Skip to main content
SpringerLink
Log in

A scatter search algorithm for the single row facility layout problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, with the objective of minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard and research has focused on heuristics to solve large instances of the problem. In this paper we present a scatter search algorithm to solve large size SRFLP instances. Our computational experiments show that the scatter search algorithm is an algorithm of choice when solving large size SRFLP instances within limited time.

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

Fig. 1

Similar content being viewed by others

References

  • Amaral, A.R.S.: On the exact solution of a facility layout problem. Eur. J. Oper. Res. 173(2), 508–518 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Amaral, A.R.S.: An exact approach to the one-dimensional facility layout problem. Oper. Res. 56(4), 1026–1033 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • Amaral, A.R.S.: A new lower bound for the single row facility layout problem. Discret. Appl. Math. 157(1), 183–190 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  • Amaral, A.R.S., Letchford, A. N.: A polyhedral approach to the single row facility layout problem. Math. Programm. doi:10.1007/s10107-012-0533-z (2012)

  • Amaral, A.R.S.: The corridor allocation problem. Comput. Oper. Res. 39(12), 3325–3330 (2012)

    Article  MathSciNet  Google Scholar 

  • Anjos, M.F., Kennings, A., Vannelli, A.: A semidefinite optimization approach for the single-row layout problem with unequal dimensions. Discret. Optim. 2(2), 113–122 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Anjos, M.F., Liers, F.: Handbook on Semidefinite, Cone and Polynomial Optimization, volume 166 of International Series in Operations Research & Management Science, chapter Global Approaches for Facility Layout and VLSI Floorplanning, pp. 849–877. Springer, Berlin (2012)

  • Anjos, M.F., Vannelli, A.: Computing globally optimal solutions for single-row layout problems using semidefinite programming and cutting planes. Inf. J. Comput. 20(4), 611–617 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  • Anjos, M.F., Yen, G.: Provably near-optimal solutions for very large single-row facility layout problems. Optim. Methods Softw. 24(4–5), 805–817 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  • Beghin-Picavet, M., Hansen, P.: Deux problèmes daffectation non linéaires. RAIRO Recherche Opérationnelle 16(3), 263–276 (1982)

    MATH  Google Scholar 

  • Chung, J., Tanchoco, J.: The double row layout problem. Int. J. Prod. Res. 48(3), 709–727 (2010)

    Article  MATH  Google Scholar 

  • Datta, D., Amaral, A.R.S., Figueira, J.R.: Single row facility layout problem using a permutation-based genetic algorithm. Eur. J. Oper. Res. 213(2), 388–394 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  • Djellab, H., Gourgand, M.: A new heuristic procedure for the single-row facility layout problem. Int. J. Comput. Integr. Manuf. 14(3), 270–280 (2001)

    Article  Google Scholar 

  • Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977)

    Article  Google Scholar 

  • Glover, F.: Tabu search for nonlinear and parametric optimization (with links to genetic algorithms). Discret. Appl. Math. 49, 231–255 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  • Glover, F.: Scatter search and star-paths: beyond the genetic metaphor. OR Spectr. 17, 125–137 (1995). doi:10.1007/BF01719256

    Article  MATH  Google Scholar 

  • Glover, F.: A template for scatter search and path relinking. Lect. Notes Comput. Sci. 1363, 13–54 (1998)

    Google Scholar 

  • Glover, F., Laguna, M., Martí, R.: Fundamentals of scatter search and path relinking. Control Cybern. 39, 653–684 (2000)

    Google Scholar 

  • Gomes de Alvarenga, A., Negreiros-Gomes, F.J., Mestria, M.: Metaheuristic methods for a class of the facility layout problem. J. Intell. Manuf. 11, 421–430 (2000)

    Article  Google Scholar 

  • Heragu, S.S., Alfa, A.S.: Experimental analysis of simulated annealing based algorithms for the layout problem. Eur. J. Oper. Res. 57(2), 190–202 (1992)

    Article  MATH  Google Scholar 

  • Heragu, S.S., Kusiak, A.: Machine layout problem in flexible manufacturing systems. Oper. Res. 36(2), 258–268 (1988)

    Article  Google Scholar 

  • Heragu, S.S., Kusiak, A.: Efficient models for the facility layout problem. Eur. J. Oper. Res. 53, 1–13 (1991)

    Article  MATH  Google Scholar 

  • Hungerländer, P., Rendl, F.: A computational study and survey of methods for the single-row facility layout problem. Comput. Optim. Appl. 55(1), 1–20 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  • Kothari, R., Ghosh, D.: Path relinking algorithms for single row facility layout (w.p. no. 2012–05-01). Ahmedabad, India: IIM Ahmedabad, Production & Quantitative Methods. Available at (2012a) http://www.iimahd.ernet.in/assets/snippets/workingpaperpdf/6038336162012-05-01.pdf

