Journal of the Operational Research Society

, Volume 58, Issue 1, pp 100–114 | Cite as

Guided construction search metaheuristics for the capacitated p-median problem with single source constraint

Theoretical Paper

Abstract

In the capacitated p-median problem with single source constraint, also known as the capacitated clustering problem, a given set of n weighted points is to be partitioned into p clusters such that the total weight of the points in each cluster does not exceed a given cluster capacity. The objective is to find a set of p centres that minimizes the total scatter of points allocated to these clusters. In this paper, a (λ, μ)-interchange neighbourhood based on the concept of λ-interchange of points restricted to μ-adjacent clusters is proposed. Structural properties of centres are identified and exploited to derive special data structures for their efficient evaluations. Different search and selection strategies including the variable neighbourhood search descent with respect to μ-nearest points are investigated. The most efficient strategies are then embedded in a guided construction search metaheuristic framework based either on a periodic local search procedure or a greedy random adaptive search procedure to solve the problem. Computational experience is reported on a standard set of benchmarks. The computational experience demonstrates the competitive performance of the proposed algorithms when compared to the best-known procedures in the literature in terms of solution quality and computational requirement.

Keywords

facility location data structures greedy random adaptive search procedure periodic 

Notes

Acknowledgements

This research was sponsored by grants from the University of Alzahra in Iran and the American University of Beirut in Lebanon. We thank our sponsors for their kind supports. The authors are also grateful to the referees and professor John Wilson for their useful comments and suggestions.

