Skip to main content

Greedy Randomized Adaptive Search for a Location Problem with Economies of Scale

  • Chapter
Developments in Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 18))

Abstract

We consider a heuristic approach for the solution of a location problem with economies of scale. The method chosen has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors. We define the various components comprising this GRASP approach and perform a step-by-step development of such a heuristic for the location problem with concave costs. Computational results for problems of dimensions up to 100 × 1000 are reported.

Research partially supported by CENIIT (Center for Industrial Information Technology)

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. A. Dowsland. Simulated annealing. In C. R. Reeves, editor, Modern Heuristic Techniques for Combinatorial Problems, chapter 2, pages 20–69. Blackwell Scientific Publications, 1993.

    Google Scholar 

  2. M. A. Efroymson and T. L. Ray. A branch-bound algorithm for plant location. Operations Research, 14(14):361–368, 1966.

    Article  Google Scholar 

  3. S. Eilon, C. D. T. Watson-Gandy, and N. Christofides. Distribution Management: Mathematical Modelling and Practical Analysis. Griffin, London, 1971.

    Google Scholar 

  4. T. A. Feo and M. G. C. Resende. Greedy randomized adaptive search procedures. Journal of Global Optimization, 6(2):109–133, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Ghannadan, A. Migdalas, H. Tuy, and P. Värbrand. Heuristics based on tabu search and Lagrangean relaxation for the concave production-transportation problem. Studies in Regional and Urban Planning, 3:127–140, 1994.

    Google Scholar 

  6. M. Guignard and S. Kim. Lagrangean decomposition: a model yielding stronger Lagrangean bounds. Mathematical Programming, 6:62–88, 1987.

    MathSciNet  Google Scholar 

  7. G. M. Guisewite and P. M. Pardalos. Minimum concave cost network flow problems: Applications, complexity, and algorithms. Annals of Operations Research, 25:75–100, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  8. K. O. Jörnsten and A. Migdalas. Design of tree-like networks subject to budget constraints. Optimization, 19:475–484, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  9. K. O. Jörnsten and M. Näsberg. A new Lagrangean relaxation approach to the generalized assignment problem. European Journal of Operations Research, 27:313–323, 1986.

    Article  MATH  Google Scholar 

  10. K. O. Jörnsten, M. Näsberg, and P. Smeds. Variable splitting — a new Lagrangean relaxation approach to some mathematical programming models. Technical Report LiTH-MAT-R-85–04, Department of Mathematics, Linköping University, Sweden, 1985.

    Google Scholar 

  11. M. Kubo and H. Kasugai. A Lagrangean approach to the facility location problemn with concave costs. Journal of the Operations Society of Japan, 34(2):125–136, June 1991.

    MathSciNet  MATH  Google Scholar 

  12. T. Larsson, A. Migdalas, and M. Rönnqvist. A Lagrangean heuristic for the capacitated concave minimum cost network flow problem. European Journal of Operations Research, 78:116–129, 1991.

    Article  Google Scholar 

  13. R. F. Love, J. G. Morris, and G. O. Wesolowsky. Facilities Location: Models and Methods. North Holland, New York, 1988.

    MATH  Google Scholar 

  14. Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, 2nd edition, 1994.

    Book  MATH  Google Scholar 

  15. P. M. Pardalos, L. Pitsoulis, T. Mavridou, and M. G. C. Resende. Parallel Search for Combinatorial Optimization: Genetic Algorithms, Simulated Annealing, Tabu Search and GRASP. In A. Ferreira and J. Rolim, editors, Parallel Algorithms for Irregularly Structured Problems, volume 980 of Lecture Notes in Computer Science, pages 317–331, Berlin, 1995. Springer-Verlag.

    Chapter  Google Scholar 

  16. C. R. Reeves. Modern Heuristic Techniques for Combinatorial Problems. Blackwell Scientific Publications, 1993.

    MATH  Google Scholar 

  17. H. Tuy, S. Ghannadan, A. Migdalas, and P. Värbrand. Strongly polynomial algorithm for a production-transportation problem with concave production costs. Optimization, 27:205–227, 1993.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Holmqvist, K., Migdalas, A., Pardalos, P.M. (1997). Greedy Randomized Adaptive Search for a Location Problem with Economies of Scale. In: Bomze, I.M., Csendes, T., Horst, R., Pardalos, P.M. (eds) Developments in Global Optimization. Nonconvex Optimization and Its Applications, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2600-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-2600-8_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4768-0

  • Online ISBN: 978-1-4757-2600-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics