# A constructive approach to examination timetabling based on adaptive decomposition and ordering

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## Abstract

In this study, we investigate an adaptive decomposition and ordering strategy that automatically divides examinations into difficult and easy sets for constructing an examination timetable. The examinations in the difficult set are considered to be hard to place and hence are listed before the ones in the easy set in the construction process. Moreover, the examinations within each set are ordered using different strategies based on graph colouring heuristics. Initially, the examinations are placed into the easy set. During the construction process, examinations that cannot be scheduled are identified as the ones causing infeasibility and are moved forward in the difficult set to ensure earlier assignment in subsequent attempts. On the other hand, the examinations that can be scheduled remain in the easy set. Within the easy set, a new subset called the boundary set is introduced to accommodate shuffling strategies to change the given ordering of examinations. The proposed approach, which incorporates different ordering and shuffling strategies, is explored on the Carter benchmark problems. The empirical results show that the performance of our algorithm is broadly comparable to existing constructive approaches.

## Keywords

Timetabling Decomposition Graph colouring Heuristic Grouping## Preview

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## References

- Abdul Rahman, S., Bargiela, A., Burke, E. K., McCollum, B., & Özcan, E. (2009). Construction of examination timetables based on ordering heuristics. In
*Proceedings of the 24th international symposium on computer and information sciences*(pp. 727–732). Google Scholar - Abdul Rahman, S., Bargiela, A., Burke, E. K., McCollum, B., & Özcan, E. (2010). A constructive approach for examination timetabling based on adaptive decomposition and ordering. In
*Proceedings of the 8th international conference on the practice and theory of automated timetabling*(pp. 353–372). Google Scholar - Abdullah, S., Ahmadi, S., Burke, E. K., & Dror, M. (2007). Investigating Ahuja-Orlin’s large neighbourhood search approach for examination timetabling.
*OR-Spektrum*,*29*(2), 351–372. CrossRefGoogle Scholar - Asmuni, H., Burke, E. K., Garibaldi, J. M., McCollum, B., & Parkes, A. J. (2009). An investigation of fuzzy multiple heuristic orderings in the construction of university examination timetables.
*Computers & Operations Research*,*36*(4), 981–1001. CrossRefGoogle Scholar - Balakrishnan, N., Lucena, A., & Wong, R. T. (1992). Scheduling examinations to reduce second order conflicts.
*Computers & Operations Research*,*19*, 353–361. CrossRefGoogle Scholar - Bilgin, B., Özcan, E., & Korkmaz, E. E. (2007). An experimental study on hyper-heuristics and exam scheduling. In E. K. Burke & H. Rudova (Eds.),
*Lecture notes in computer science: Vol.**3867*.*Practice and theory of automated timetabling VI: Selected papers from the 6th international conference*(pp. 394–412). Berlin: Springer. CrossRefGoogle Scholar - Boizumault, P., Delon, Y., & Peridy, L. (1996). Constraint logic programming for examination timetabling.
*The Journal of Logic Programming*,*26*(2), 217–233. CrossRefGoogle 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. CrossRefGoogle Scholar - Burke, E. K., & Newall, J. P. (2003). Enhancing timetable solutions with local search methods. In
*Lecture notes in computer science: Vol.**2740*.*Practice and theory of automated timetabling IV: selected papers from the 4th international conference*(pp. 195–206). Berlin: Springer. CrossRefGoogle Scholar - Burke, E. K., & Newall, J. P. (2004). Solving examination timetabling problems through adaptation of heuristic orderings.
*Annals of Operations Research*,*129*, 107–134. CrossRefGoogle Scholar - Burke, E. K., Elliman, D. G., & Weare, R. (1995). A hybrid genetic algorithm for highly constrained timetabling problems. In