References

  1. Ahmadi S and Osman IH (2004). Density based problem space search for the capacitated clustering p-median problem. Ann Opl Res 131: 21–43.CrossRefGoogle Scholar
  2. Ahmadi S and Osman IH (2005). Greedy random adaptive memory programming search for the capacitated clustering problem. Eur J Opl Res 162: 30–44.CrossRefGoogle Scholar
  3. Baldacci R, Hadjiconstantinou E, Maniezzo V and Mingozzi A (2002). A new method for solving capacitated location problems based on a set partitioning approach. Comput Opl Res 29: 365–386.CrossRefGoogle Scholar
  4. Beck MP and Mulvey JM (1982). Constructing optimal index funds Technical report, Report No. EES-82-1, Princeton University.Google Scholar
  5. Bellman RE (1957). Dynamic Programming. Princeton University Press: Princeton, New Jersey.Google Scholar
  6. Breedam AV (2001). Comparing descent heuristics and metaheuristics for the vehicle routing problem. Comput Opl Res 28: 289–315.CrossRefGoogle Scholar
  7. Brücker P (1977). On the complexity of clustering problems. In: Henn R, Korte B, Oettli W (eds). Optimization and Operations Research: Proceedings of a Workshop held at the University of Bonn, October 2–8. Springer-Verlag, Heidelberg, pp 45–54.Google Scholar
  8. Chhajed D, Francis RL and Lowe TJ (1993). Contributions of operations research to location analysis. Location Sci 1: 263–287.Google Scholar
  9. Chiang WC and Russell RA (1997). A reactive tabu search metaheuristic for the vehicle routing problem with time windows. INFORMS J Comput 9: 417–430.CrossRefGoogle Scholar
  10. Diaz JA and Fernandez E (2004). Hybrid scatter search and path relinking for the capacitated p-median problem. Eur J Opl Res (in press); Available online, accessed 21 November 2004.Google Scholar
  11. Dongarra J (2005). Performance of various computers using standard linear equations software. Technical Report CS-89-85, Computer Science Department, University of Tennessee, Knoxville, Available at http://www.netlib.org/benchmark/performance.ps.Google Scholar
  12. Festa P and Resende M (2002). GRASP: An annotated bibliography. In: Ribeiro C and Hansen P (eds). Essays and Surveys on Metaheuristics. Kluwer Academic Publishers, Boston, pp 325–367.CrossRefGoogle Scholar
  13. Franca PM, Sosa NG and Pureza VM (1999). An adaptive tabu search approach for the capacitated clustering problem. Int Transac Opl Res 6: 665–678.CrossRefGoogle Scholar
  14. Gendreau M, Hertz A and Laporte G (1992). New insertion and postoptimization procedures for the traveling salesman problem. Opl Res 40: 1086–1094.CrossRefGoogle Scholar
  15. Glover F (1997). Tabu search and adaptive memory programming- advances, applications and challenges. In: Barr R, Helgason and Kennington (eds). Advances in Metaheuristics, Optimization and Stochastic Modeling Technologies. Kluwer, Boston, MA, pp 1–75.Google Scholar
  16. Hansen P and Jaumard B (1997). Cluster analysis and mathematical programming. Math Program 79: 191–215.Google Scholar
  17. Hansen P, Jaumard B and Sanlaville E (1993). Weight constrained minimum sum-of-stars clustering. Technical report, Gerad Technical Report G-93-38.Google Scholar
  18. Hansen P and Mladenovic N (2001). Variable neighborhood search: Principles and applications. Eur J Opl Res 130: 449–467.CrossRefGoogle Scholar
  19. Hansen P, Mladenovic N and Perez-Britos D (2001). Variable neighborhood decomposition search. J Heuristics 7: 335–350.CrossRefGoogle Scholar
  20. Hansen P, Pedrosa ED and Ribeiro CC (1994). Modelling location and sizing of offshore platforms. Eur J Opl Res 72: 602–606.CrossRefGoogle Scholar
  21. Hasan M and Osman IH (1995). Local search algorithms for the maximal planar layout problem. Int Transac Opl Res 2: 89–106.CrossRefGoogle Scholar
  22. Karimi J (1986). An automated software design methodology using capo. J Mngt Inform Syst 3: 71–100.CrossRefGoogle Scholar
  23. Klein K and Aronson JE (1991). Optimal clustering: a model and method. Naval Res Logistics 38: 447–461.CrossRefGoogle Scholar
  24. Koskosidis YA and Powell WB (1992). Clustering algorithms for consolidation of customer orders into vehicle shipments. Transport Res 26B: 365–379.CrossRefGoogle Scholar
  25. Lorena LAN and Senne ELF (2004). A column generation approach to capacitated p-median problems. Comput Opl Res 31: 863–876.CrossRefGoogle Scholar
  26. Maniezzo V, Mingozzi A and Baldacci R (1998). A bionomic approach to the capacitated p-median problem. J Heuristics 4: 263–280.CrossRefGoogle Scholar
  27. Mirzaian A (1985). Lagrangian relaxation for the start–star concentrator location problem: approximation algorithms and bounds. Networks 15: 1–20.CrossRefGoogle Scholar
