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Managing the tabu list length using a fuzzy inference system: an application to examination timetabling

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Abstract

In this paper, we present an application of Tabu Search (TS) to the examination timetabling problem. One of the drawbacks of this meta-heuristic is related to the need of tuning some parameter (like tabu tenure) whose value affects the performance of the algorithm. The importance of developing an automatic procedure is clear considering that most of the users of timetabling software, like academic staff, do not have the expertise to conduct such tuning. The goal of this paper is to present a method to automatically manage the memory in the TS using a Decision Expert System. More precisely a Fuzzy Inference Rule Based System (FIRBS) is implemented to handle the tabu tenure based on two concepts, “Frequency” and “Inactivity”. These concepts are related respectively with the number of times a move is introduced in the tabu list and the last time (in number of iterations) the move was attempted and prevented by the tabu status. Computational results show that the implemented FIRBS handles well the tuning of the tabu status duration improving, as well, the performance of Tabu Search.

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References

  • Abdullah, S. (2006). Heuristic approaches for university timetabling problems. PhD thesis, University of Nottingham.

  • Abdullah, S., Ahmadi, S., Burke, E. K., & Dror, M. (2007). Investigating Ahuja-Orlin’s large neighbourhood search approach for examination timetabling. OR Spectrum, 29(2), 351–372.

    Article  Google Scholar 

  • Abramson, D., Krishnamoorthy, M., & Dang, H. (1999). Simulated annealing cooling schedules for the school timetabling problem. Asia-Pacific Journal of Operational Research, 16, 1–22.

    Google Scholar 

  • Ahuja, R. K., Orlin, J. B., & Sharma, D. (2001). Multi-exchange neighborhood structures for the capacitated minimum spanning tree problem. Mathematical Programming, 91(1), 71–97.

    Google Scholar 

  • Arani, T., & Lotfi, V. (1989). A three phased approach to final exam scheduling. IIE Transactions, 21(1), 86–96.

    Article  Google Scholar 

  • Asmuni, H., Burke, E. K., Garibaldi, J. M., & McCollum, B. (2004). In PATAT: Vol. 3616. Fuzzy multiple ordering criteria for examination timetabling.

    Google Scholar 

  • Assilian, S., & Mamdani, E. H. (1974). An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies, 7(1), 1–13.

    Google Scholar 

  • Awad, R., & Chinneck, J. (1998). Proctor assignment at Carleton University. Interfaces, 28(2), 58–71.

    Article  Google Scholar 

  • Brailsford, S. C., Potts, C. N., & Smith, B. M. (1999). Constraint satisfaction problems: algorithms and applications. European Journal of Operational Research, 119(3), 557–581.

    Article  Google Scholar 

  • Brélaz, D. (1979). New methods to color the vertices of a graph. Communications of the ACM, 22(4), 251–256.

    Article  Google Scholar 

  • Broder, S. (1964). Final examination scheduling. Communications of the ACM, 7, 494–498.

    Article  Google Scholar 

  • Burke, E. K., & Newall, J. P. (1999). A multistage evolutionary algorithm for the timetable problem. IEEE Transactions on Evolutionary Computation, 3(1), 63–74.

    Article  Google Scholar 

  • Burke, E. K., & Newall, J. P. (2003). Enhancing timetable solutions with local search methods. Lecture notes in computer science (pp. 195–206).

    Google Scholar 

  • Burke, E., Jackson, K., Kingston, J. H., & Weare, R. (1997). Automated university timetabling: the state of the art. The Computer Journal, 40(9), 565–571.

    Article  Google Scholar 

  • Burke, E., Bykov, Y., Newall, J., & Petrovic, S. (2004a). A time-predefined local search approach to exam timetabling problems. IIE Transactions, 36(6), 509–528.

    Article  Google Scholar 

  • Burke, E. K., Kingston, J., & de Werra, D. (2004b). Applications to timetabling. In Handbook of graph theory (pp. 445–474).

    Google Scholar 

  • Burke, E. K., Eckersley, A. J., McCollum, B., Petrovic, S., & Qu, R. (2006). Hybrid variable neighbourhood approaches to university exam timetabling. Technical report, Technical Report NOTTCS-TR-2006-2, School of CSiT, University of Nottingham.

  • Caprara, A., Fischetti, M., Guida, P. L., Monaci, M., Sacco, G., & Toth, P. (2001). Solution of real-world train timetabling problems. In Proceedings of the 34th annual Hawaii international conference on system sciences (p. 10).

