GRASP with Path-Relinking for Facility Layout

  • R. M. A. SilvaEmail author
  • M. G. C. Resende
  • P. M. Pardalos
  • G. R. Mateus
  • G. De Tomi
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 59)


This paper proposes a mathematical formulation for the facility layout problem (FLP) based on the generalized quadratic assignment problem (GQAP). The GQAP is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. As a case study, we adapt the GRASP with path-relinking (GRASP-PR) heuristic introduced in Mateus et al. (J. Heuristics 17:527–565, 2011) for the hospital layout problem (HLP). In the HLP, we are given a set of areas in a hospital where medical facilities, such as surgery and recovery rooms, can be located and a set of medical facilities, each facility with a required area, that must be located in the hospital. Furthermore, we are given a matrix specifying, for each ordered pair of facilities, the number of patients that transition from the first to the second facility. The objective of the assignment is to minimize the total distance traveled by the patients. We illustrate our algorithm with a numerical example.


Hospital layout Generalized quadratic assignment problem GRASP Path-relinking Heuristics 



The research of R.M.A Silva was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq), the Foundation for Support of Research of the State of Minas Gerais, Brazil (FAPEMIG), Coordination for the Improvement of Higher Education Personnel, Brazil (CAPES), Foundation for the Support of Development of the Federal University of Pernambuco, Brazil (FADE), the Office for Research and Graduate Studies of the Federal University of Pernambuco (PROPESQ), and the Foundation for Support of Science and Technology of the State of Pernambuco (FACEPE).


  1. 1.
    Bazaraa, M.S.: Computerized layout design: a branch and bound approach. AIIE Trans. 7(4), 432–438 (1975) MathSciNetCrossRefGoogle Scholar
  2. 2.
    Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989) MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995) MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Foulds, L.R., Robinson, D.F.: A strategy for solving the plant layout problem. Oper. Res. Q. 27(4), 845–855 (1976) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Glover, F.: Tabu search and adaptive memory programing—advances, applications and challenges. In: Barr, R.S., Helgason, R.V., Kennington, J.L. (eds.) Interfaces in Computer Science and Operations Research, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 1–75. Kluwer Academic, Dordrecht (1996) Google Scholar
  6. 6.
    Kaufman, L., Broeckx, F.: An algorithm for the quadratic assignment problem using Bender’s decomposition. Eur. J. Oper. Res. 2(3), 207–211 (1978) CrossRefzbMATHGoogle Scholar
  7. 7.
    Koopmans, T.C., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica 25(1), 53–76 (1957) MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kusiak, A., Heragu, S.S.: The facility layout problem. Eur. J. Oper. Res. 29(3), 229–251 (1987) MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Laguna, M., Marti, R.: GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J. Comput. 11, 44–52 (1999) CrossRefzbMATHGoogle Scholar
  10. 10.
    Lawler, E.L.: The quadratic assignment problem. Manag. Sci. 9(4), 586–599 (1963) MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Mateus, G.R., Resende, M.G.C., Silva, R.M.A.: GRASP with path-relinking for the generalized quadratic assignment problem. J. Heuristics 17, 527–565 (2011) CrossRefzbMATHGoogle Scholar
  12. 12.
    Resende, M.G.C., Ribeiro, C.C.: GRASP with path-relinking: recent advances and applications. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Metaheuristics: Progress as Real Problem Solvers, pp. 29–63. Springer, Berlin (2005) CrossRefGoogle Scholar
  13. 13.
    Resende, M.G.C., Ribeiro, C.C.: Greedy randomized adaptive search procedures: advances and applications. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, 2nd edn., pp. 293–319. Springer, Berlin (2010) Google Scholar
  14. 14.
    Ribeiro, C.C., Resende, M.G.C.: Path-relinking intensification methods for stochastic local search algorithms. J. Heuristics 18, 193–214 (2012) CrossRefGoogle Scholar
  15. 15.
    Rosenblatt, M.J.: The facilities layout problem: a multigoal approach. J. Prod. Res. 17 (1979) Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • R. M. A. Silva
    • 1
    Email author
  • M. G. C. Resende
    • 2
  • P. M. Pardalos
    • 3
  • G. R. Mateus
    • 4
  • G. De Tomi
    • 5
  1. 1.Centro de InformáticaFederal University of PernambucoRecifeBrazil
  2. 2.Algorithms and Optimization Research DepartmentAT&T Labs ResearchFlorham ParkUSA
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  4. 4.Dept. of Computer ScienceFederal University of Minas GeraisBelo HorizonteBrazil
  5. 5.Departamento de Engenharia de Minas e de PetróleoEscola Politécnica da Universidade de São PauloSão PauloBrazil

Personalised recommendations