  28. Mulvey JM and Beck MP (1984). Solving capacitated clustering problems. Eur J Opl Res 18: 339–348.CrossRefGoogle Scholar
  29. Osman IH (1993). Metastrategy simulated annealing and tabu search algorithms for the vehicle routing problem. Ann Opl Res 41: 421.CrossRefGoogle Scholar
  30. Osman IH (1995a). Heuristics for the generalised assignment problem: simulated annealing and tabu search approaches. OR Spektrum 17: 211–225.CrossRefGoogle Scholar
  31. Osman IH (1995b). An introduction to metaheuristics. In: Lawrence M and Wilsdon C (eds). Operational Research Tutorial Papers. Operational Research Society Press, Birmingham, pp 92–122.Google Scholar
  32. Osman IH (2003a). Focused issue on applied meta-heuristics. Comput Indust Eng 44: 205–207.CrossRefGoogle Scholar
  33. Osman IH (2003b). Metaheuristics: models, analysis and directions. A tutorial paper presented at the joint EURO/INFORMS meeting, Instanbul, Turkey, July 6–10.Google Scholar
  34. Osman IH (2004). Metaheuristics: models, design and analysis. In: Kozan E (ed). Proceedings of the Fifth Asia-Pacific Industrial Engineering and Management Systems Conference & the Seventh Asia-Pacific division meeting of the International Foundation of Production Research, December 12–15, 2004. ANA Hotel, Gold Coast, Australia: Queensland University of Technology, Brisbane, Australia, pp 1–16.Google Scholar
  35. Osman IH (2006). A tabu search procedure based on a random roulette diversification for the weighted maximal planar graph problem. Comput Opl Res 33: 2526–2546.CrossRefGoogle Scholar
  36. Osman IH and Al-Ayoubi B (2005). MIC analysis for comparing meta-heuristics. In: Proceedings of the 6th Metaheuristics International Conference. University of Vienna, Vienna, Austria, pp 725–732.Google Scholar
  37. Osman IH, Al Ayoubi B and Barake M (2003). A greedy random adaptive search procedure for the weighted maximal planar graph problem. Comput Industl Eng 45: 635–651.Google Scholar
  38. Osman IH and Christofides N (1994). Capacitated clustering problems by hybrid simulated annealing and tabu search. Int Transac Opl Res 1: 317–336.CrossRefGoogle Scholar
  39. Osman IH and Kelly JP (1996a). Metaheuristics: an overview. In: Osman IH and Kelly JP (eds). Metaheuristics, Theory and Applications. Kluwer Academic Publishers, Boston, pp 1–21.Google Scholar
  40. Osman IH and Kelly JP (1996b). Metaheuristics, Theory and Applications. Kluwer Academic Publishers: Boston.Google Scholar
  41. Osman IH and Laporte G (1996). Metaheuristics: a bibliography. Ann Opl Res 63: 513–623.Google Scholar
  42. Osman IH and Wassan NA (2002). A reactive tabu search meta-heuristic for the vehicle routing problem with backhauls. J Scheduling 5: 265–285.CrossRefGoogle Scholar
  43. Pitsoulis L and Resende M (2002). Greedy randomized adaptive search procedures. In: Pardalos P and Resende M (eds). Handbook of Applied Optimization. Oxford University Press, Oxford, UK, pp 168–183.Google Scholar
  44. Ribeiro C and Hansen P (2001). Essays and Surveys on Metaheuristics. Kluwer Academic Publishers: Boston, USA.Google Scholar
  45. Russell RA (1995). Hybrid heuristics for the vehicle routing problem with time windows. Transport Sci 29: 156.CrossRefGoogle Scholar
  46. Scheuerer S and Wendolsky R (2004). A scatter search heuristic for the capacitated clustering problem. Eur J Opl Res 169: 533–547.CrossRefGoogle Scholar
  47. Steiglitz K and Weiner P (1968). Some improved algorithms for computer solution of the traveling salesman problem. In: Chien RT and Trick TN (eds). Proceedings of the 6th Annual Allerton Conference on Circuit Theory, Urbana, Illinois, pp 814–821.Google Scholar
  48. Taillard ED et al (1997). A tabu search heuristic for the vehicle routing problem with soft time windows. Transport Sci 31: 170–186.CrossRefGoogle Scholar
  49. Thangiah SR, Osman IH, Vinayagamoorthy R and Sung T (1993). Algorithms for the vehicle routing with time deadline. Am J Math M Sci 13: 323–355.Google Scholar
  50. Vakharia A and Mahajan J (2000). Clustering of objects and attributes for manufacturing and marketing applications. Euro J Opl Res 123: 640–651.CrossRefGoogle Scholar
  51. Voss S, Martello S, Osman IH and Roucairol C (1998). Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic Publishers: Boston, USA.CrossRefGoogle Scholar
  52. Wassan NA and Osman IH (2002). Tabu search variants for the mix fleet vehicle routing problem. J Opl Res Soc 53: 768–782.CrossRefGoogle Scholar

Copyright information

© Palgrave Macmillan Ltd 2006

Authors and Affiliations

  1. 1.American University of BeirutBeirutLebanon
  2. 2.De Monfort UniversityLeicesterUK

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