    Chapter  Google Scholar 

  • Caramia, M., Dell Olmo, P., & Italiano, G. F. (2001). New algorithms for examination timetabling. Lecture notes in computer science (pp. 230–242).

    Google Scholar 

  • Carter, M. W. (1986). A survey of practical applications of examination timetabling algorithms. Operations Research, 34(2), 193–202.

    Article  Google Scholar 

  • Carter, M. W., & Laporte, G. (1996). Recent developments in practical examination timetabling. In Selected papers from the first international conference on practice and theory of automated timetabling (pp. 3–21). London: Springer.

    Google Scholar 

  • Carter, M. W., Laporte, G., & Chinneck, J. W. (1994). A general examination scheduling system. Interfaces, 24(3), 109–120.

    Article  Google Scholar 

  • Carter, M. W., Laporte, G., & Lee, S. Y. (1996). Examination timetabling: Algorithmic strategies and applications. The Journal of the Operational Research Society, 47(3), 373–383.

    Google Scholar 

  • Casey, S., & Thompson, J. (2003). GRASPing the examination scheduling problem. Lecture notes in computer science (pp. 232–246).

    Google Scholar 

  • Colorni, A., Dorigo, M., & Maniezzo, V. (1998). Metaheuristics for high school timetabling. Computational Optimization and Applications, 9(3), 275–298.

    Article  Google Scholar 

  • Corr, P. H., McCollum, B., McGreevy, M. A. J, & McMullan, P. (2006). A new neural network based construction heuristic for the examination timetabling problem. Lecture notes in computer science (Vol. 4193, p. 392).

    Google Scholar 

  • Costa, D., & Hertz, A. (1998). Ants can colour graphs. The Journal of the Operational Research Society, 48, 295–305.

    Google Scholar 

  • de Werra, D. (1985). An introduction to timetabling. European Journal of Operational Research, 19(2), 151–162.

    Article  Google Scholar 

  • Desroches, S., Laporte, G., & Rousseau, J. M. (1978). Horex: a computer program for the construction of examination schedules. INFOR Information Systems and Operational Research, 16, 294–298.

    Google Scholar 

  • Di Gaspero, L. (2000). Recolour, shake and kick: A recipe for the examination timetabling problem. In Proceedings of the fourth international conference on the practice and theory of automated timetabling (pp. 404–407). Gent, Belgium

    Google Scholar 

  • Di Gaspero, L., & Schaerf, A. (2001). Tabu search techniques for examination timetabling. Lecture notes in computer science (pp. 104–117).

    Google Scholar 

  • Dowsland, K. A., & Thompson, J. M. (2005). Ant colony optimisation for the examination scheduling problem. The Journal of the Operational Research Society, 56(4), 426–438.

    Article  Google Scholar 

  • Dueck, G. (1993). New optimization heuristics: the great deluge algorithm and the record-to-travel. Journal of Computational Physics, 104, 86–92.

    Article  Google Scholar 

  • Easton, K., Nemhauser, G., & Trick, M. (2004). Sports scheduling. In: Handbook of scheduling: algorithms, models, and performance analysis.

  • Erben, W. (2001). A grouping genetic algorithm for graph colouring and exam timetabling. Lecture notes in computer science (pp. 132–158).

    Google Scholar 

  • Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers and Operations Research, 13(5), 533–549.

    Article  Google Scholar 

  • Glover, F., & Laguna, M. (1997). Tabu search. Norwell: Kluwer Academic.

    Book  Google Scholar 

  • Hansen, P., & Mladenovic, N. (2001). Variable neighbourhood search. European Journal of Operational Research, 130, 449–467.

    Article  Google Scholar 

  • Hansen, M. P., & Vidal, R. V. V. (1995). Planning of high school examinations in Denmark. European Journal of Operational Research, 87(3), 519–534.

    Article  Google Scholar 

  • Isaai, M. T., & Singh, M. G. (2001). Hybrid applications of constraint satisfaction and meta-heuristics to railway timetabling: a comparative study. IEEE Transactions on Systems, Man and Cybernetics, Part C, 31(1), 87–95.

    Article  Google Scholar 

  • Kendall, G., & Mohd Hussin, N. (2003). In An investigation of a tabu search based hyper-heuristic for examination timetabling. Selected papers from MISTA (pp. 309–328).

