Abstract
In this paper we present a parallel implementation of a Greedy Randomized Adaptive Search Procedure (GRASP) for finding approximate solutions to the quadratic assignment problem. In particular, we discuss efficient techniques for large-scale sparse quadratic assignment problems on an MIMD parallel computer. We report computational experience on a collection of quadratic assignment problems. The code was run on a Kendall Square Research KSR-1 parallel computer, using 1, 4, 14, 24, 34, 44, 54, and 64 processors, and achieves an average speedup that is almost linear in the number of processors.
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References
R.E. Burkard, S. Karisch, and F. Rendi. QAPLIB — a quadratic assignment problem library. European Journal of Operations Research, 55:115–119, 1991. Updated version Feb. 1993.
R.E. Burkard and F. Rendi. A thermodynamically motivated simulation procedure for combinatorial optimization problems. European Journal of Operations Research, 17:169–174, 1984.
T.A. Feo and M.G.C. Resende. Greedy randomized adaptive search procedures. Technical report, AT & T Bell Laboratories, Murray Hill, NJ 079742070,February 1994. To appear in Journal of Global Optimization.
T.A. Feo, M.G.C. Resende, and S.H. Smith. A greedy randomized adaptive search procedure for maximum independent set. Operations Research, 42:860–878, 1994.
J.W. Gavett and N.V. Plyter. The optimal assignment of facilities to locations by branch and bound. Operations Research, 14:210–232, 1966.
B. Gendronu and T.G. Crainic Parallel branch-and-bound algorithms: Survey and synthesis. Technical report, Center for Research on Transportation, University of Montréal, Montréal, Canada, 1994.
P.C. Gilmore. Optimal and suboptimal algorithms for the quadratic assignment problem. J. SIAM, 10:305–313, 1962.
A.Y. Grama, V. Kumar, and P.M. Pardalos. Parallel processing of discrete optimization problems. In Encyclopedia of Microcomputers,pages 129–147. Marcel Dekker, 1993.
T.C. Koopmans and M.J. Beckmann. Assignment problems and the location of economic activities. Econometrica, 25:53–76, 1957.
A. M. Land. A problem of assignment with interrelated costs. Operations Research Quarterly, 14:185–198, 1963.
E.L. Lawler. The quadratic assignment problem. Management Science, 9: 586–599, 1963.
Y. Li. Heuristic and exact algorithms for the quadratic assignment problem. PhD thesis, The Pennsylvania State University, 1992.
Y. Li, P.M. Pardalos, and M.G.C. Resende. A greedy randomized adaptive search procedure for the quadratic assignment problem. In P.M. Pardalos and H. Wolkowicz, editors, Quadratic assignment and related problems, volume 16 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science, pages 237–261. American Mathematical Society, 1994.
Y. Li, P.M. Pardalos, and M.G.C. Resende. Fortran subroutines for approximate solution of dense quadratic assignment problems using GRASP. Technical report, AT & T Bell Laboratories, 1994.
Yong Li and Panos M. Pardalos. Generating quadratic assignment test problems with known optimal permutations. Computational Optimization and Applications, 1 (2): 163–184, 1992.
P.B. Mirchandani and T. Obata. Locational decisions with interactions between facilities: the quadratic assignment problem a review. Working Paper Ps-79–1, Rensselaer Polytechnic Institute, Troy, New York, May 1979.
C.E. Nugent, T.E. Vollmann, and J. Ruml. An experimental comparison of techniques for the assignment of facilities to locations. Journal of Operations Research, 16: 150–173, 1969.
P.M. Pardalos and J. Crouse. A parallel algorithm for the quadratic assignment problem. In Proceedings of the Supercomputing 1989 Conference, pages 351–360. ACM Press, 1989.
P.M. Pardalos, F. Rendi, and H. Wolkowicz. The quadratic assignment problem: A survey and recent developments. In P.M. Pardalos and H. Wolkowicz, editors, Quadratic assignment and related problems, volume 16 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science, pages 1–42. American Mathematical Society, 1994.
P.M. Pardalos, M.G.C. Resende, and K.G. Ramakrishnan, editors. Parallel processing of discrete optimization problems. DIMACS Series on Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1995.
C. Roucairol. A parallel branch and bound algorithm for the quadratic assignment problem. Discrete Applied Mathematics, 18: 211–225, 1987.
S. Sahni and T. Gonzalez. P-complete approximation problems. Journal of the Association of Computing Machinery, 23: 555–565, 1976.
J. Skorin-Kapov. Tabu search applied to the quadratic assignment problem. ORSA Journal on Computing, 2 (1): 33–45, 1990.
E. Taillard. Robust tabu search for the quadratic assignment problem. Parallel Computing, 17: 443–455, 1991.
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Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C. (1995). A Parallel Grasp Implementation for the Quadratic Assignment Problem. In: Ferreira, A., Rolim, J.D.P. (eds) Parallel Algorithms for Irregular Problems: State of the Art. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6130-6_6
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DOI: https://doi.org/10.1007/978-1-4757-6130-6_6
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