*The proceedings of the 6th international conference on genetic algorithms (ICGA’95)*, San Francisco, CA, USA, Pittsburgh, USA. Google Scholar - Burke, E. K., Hart, E., Kendall, G., Newall, J., Ross, P., & Schulenburg, S. (2003). Hyper-heuristics: an emerging direction in modern search technology. In F. Glover & G. Kochenberger (Eds.),
*Handbook of meta-heuristics*(pp. 457–474). Dordrecht: Kluwer. Google Scholar - Burke, E. K., Bykov, Y., Newall, J. P., & Petrovic, S. (2004a). A time-predefined local search approach to exam timetabling problem.
*IIE Transactions*,*36*(6), 509–528. CrossRefGoogle Scholar - Burke, E. K., Kingston, J., & de Werra, D. (2004b). Applications to timetabling. In J. Gross & J. Yellen (Eds.),
*Handbook of graph theory*(pp. 445–474). London: Chapman Hall/CRC Press. Google Scholar - Burke, E. K., Petrovic, S., & Qu, R. (2006). Case based heuristic selection for timetabling problems.
*Journal of Scheduling*,*9*(2), 115–132. CrossRefGoogle Scholar - Burke, E. K., Eckersley, A. J., McCollum, B., Petrovic, S., & Qu, R. (2010a). Hybrid variable neighbourhood approaches to university exam timetabling.
*European Journal of Operational Research*,*206*(1), 46–53. CrossRefGoogle Scholar - Burke, E. K., Kendall, G., Misir, M., & Özcan, E. (2010b). Monte Carlo hyper-heuristics for examination timetabling.
*Annals of Operations Research*. doi: 10.1007/s10479-010-0782-2. - Burke, E. K., Pham, N., Qu, R., & Yellen, J. (2010c). Linear combinations of heuristics for examination timetabling.
*Annals of Operations Research*. doi: 10.1007/s10479-011-0854-y. - Caramia, M., Dell’Olmo, P., & Italiano, G. F. (2008). Novel local search based approaches to university examination timetabling.
*INFORMS Journal on Computing*,*20*, 86–99. CrossRefGoogle Scholar - Carter, M. W. (1986). A survey of practical applications of examination timetabling algorithms.
*Operational Research*,*34*(2), 193–202. CrossRefGoogle 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., & Lee, S. (1996). Examination timetabling: algorithmic strategies and applications.
*The Journal of the Operational Research Society*,*47*(3), 373–383. CrossRefGoogle Scholar - Casey, S., & Thompson, J. (2003). Grasping the examination scheduling problem. In
*Lecture notes in computer science: Vol.**2740*.*Practice and theory of automated timetabling IV: selected papers from the 4th international conference*(pp. 234–244). Berlin: Springer. CrossRefGoogle Scholar - Corr, P., McCollum, B., McGreevy, M., & McMullan, P. (2006). A new neural network based construction heuristic for the examination timetabling problem. In
*Lecture notes in computer science: Vol.**4193*.*Parallel problem solving from nature—PPSN IX*(pp. 392–401). Berlin: Springer. CrossRefGoogle Scholar - David, P. (1998). A constraint-based approach for examination timetabling using local repair techniques. In E. K. Burke & M. W. Carter (Eds.),
*Lecture notes in computer science: Vol.**1408*.*Practice and theory of automated timetabling II: selected papers from the 2nd international conference*(pp. 169–186). Berlin: Springer. CrossRefGoogle Scholar - Di Gaspero, L., & Schaerf, A. (2001). Tabu search techniques for examination timetabling. In
*Lecture notes in computer science*.*Practice and theory of automated timetabling III: selected papers from the 3rd international conference*(pp. 104–117). Berlin: Springer. CrossRefGoogle Scholar - Eley, M. (2007). Ant algorithms for the exam timetabling problem. In E. K. Burke & H. Rudova (Eds.),
*Lecture notes in computer science: Vol.**3867*.*Practice and theory of automated timetabling VI: selected papers from the 6th international conference*(pp. 364–382). Berlin: Springer. CrossRefGoogle Scholar - Ersoy, E., Özcan, E., & Sima Uyar, A. (2007). Memetic algorithms and hyperhill-climbers. In P. Baptiste, G. Kendall, A. M. Kordon, & F. Sourd (Eds.),
