Abstract
The generalized quadratic assignment problem (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. The GQAP has numerous applications, including facility design, scheduling, and network design. In this paper, we propose several GRASP with path-relinking heuristics for the GQAP using different construction, local search, and path-relinking procedures. We introduce a novel approximate local search scheme, as well as a new variant of path-relinking that deals with infeasibilities. Extensive experiments on a large set of test instances show that the best of the proposed variants is both effective and efficient.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aiex, R.M., Resende, M.G.C., Ribeiro, C.C.: Probability distribution of solution time in GRASP: An experimental investigation. J. Heuristics 8, 343–373 (2002)
Aiex, R.M., Binato, S., Resende, M.G.C.: Parallel GRASP with path-relinking for job shop scheduling. Parallel Comput. 29, 393–430 (2003)
Aiex, R.M., Pardalos, P.M., Resende, M.G.C., Toraldo, G.: GRASP with path-relinking for three-index assignment. INFORMS J. Comput. 17, 224–247 (2005)
Aiex, R.M., Resende, M.G.C., Ribeiro, C.C.: TTTPLOTS: A Perl program to create time-to-target plots. Opt. Lett. 1, 201–212 (2007)
Anstreicher, K., Brixius, N., Goux, J.P., Linderoth, J.: Solving large quadratic assignment problems on computational grids. Math. Program. 91, 563–588 (2002)
Barahona, F., Anbil, R.: The volume algorithm: producing primal solutions with a subgradient method. Math. Program. 87, 385–399 (2000)
Burkard, R.E.: Locations with spatial interactions: the quadratic assignment problem. In: Discrete Location Theory, pp. 89–98. Wiley, New York (1991)
Cordeau, J.-F., Gaudioso, M., Laporte, G., Moccia, L.: A memetic heuristic for the generalized quadratic assignment problem. INFORMS J. Comput. 18, 433–443 (2006)
Elloumi, S.: Contribution à la résolution des programmes non linéaires en variables 0-1, application aux problèmes de placement de tâches dans les systèmes distribués (thèse de doctorat in informatique). Technical report, Conservatoire National des Arts et Métiers, Paris (1991)
Elloumi, S., Roupin, F., Soutif, E.: Comparison of different lower bounds for the constrained module allocation problem. Technical Report 473, CNAM-Laboratoire Cédric, 292 Rue St Martin, 75141 Paris Cedex 03, France (2003)
Faria, H. Jr., Binato, S., Resende, M.G.C., Falcão, D.J.: Transmission network design by a greedy randomized adaptive path relinking approach. IEEE Trans. Power Syst. 20(1), 43–49 (2005)
Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)
Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Global Optim. 6, 109–133 (1995)
Festa, P., Resende, M.G.C.: GRASP: An annotated bibliography. In: Ribeiro, C.C., Hansen, P. (eds.) Essays and Surveys on Metaheuristics, pp. 325–367. Kluwer Academic, Norwell (2002)
Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP—Part I: Algorithms. Int. Trans. Oper. Res. 16, 1–24 (2009a)
Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP—Part II: Applications. Int. Trans. Oper. Res. 16, 131–172 (2009b)
Frieze, A., Yadegar, J.: On the quadratic assignment problem. Discrete Appl. Math. 5, 89–98 (1983)
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, pp. 1–75. Kluwer Academic, Norwell (1996)
Glover, F., Laguna, M., Martí, R.: Fundamentals of scatter search and path relinking. Control Cybern. 39, 653–684 (2000)
Hahn, P.M., Kim, B.-J., Guignard, M., MacGregor Smith, J., Zhu, Y.-R.: An algorithm for the generalized quadratic assignment problem. Comput. Optim. Appl. 401, 351–372 (2008)
Kaufman, L., Broeckx, F.: An algorithm for the quadratic assignment problem using benders decomposition. Eur. J. Oper. Res. 2, 204–211 (1978)
Laguna, M., Martí, R.: GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J. Comput. 11, 44–52 (1999)
Lee, C.-G., Ma, Z.: The generalized quadratic assignment problem. Technical Report MIEOR TR2005-01, Department of Mechanical and Industrial Engineering at the University of Toronto (2005)
Li, Y., Pardalos, P.M., Resende, M.G.C.: A greedy randomized adaptive search procedure for the quadratic assignment problem. In: Pardalos, P.M., Wolkowicz, H. (eds.) Quadratic Assignment and Related Problems. DIMACS Series in Discrete Matehematics and Theoretical Computer Science, vol. 16, pp. 237–261. American Mathematical Society, Providence (1994)
Matsumoto, M., Nishimura, T.: Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8, 3–30 (1998)
Oliveira, C.A.S., Pardalos, P.M., Resende, M.G.C.: GRASP with path-relinking for the quadratic assignment problem. In: Ribeiro, C.C., Martins, S.L. (eds.) Efficient and Experimental Algorithms. Lecture Notes in Computer Science, vol. 3059, pp. 356–368. Springer-Verlag, Berlin (2004)
Padberg, M., Rijal, M.: Location, Scheduling, Design and Integer Programming. Kluwer Academic, Norwell (1996)
Pardalos, P.M., Rendl, F., Wolkowicz, H.: The quadratic assignment problem: A survey and recent development. In: Pardalos, P.M., Wolkowicz, H. (eds.) The Quadratic Assignment and Related Problems. DIMACS Series in Discrete Matehematics and Theoretical Computer Science, vol. 16, pp. 1–42. American Mathematical Society, Providence (1994)
Pessoa, A.A., Hahn, P.M., Guignard, M., Zhu, Y.-R.: An improved algorithm for the generalized quadratic assignment problem. Technical Report MIEOR TR2005-01, Electrical and Systems Engineering at the University of Pennsylvania (2008)
Resende, M.G.C., Ribeiro, C.C.: Greedy randomized adaptive search procedures. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 219–249. Kluwer Academic, Norwell (2002)
Resende, M.G.C., Ribeiro, C.C.: A GRASP with path-relinking for private virtual circuit routing. Networks 41(1), 104–114 (2003)
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-Verlag, Berlin (2005)
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. Springer Science+Business Media, Berlin (2010)
Ribeiro, C.C., Rosseti, I.: A parallel GRASP for the 2-path network design problem. In: Lecture Notes in Computer Science, vol. 2004, pp. 922–926. Springer-Verlag, Berlin (2002)
Ribeiro, C.C., Uchoa, E., Werneck, R.F.: A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS J. Comput. 14, 228–246 (2002)
Roupin, F.: From linear to semidefinite programming: An algorithm to obtain semidefinite relaxations for bivalent quadratic problems. J. Combin. Optim. 8, 469–493 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/s10732-010-9144-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-010-9144-0