Abstract
We consider a simplification of a typical university course timetabling problem involving three types of hard and three types of soft constraints. A MAX-MIN Ant System, which makes use of a separate local search routine, is proposed for tackling this problem. We devise an appropriate construction graph and pheromone matrix representation after considering alternatives. The resulting algorithm is tested over a set of eleven instances from three classes of the problem. The results demonstrate that the ant system is able to construct significantly better timetables than an algorithm that iterates the local search procedure from random starting solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Blum, M. Dorigo, S. Correia, O. Rossi-Doria, B. Paechter, and M. Snoek. A GA evolving instructions for a timetable builder. In Proceedings of the 4th International Conference on Practice and Theory of Automated Timetabling (PATAT 2002 ) (to appear), 2002.
E. Bonabeau, M. Dorigo, and G. Theraulaz. From Natural to Artificial Swarm Intelligence. Oxford University Press, 1999.
E. K. Burke, J. P. Newall, and R. F. Weare. A memetic algorithm for university exam timetabling. In Proceedings of the 1st International Conference on Practice and Theory of Automated Timetabling (PATAT 1995), LNCS 1153, pages 241–251. Springer-Verlag, 1996.
W. J. Conover. Practical Nonparametric Statistics. John Wiley & Sons, 3rd edition, 1999.
T. B. Cooper and J. H. Kingston. The complexity of timetable construction problems. In Proceedings of the 1st International Conference on Practice and Theory of Automated Timetabling (PATAT 1995), LNCS 1153, pages 283–295. Springer-Verlag, 1996.
D. Corne, P. Ross, and H.-L. Fang. Evolutionary timetabling: Practice, prospects and workin progress. In Proceedings of the UK Planning and Scheduling SIG Workshop, Strathclyde, 1994.
P. Cowling, G. Kendall, and E. Soubeiga. A hyperheuristic approach to scheduling a sales summit. In Proceedings of the 3rd International Conference on Practice and Theory of Automated Timetabling (PATAT 2000), LNCS 2079, pages 176–190. Springer-Verlag, 2001.
D. Costa and A. Hertz. Ants can colour graphs. Journal of the Operational Research Society, 48:295–305, 1997.
D. de Werra. The combinatorics of timetabling. European Journal of Operational Research, 96:504–513, 1997.
M. Dorigo and G. Di Caro. The Ant Colony Optimization meta-heuristic. In D. Corne, M. Dorigo, and F. Glover, editors, New Ideas in Optimization. McGraw-Hill, 1999.
M. Dorigo, G. Di Caro, and L. M. Gambardella. Ant algorithms for discrete optimization. Artificial Life, 5:137–172, 1999.
M. Dorigo, V. Maniezzo, and A. Colorni. The Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, 26:29–41, 1996.
M. A. S. Elmohamed, P. Coddington, and G. Fox. A comparison of annealing techniques for academic course scheduling. In Proceedings of the 2nd International Conference on Practice and Theory of Automated Timetabling (PATAT 1997), pages 92–115, 1998.
L. D. Gaspero and A. Schaerf. Tabu search techniques for examination timetabling. In Proceedings of the 3rd International Conference on Practice and Theory of Automated Timetabling (PATAT 2000), LNCS 2079, pages 104–117. Springer-Verlag, 2001.
B. Paechter. Course timetabling. Evonet Summer School, 2001. http://evonet.dcs.napier.ac.uk/summerschool2001/problems.html.
B. Paechter, R. C. Rankin, A. Cumming, and T. C. Fogarty. Timetabling the classes of an entire university with an evolutionary algorithm. In Proceedings of the 5th International Conference on Parallel Problem Solving from Nature (PPSN V), LNCS 1498, pages 865–874. Springer-Verlag, 1998.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C. Cambridge University Press, 2nd edition, 1993.
A. Roli, C. Blum, and M. Dorigo. ACO for maximal constraint satisfaction problems. In Proceedings of the 4th Metaheuristics International Conference (MIC 2001), volume 1, pages 187–191, Porto, Portugal, 2001.
O. Rossi-Doria, C. Blum, J. Knowles, M. Sampels, K. Socha, and B. Paechter. A local search for the timetabling problem. In Proceedings of the 4th International Conference on Practice and Theory of Automated Timetabling (PATAT 2002 ) (to appear), 2002.
O. Rossi-Doria, M. Sampels, M. Chiarandini, J. Knowles, M. Manfrin, M. Mastrolilli, L. Paquete, and B. Paechter. A comparison of the performance of different metaheuristics on the timetabling problem. In Proceedings of the 4th International Conference on Practice and Theory of Automated Timetabling (PATAT 2002 ) (to appear), 2002.
T. Stützle and H. H. Hoos. MAX-MIN Ant System. Future Generation Computer Systems, 16(8):889–914, 2000.
H. M. M. ten Eikelder and R. J. Willemen. Some complexity aspects of secondary school timetabling problems. In Proceedings of the 3rd International Conference on Practice and Theory of Automated Timetabling (PATAT 2000), LNCS 2079, pages 18–29. Springer-Verlag, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Socha, K., Knowles, J., Sampels, M. (2002). A MAX-MIN Ant System for the University Course Timetabling Problem. In: Dorigo, M., Di Caro, G., Sampels, M. (eds) Ant Algorithms. ANTS 2002. Lecture Notes in Computer Science, vol 2463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45724-0_1
Download citation
DOI: https://doi.org/10.1007/3-540-45724-0_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44146-5
Online ISBN: 978-3-540-45724-4
eBook Packages: Springer Book Archive