*Lecture notes in computer science*.*Multidisciplinary international conference on scheduling: theory and applications: selected papers from the 3rd international conference*(pp. 159–166). Berlin: Springer. Google Scholar - Joslin, D. E., & Clements, D. P. (1999). “Squeaky wheel” optimization.
*The Journal of Artificial Intelligence Research*,*10*, 353–357. Google Scholar - Merlot, L. T. G., Boland, N., Hughes, B. D., & Stuckey, P. J. (2003). A hybrid algorithm for the examination timetabling problem. In E. K. Burke & W. Erben (Eds.),
*Lecture notes in computer science: Vol.**2740*.*Practice and theory of automated timetabling V: selected papers from the 4th international conference*(pp. 207–231). Berlin: Springer. CrossRefGoogle Scholar - Mumford, C. L. (2010). A multiobjective framework for heavily constrained examination timetabling problems.
*Annals of Operations Research*,*180*(1), 3–31. CrossRefGoogle Scholar - Özcan, E., & Ersoy, E. (2005). Final exam scheduler—FES. In
*Proceedings of the IEEE congress on evolutionary computation (CEC’05)*(Vol. 2, pp. 1356–1363). CrossRefGoogle Scholar - Özcan, E., Bilgin, B., & Korkmaz, E. E. (2008). A comprehensive analysis of hyper-heuristics.
*Intelligent Data Analysis*,*12*(1), 3–23. Google Scholar - Özcan, E., Bykov, Y., Birben, M., & Burke, E. K. (2009). Examination timetabling using late acceptance hyper-heuristics. In
*Proceedings of the 2009 IEEE congress on evolutionary computation (CEC 2009)*, Trondheim, Norway (pp. 997–1004). New York: IEEE Press. CrossRefGoogle Scholar - Özcan, E., Misir, M., Ochoa, G., & Burke, E. K. (2010). A reinforcement learning—great-deluge hyper-heuristic for examination timetabling.
*International Journal of Applied Metaheuristic Computing*,*1*(1), 39–59. CrossRefGoogle Scholar - Paquete, L., & Stuetzle, T. (2002). Empirical analysis of tabu search for the lexicographic optimization of the examination timetabling problem. In
*The proceedings of the 4th international conference on the practice and theory of automated timetabling (PATAT IV)*, Gent, Belgium (pp. 413–420). Google Scholar - Petrovic, S., & Burke, E. (2004). University timetabling. In
*Handbook of scheduling: algorithms, models, and performance analysis,*Chap. 45. London: Chapman Hall/CRC Press. Google Scholar - Petrovic, S., & Bykov, Y. (2003). A multiobjective optimisation technique for exam timetabling based on trajectories. In E. K. Burke & P. De Causmaecker (Eds.),
*Lecture notes in computer science: Vol.**2740*.*Practice and theory of automated timetabling IV: selected papers from the 4th international conference*(pp. 179–192). Berlin: Springer. Google Scholar - Pillay, N., & Banzhaf, W. (2009). A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examination timetabling problem.
*European Journal of Operational Research*,*197*(2), 482–491. CrossRefGoogle Scholar - Qu, R., & Burke, E. K. (2007). Adaptive decomposition and construction for examination timetabling problems. In
*Multidisciplinary international scheduling: theory and applications (MISTA’07)*, Paris, France (pp. 418–425). Google Scholar - Qu, R., Burke, E. K., Mccollum, B., Merlot, L. T., & Lee, S. Y. (2009). A survey of search methodologies and automated system development for examination timetabling.
*Journal of Scheduling*,*12*(1), 55–89. CrossRefGoogle Scholar - Thompson, J., & Dowsland, K. (1996). Variants of simulated annealing for the examination timetabling problem.
*Annals of Operations Research*,*63*, 105–128. CrossRefGoogle Scholar - Ülker, Ö., Özcan, E., & Korkmaz, E. E. (2007). Linear linkage encoding in grouping problems: applications on graph coloring and timetabling. In
*Lecture notes in computer science: Vol.**3867*.*Selected papers from the Practice and theory of automated timetabling 2006*(pp. 347–363). Berlin: Springer. Google Scholar - White, G. M., & Xie, B. S. (2001). Examination timetables and tabu search with longer-term memory. In E. K. Burke & W. Erben (Eds.),
*Lecture notes in computer science: Vol.**2079*.*Practice and theory of automated timetabling III: selected papers from the 3rd international conference*(pp. 85–103). Berlin: Springer. CrossRefGoogle Scholar