Skip to main content
Log in

A matheuristic for the cell formation problem

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper we propose a GRASP matheuristic coupled with an Integer Programming refinement based on Set Partitioning to solve the Cell Formation Problem. We use the grouping efficacy measure to evaluate the solutions. As this measure is nonlinear, we propose a fractional Set Partitioning approach and its linearization. Our method is validated on a set of 35 instances from the literature. The experiments found four unknown solutions. For all instances with known optima, our method is able to determine the optimum solutions.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

Notes

  1. The instances are available at http://www.ic.uff.br/~fabio/Instances_CFP_OPTL.zip.

References

  1. Agarwal, Y., Mathur, K., Salkin, H.M.: A set-partitioning-based exact algorithm for the vehicle routing problem. Networks 19(7), 731–749 (1989). doi:10.1002/net.3230190702

    Article  MathSciNet  MATH  Google Scholar 

  2. Balas, E., Padberg, M.W.: Set partitioning: a survey. SIAM Rev. 18(4), 710–760 (1976). doi:10.1137/1018115

    Article  MathSciNet  MATH  Google Scholar 

  3. Bastos, L., Ochi, L.S., Protti, F., Subramanian, A., Martins, I.C., Pinheiro, R.G.S.: Efficient algorithms for cluster editing. J. Comb. Optim. 31(1), 347–371 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boschetti, M.A., Maniezzo, V., Roffilli, M., Bolufé Röhler, A.: Matheuristics: Optimization, Simulation and Control, pp. 171–177. Springer, Berlin (2009). doi:10.1007/978-3-642-04918-7_13

    Google Scholar 

  5. Daz, J., Luna, D., Zetina, C.: A hybrid algorithm for the manufacturing cell formation problem. J. Heuristics 19(1), 77–96 (2013)

    Article  Google Scholar 

  6. Dimopoulos, C., Zalzala, A.: Recent developments in evolutionary computations for manufacturing optimization: problem, solutions, and comparisons. IEEE Trans. Evol. Comput. 4(2), 93–113 (2000)

    Article  Google Scholar 

  7. Elbenani, B., Ferland, J.A., Bellemare, J.: Genetic algorithm and large neighbourhood search to solve the cell formation problem. Expert Syst. Appl. 39(3), 2408–2414 (2012)

    Article  Google Scholar 

  8. Feo, T., Resende, M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ghosh, T., Sengupta, S., Chattopadhyay, M., Dan, K.P.: Meta-heuristics in cellular manufacturing: a state-of-art review. Int. J. Ind. Eng. Comput. 2, 87–122 (2011)

    Google Scholar 

  10. Gonçalves, J., Resende, M.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47(2–3), 247–273 (2004)

    Article  Google Scholar 

  11. Kumar, C.S., Chandrasekharan, M.P.: Group efficacy: a quantitative criterion for goodness of block diagonal forms of binary matrices in group technology. Int. J. Prod. Res. 28(2), 233–243 (1990)

    Article  Google Scholar 

  12. Maniezzo, V., Stützle, T., Voß, S.: Matheuristics: Hybridizing Metaheuristics and Mathematical Programming, 1st edn. Springer, Berlin (2009)

    MATH  Google Scholar 

  13. Martins, I.C., Pinheiro, R.G.S., Protti, F., Ochi, L.S.: A hybrid iterated local search and variable neighborhood descent heuristic applied to the cell formation problem. Expert Syst. Appl. 42(22), 8947–8955 (2015)

    Article  Google Scholar 

  14. Mladenovic, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pailla, A., Trindade, A.R., Parada, V., Ochi, L.S.: A numerical comparison between simulated annealing and evolutionary approaches to the cell formation problem. Expert Syst. Appl. 37, 5476–5483 (2010)

    Article  Google Scholar 

  16. Paydar, M.M., Saidi-Mehrabad, M.: A hybrid genetic-variable neighborhood search algorithm for the cell formation problem based on grouping efficacy. Comput. Oper. Res. 40(4), 980–990 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Penna, P.H.V., Subramanian, A., Ochi, L.S.: An iterated local search heuristic for the heterogeneous fleet vehicle routing problem. J. Heuristics 19(2), 201–232 (2013)

    Article  Google Scholar 

  18. Pinheiro, R.G., Martins, I.C., Protti, F., Ochi, L.S., Simonetti, L.G., Subramanian, A.: Eur. J. Oper. Res. 254(3), 769–779 (2016). doi:10.1016/j.ejor.2016.05.010

    Article  Google Scholar 

  19. Sarker, B., Khan, M.: A comparison of existing grouping efficiency measures and a new weighted grouping efficiency measure. IIE Trans. 33, 11–27 (2001)

    Google Scholar 

  20. Subramanian, A., Uchoa, E., Ochi, L.S.: A hybrid algorithm for a class of vehicle routing problems. Comput. Oper. Res. 40, 2519–2531 (2013)

    Article  MATH  Google Scholar 

  21. Wu, T.H., Chang, C.C., Yeh, J.Y.: A hybrid heuristic algorithm adopting both boltzmann function and mutation operator for manufacturing cell formation problems. Int. J. Prod. Econ. 120(2), 669–688 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fábio Protti.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pinheiro, R.G.S., Martins, I.C., Protti, F. et al. A matheuristic for the cell formation problem. Optim Lett 12, 335–346 (2018). https://doi.org/10.1007/s11590-017-1200-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-017-1200-3

Keywords

Navigation