Abstract
The multidimensional assignment problem (MAPs) is a higher dimensional version of the standard linear assignment problem. Test problems of known solution are useful in exercising solution methods. A method of generating an axial MAP of controllable size with a known unique solution is presented. Certain characteristics of the generated MAPs that determine realism and difficulty are investigated.
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R.M. Aiex, M.G.C. Resende, P.M. Pardalos, and G. Toraldo, “GRASP with path relinking for the three-index assignment problem” Technical Report, AT&T Labs Research, Florham Park, NJ 07733, 2001.
E. Balas and M.J. Saltzman, “An algorithm for the three-index assignment problem” Operations Research, vol. 39, pp. 150–161, 1991.
J.E. Beasley, “OR-Library: Distributing test problems by electronic mail” Journal of the Operational Research Society, vol. 41, no. 11, pp. 1069–1072, 1990.
J.E. Beasley, OR-Library, http://www.ms.ic.ac.uk/info.html.
R.E. Burkard, “Selected topics on assignment problems” Discrete Applied Mathematics, vol. 123, pp. 257–302, 2002.
R.E. Burkard, E. Çela, S.E. Karisch, and F. Rendlqaplib, A Quadratic Assignment Problem Library, http://www.opt.math.tu-graz.ac.at/qaplib/.
R.E. Burkard, R. Rudolf, and G.J. Woeginger, “Three-dimensional axial assignment problems with decomposible cost coefficients” Discrete Applied Mathematics, vol. 65, pp. 123–139, 1996.
Y. Crama and F.C.R. Spieksma, “Approximation algorithms for three-dimensional assignment problems with triangle inequalities” European Journal of Operational Research, vol. 60, pp. 273–279, 1992.
C.A. Floudas, P.M. Pardalos, C.S. Adjiman, W.R. Esposito, Z.H. Gms, S.T. Harding, J.L. Klepeis, C.A. Meyer, and C.A. Schweiger, Handbook of Test Problems in Local and Global Optimization, Kluwer, Dordrecht, Netherlands, 1999.
A.M. Frieze and J. Yadegar, “An algorithm for solving 3-dimensional assignment problems with application to scheduling a teaching practice” Journal of Operational Research Society, vol. 32, pp. 989–995, 1981.
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman: New York, 1979.
E.E. Lewis, Introduction to Reliability Engineering, 2nd ediition, John Wiley and Sons: New York, 1996, pp. 25–30.
D. Magos and P. Miliotis, “An algorithm for the planar three-index assignment problem” European Journal of Operational Research, vol. 77, pp. 141–153, 1994.
R. Murphey, P. Pardalos, and L. Pitsoulis, “A greedy randomized adaptive search procedure for the multitarget multisensor tracking problem” in DIMACS Series, vol. 40, American Mathematical Society, 1998, pp. 277–302.
P. Pardalos and L. Pitsoulis (Eds.), Nonlinear Assignment Problems, Algorithms and Applications, Kluwer: Dordrecht, 2000, pp. 1–12.
W. Pierskalla, “The multidimensional assignment problem” Operations Research, vol. 16, pp. 422–431, 1968.
A. Poore and N. Rijavec, “A lagrangian relaxation algorithm for multidimensional assignment problems arising from multitarget tracking” Society of Industrial and Applied Mathmatics Journal on Optimization, vol. 3, pp. 544–563, 1993.
J. Pusztaszeri, P.E. Rensing, and T.M. Liebling, “Tracking elementary particles near their primary vertex: A combinatorial approach.” Journal of Global Optimization, vol. 16, pp. 422–431, 1995.
L. Yong and P.M. Pardalos, “Generating quadratic assignment test problems with know optimal permutations” Computational Optimization and Applications, vol. 1, no. 2, pp. 163–184, 1992.
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Grundel, D.A., Pardalos, P.M. Test Problem Generator for the Multidimensional Assignment Problem. Comput Optim Applic 30, 133–146 (2005). https://doi.org/10.1007/s10589-005-4558-6
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DOI: https://doi.org/10.1007/s10589-005-4558-6