Abstract
We consider the problem of assigning the test variants of a written exam to the desks of a classroom in such a way that desks that are close-by receive different variants. The problem is a generalization of the Vertex Coloring and we model it as a binary quadratic problem. Exact solution methods based on reformulating the problem in a convex way and applying a general-purpose solver are discussed as well as a Tabu Search algorithm. The methods are extensively evaluated through computational experiments on real-world instances.
The problem arises from a real need at the Faculty of Engineering of the University of Bologna where the solution method is now implemented.
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Aardal, K.I., van Hoesel, S.P.M., Koster, A.M.C.A., Mannino, C., Sassano, A.: Models and solution techniques for the frequency assignment problem. 4OR 1, 261–317 (2003)
Billionnet, A., Elloumi, S.: Using a mixed integer quadratic programming solver for the unconstrained quadratic 0-1 problem. Math. Program. 109, 55–68 (2007)
Billionnet, A., Elloumi, S., Plateau, M.-C.: Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: the QCR method. Discrete Appl. Math. 157, 1185–1197 (2009)
Billionnet, A., Elloumi, S., Lambert, A.: Extending the QCR method to general mixed-integer programs. Math. Program. (2010). doi:10.1007/BF01586044
Burkard, R., Dell’Amico, M., Martello, S.: Assignment Problems. SIAM, Philadelphia (2009)
Hammer, P.L., Rubin, A.A.: Some remarks on quadratic programming with 0-1 variables. Rev. Fr. Inform. Rech. Oper. 4, 69–74 (1970)
Helmberg, C., Rendl, F., Vanderbei, R.J., Wolkowicz, H.: An interior-point method for semidefinite programming. SIAM J. Optim. 6, 342–361 (1996)
Hertz, A., de Werra, D.: Using tabu search techniques for graph coloring. Computing 39, 345–351 (1987)
Malaguti, E., Toth, P.: A survey on vertex coloring problems. Int. Trans. Oper. Res. 17, 1–34 (2010)
Mehrotra, S.: On the implementation of a primal-dual interior point method. SIAM J. Optim. 2, 575–601 (1992)
Nesterov, Y.E., Todd, M.J.: Self-scaled barriers and interior-point methods for convex programming. Math. Oper. Res. 22, 1–42 (1997)
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Duives, J., Lodi, A. & Malaguti, E. Test-assignment: a quadratic coloring problem. J Heuristics 19, 549–564 (2013). https://doi.org/10.1007/s10732-011-9176-0
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DOI: https://doi.org/10.1007/s10732-011-9176-0