  • Kothari, R., Ghosh, D.: The single row facility layout problem: state of the art. Opsearch 49, 442–462 (2012b)

    Article  MATH  MathSciNet  Google Scholar 

  • Kothari, R., Ghosh, D.: An efficient genetic algorithm for single row facility layout. Optim. Lett.10.1007/s11590-012-0605-2 (2013a)

  • Kothari, R., Ghosh, D.: Insertion based Lin–Kernighan heuristic for single row facility layout. Comput. Oper. Res. 40(1), 129–136 (2013b)

    Article  MathSciNet  Google Scholar 

  • Kothari, R., Ghosh, D.: Tabu search for the single row facility layout problem using exhaustive 2-opt and insertion neighborhoods. Eur. J. Oper. Res. 224(1), 93–100 (2013c)

    Article  MathSciNet  Google Scholar 

  • Kumar, R.K., Hadjinicola, G.C., Lin, T.-L.: A heuristic procedure for the single-row facility layout problem. Eur. J. Oper. Res. 87(1), 65–73 (1995)

    Article  MATH  Google Scholar 

  • Kumar, S., Asokan, P., Kumanan, S., Varma, B.: Scatter search algorithm for single row layout problem in fms. Adv. Prod. Eng. Manag. 3(4), 193–204 (2008)

    Google Scholar 

  • Laguna, M., Martí, R.: Scatter Search: Methodology and Implementations in C. Kluwer Academic Publishers, Boston (2003)

    Book  Google Scholar 

  • Larrañaga, P., Kuijpers, C.M.H., Murga, R.H., Inza, I., Dizdarevic, S.: Genetic algorithms for the travelling salesman problem: a review of representations and operators. Artif. Intell. Rev. 13(2), 129–170 (1999)

    Article  Google Scholar 

  • Letchford, A.N., Amaral, A.R.S.: A polyhedral approach to the single row facility layout problem. Technical report, The Department of Management Science, Lancaster University, (2011)

  • Love, R.F., Wong, J.Y.: On solving a one-dimensional space allocation problem with integer programming. INFOR 14(2), 139–144 (1976)

    MATH  Google Scholar 

  • Martí, R., Glover, F., Laguna, M.: Principles of scatter search. Eur. J. Oper. Res. 169(2), 359–372 (2006)

    Article  MATH  Google Scholar 

  • Ozcelik, F.: A hybrid genetic algorithm for the single row layout problem. Int. J. Prod. Res. (2011)

  • Picard, J.-C., Queyranne, M.: On the one-dimensional space allocation problem. Oper. Res. 29(2), 371–391 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  • Romero, D., Sánchez-Flores, A.: Methods for the one-dimensional space allocation problem. Comput. Oper. Res. 17(5), 465–473 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • Samarghandi, H., Eshghi, K.: An efficient tabu algorithm for the single row facility layout problem. Eur. J. Oper. Res. 205(1), 98–105 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  • Samarghandi, H., Taabayan, P., Jahantigh, F.F.: A particle swarm optimization for the single row facility layout problem. Comput. Ind. Eng. 58(4), 529–534 (2010)

    Article  Google Scholar 

  • Sanjeevi, S., Kianfar, K.: A polyhedral study of triplet formulation for single row facility layout problem. Discret. Appl. Math. 158(16), 1861–1867 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  • Simmons, D.M.: One-dimensional space allocation: an ordering algorithm. Oper. Res. 17(5), 812–826 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  • Solimanpur, M., Vrat, P., Shankar, R.: An ant algorithm for the single row layout problem in flexible manufacturing systems. Comput. Oper. Res. 32(3), 583–598 (2005)

    Article  MATH  Google Scholar 

  • Sörensen, K.: Distance measures based on the edit distance for permutation-type representations. J. Heuristics 13, 35–47 (2007). doi:10.1007/s10732-006-9001-3

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. HSBC, HSBC House, HDPI, Kolkata , 700091, India

    Ravi Kothari

  2. P&QM Area, IIM Ahmedabad, Ahmedabad , 380015, India

    Diptesh Ghosh

Authors
  1. Ravi Kothari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diptesh Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ravi Kothari.

Appendix

Appendix

The permutation of facilities for the instance sko-81-01 for which the SS-1P algorithm improved the best solution known in the literature is given below. The facilities are numbered from 1 through 81.

66 74 3 61 30 25 50 9 48 56 67 65 33 69 23 17 4 6 41 21 81 14 15 19 38 49 31 7 39 36 26 70 35 42 22 55 11 57 78 44 2 45 52 32 68 13 62 1 5 27 58 20 18 73 43 59 24 51 37 63 12 79 75 80 77 71 72 29 64 46 28 10 40 34 76 16 54 53 60 47 8

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kothari, R., Ghosh, D. A scatter search algorithm for the single row facility layout problem. J Heuristics 20, 125–142 (2014). https://doi.org/10.1007/s10732-013-9234-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-013-9234-x

Keywords

Search

Navigation