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.

Similar content being viewed by others
Notes
The instances are available at http://www.ic.uff.br/~fabio/Instances_CFP_OPTL.zip.
References
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
Balas, E., Padberg, M.W.: Set partitioning: a survey. SIAM Rev. 18(4), 710–760 (1976). doi:10.1137/1018115
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)
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
Daz, J., Luna, D., Zetina, C.: A hybrid algorithm for the manufacturing cell formation problem. J. Heuristics 19(1), 77–96 (2013)
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)
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)
Feo, T., Resende, M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)
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)
Gonçalves, J., Resende, M.: An evolutionary algorithm for manufacturing cell formation. Comput. Ind. Eng. 47(2–3), 247–273 (2004)
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)
Maniezzo, V., Stützle, T., Voß, S.: Matheuristics: Hybridizing Metaheuristics and Mathematical Programming, 1st edn. Springer, Berlin (2009)
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)
Mladenovic, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)
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)
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)
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)
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
Sarker, B., Khan, M.: A comparison of existing grouping efficiency measures and a new weighted grouping efficiency measure. IIE Trans. 33, 11–27 (2001)
Subramanian, A., Uchoa, E., Ochi, L.S.: A hybrid algorithm for a class of vehicle routing problems. Comput. Oper. Res. 40, 2519–2531 (2013)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-017-1200-3