. Math. Algorithms. 1, 133–151 (1999)

    MATH  Google Scholar 

  17. Beasley, J.E.: Lagrangean heuristics for location problems. Eur. J. Oper. Res. 65, 383–399 (1993)

    Article  Google Scholar 

  18. Sridharan, R.: The capacitated plant location problem. Eur. J. Oper. Res. 87, 203–213 (1995)

    Article  Google Scholar 

  19. Van Roy, T.: A cross decomposition algorithm for capacitated facility location. Eur. J. Oper. Res. 34, 145–163 (1986)

    Article  MathSciNet  Google Scholar 

  20. Bornstein, C.T.: An ADD/DROP procedure for the capacitated plant location problem. Pesqui. Operacional. 151–162 (2003)

  21. Bornstein, C.T.C., Azlan, H.H.B.: The use of reduction tests and simulated annealing for the capacitated plant location problem. Locat. Sci. 6, 67–81 (1998)

    Article  Google Scholar 

  22. Lai, M.-C., Sohn, H., Tseng, T.-L. (Bill), Chiang, C.: A hybrid algorithm for capacitated plant location problem. Expert Syst. Appl. 37, 8599–8605 (2010)

  23. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238–252 (1962)

    Article  MathSciNet  Google Scholar 

  24. Sastry, K., Goldberg, D.E., Kendall, G.: Genetic Algorithms. In: Search Methodologies. pp. 93–117. Springer US, Boston, MA (2014)

  25. Glover, F., Laguna, M.: Tabu Search. (1997)

    Book  Google Scholar 

  26. Glover, F.: Tabu search—part I. ORSA J. Comput. 1, 190–206 (1989)

    Article  Google Scholar 

  27. Feo, T., Resende, M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 134, 109–134 (1995)

    Article  MathSciNet  Google Scholar 

  28. Sun, M.: A tabu search heuristic procedure for the capacitated facility location problem. J. Heuristics. 18, 91–118 (2012)

    Article  Google Scholar 

  29. Kennington, Jeff L. and Helgason, R. V.: Algorithms for network programming. John Wiley & Sons, Inc. (1980)

  30. Ronaldo Silva, V.F.: Um Algoritmo GRASP Híbrido para o Problema de Localização Capacitada de Custo Fixo, (2007)

    Google Scholar 

  31. Guastaroba, G., Speranza, M.G.: Kernel search for the capacitated facility location problem. J. Heuristics. 18, 877–917 (2012)

    Article  Google Scholar 

  32. Guastaroba, G., Speranza, M.G.: Kernel search: an application to the index tracking problem. Eur. J. Oper. Res. 217, 54–68 (2012)

    Article  MathSciNet  Google Scholar 

  33. Rahmani, A., Mirhassani, S.A.: A hybrid firefly-genetic algorithm for the capacitated facility location problem. Inf. Sci. (Ny). 283(70–78), 70–78 (2014)

    Article  MathSciNet  Google Scholar 

  34. Venables, H., Moscardini, A.: Ant based heuristics for the capacitated fixed charge location problem. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.T. (eds.) Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 235–242. Springer, Berlin Heidelberg, Berlin, Heidelberg (2008)

    Google Scholar 

  35. Cabrera, G., Cabrera, E., Soto, R., Rubio, L.J.M., Crawford, B., Paredes, F.: A hybrid approach using an artificial bee algorithm with mixed integer programming applied to a large-scale capacitated facility location problem. Math. Probl. Eng. 2012, 14 (2012)

    Article  Google Scholar 

  36. Levanova, T., Tkachuk, E.: Development of a bee colony optimization algorithm for the capacitated plant location problem. In: II International Conference Optimization and Applications (OPTIMA-2011). pp. 153–156. , Petrovac, Montenegro (2011)

  37. Daskin, M.M.S.: Network and discrete location: models, algorithms, and applications. Wiley, New York. 283–292 (1995)

  38. Roosta, S.H.: Principles of parallel algorithm design. In: Parallel Processing and Parallel Algorithms. pp. 217–258 (2000)

  39. Blelloch, G.E., Tangwongsan, K.: Parallel approximation algorithms for facility-location problems. Proc. 22nd ACM Symp. Parallelism algorithms Archit. SPAA 10. 315 (2010)

  40. Zhang, J., Chen, B., Ye, Y.: A multiexchange local search algorithm for the capacitated facility location problem, (2005)

  41. Alba, E., Luque, G., Nesmachnow, S.: Parallel metaheuristics: recent advances and new trends. Int. Trans. Oper. Res. 20, 1–48 (2013)

    Article  Google Scholar 

  42. Beasley, J.: OR-library: distributing test problems by electronic mail. J. Oper. Res. Soc. 65, 1069–1072 (1990)

    Article  Google Scholar 

  43. Beasley, J.E.: An algorithm for solving large capacitated warehouse location problems. Eur. J. Oper. Res. 33, 314–325 (1988)

    Article  MathSciNet  Google Scholar 

  44. Avella, P., Boccia, M.: A cutting plane algorithm for the capacitated facility location problem. Comput. Optim. Appl. 43, 39–65 (2009)

    Article  MathSciNet  Google Scholar 

Download references

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

  1. CIICESI, Escola Superior de Tecnologia e Gestão, Politécnico do Porto, Felgueiras, Portugal

    Telmo Matos, Óscar Oliveira & Dorabela Gamboa

Authors
  1. Telmo Matos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Óscar Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dorabela Gamboa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Telmo Matos.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matos, T., Oliveira, Ó. & Gamboa, D. RAMP algorithms for the capacitated facility location problem. Ann Math Artif Intell 89, 799–813 (2021). https://doi.org/10.1007/s10472-021-09757-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-021-09757-z

Keywords

Search

Navigation