    Google Scholar 

  • Klir, G. J., & Yuan, B. (1995). Fuzzy sets and fuzzy logic. New York: Prentice Hall.

    Google Scholar 

  • Merlot, L. T. G., Boland, N., Hughes, B. D., & Stuckey, P. J. (2003). A hybrid algorithm for the examination timetabling problem. Lecture notes in computer science (pp. 207–231).

    Google Scholar 

  • Mladenovic, N., & Hansen, P. (1997). Variable neighbourhood search. Computers and Operations Research, 24(11), 1097–1100.

    Article  Google Scholar 

  • Morgenstern, C. (1989). Algorithms for general graph coloring. PhD thesis, Department of Computer Science, University of New Mexico.

  • Paquete, L. F., & Fonseca, C. M. (2001). A study of examination timetabling with multiobjective evolutionary algorithms. In Proceedings of the 4th metaheuristics international conference (MIC2001) (pp. 149–153).

    Google Scholar 

  • Petrovic, S., & Burke, E. K. (2004). University timetabling. In Handbook of scheduling: algorithms, models, and performance analysis.

    Google Scholar 

  • Petrovic, S., & Bykov, Y. (2003). A multiobjective optimisation technique for exam timetabling based on trajectories. Lecture notes in computer science (pp. 181–194).

    Google Scholar 

  • Qi, X., Yang, J., & Yu, G. (2004). Scheduling problems in the airline industry. In Handbook of scheduling: algorithms, models, and performance analysis.

    Google Scholar 

  • Qu, R., Burke, E. K., McCollum, B., Merlot, L. T. G., & Lee, S. Y. (2006). A survey of search methodologies and automated approaches for examination timetabling. Computer science (Technical Report No. NOTTCS-TR-2006-4).

  • Ribeiro Filho, G., & Lorena, L. A. N. (2001). A constructive evolutionary approach to school timetabling. In Lecture notes in computer science: Vol. 2037. Applications of evolutionary computing (pp. 130–139).

    Chapter  Google Scholar 

  • Schaerf, A. (1999). Local search techniques for large high school timetabling problems. IEEE Transactions on Systems, Man and Cybernetics, Part A, 29(4), 368–377.

    Article  Google Scholar 

  • Schimmelpfeng, K., & Helber, S. (2007). Application of a real-world university-course timetabling model solved by integer programming. OR-Spektrum, 29(4), 783–803.

    Article  Google Scholar 

  • Sugeno, M., & Kang, G. T. (1988). Structure identification of fuzzy model. Fuzzy Sets and Systems, 28(1), 15–33.

    Article  Google Scholar 

  • Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its applications to modelling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15(1), 116–132.

    Google Scholar 

  • Thompson, J. M., & Dowsland, K. A. (1996). Variants of simulated annealing for the examination timetabling problem. Annals of Operation Research, 63(1), 105–128.

    Article  Google Scholar 

  • Thompson, J. M., & Dowsland, K. A. (1998). A robust simulated annealing based examination timetabling system. Computers and Operations Research, 25(7–8), 637–648.

    Article  Google Scholar 

  • Trick, M. A. (2001). A schedule-then-break approach to sports timetabling Lecture notes in computer science (pp. 242–253).

    Google Scholar 

  • White, G. M., & Xie, B. S. (2001). Examination timetables and tabu search with longer-term memory. Lecture notes in computer science (pp. 85–103).

    Google Scholar 

  • Wood, D. C. (1968). A system for computing examination timetables. The Computer Journal, 11(1), 41–47.

    Article  Google Scholar 

  • Yang, Y., & Petrovic, S. (2005). A novel similarity measure for heuristic selection in examination timetabling. Lecture notes in computer science (Vol. 3616, p. 247).

    Google Scholar 

  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

    Article  Google Scholar 

  • Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning, Part I. Information Sciences, 8(3), 199–249.

    Article  Google Scholar 

  • Zadeh, L. A. (1979). A theory of approximate reasoning. New York: Wiley.

    Google Scholar 

  • Zimmermann, H. J. (1996). Fuzzy set theory and its applications. Norwell: Kluwer Academic.

    Google Scholar 

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Correspondence to Tiago Cardal Pais.

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Pais, T.C., Amaral, P. Managing the tabu list length using a fuzzy inference system: an application to examination timetabling. Ann Oper Res 194, 341–363 (2012). https://doi.org/10.1007/s10479-011-0867-6

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