Abstract
As well as nearly always belonging to the class of NP-complete problems, university timetabling problems can be further complicated by the often idiosyncratic requirements imposed by the particular institution being considered. It is perhaps due to this characteristic that in the past decade-or-so, metaheuristics have become increasingly popular in the field of automated timetabling. In this paper we carry out an overview of such applications, paying particular attention to the various methods that have been proposed for dealing and differentiating between constraints of varying importance. Our review allows us to classify these algorithms into three general classes, and we make some instructive comments on each of these.
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References
Abramson D (1991) Constructing school timetables using simulated annealing: sequential and parallel algorithms. Manag Sci 37(1):98–113
Abramson D, Krishnamoorthy H, Dang H (1996) Simulated annealing cooling schedules for the school timetabling problem. Asia Pacific J Operational Res 16:1–22
Arntzen H, Løkketangen A (2005) A tabu search heuristic for a university timetabling problem. In: Ikabaki T, Nonobe K, Yagiura M (eds) Metaheuristics: progress as real problem solvers, vol 32. Springer, Berlin, pp 65–86
Balakrishnan N (1991) Examination scheduling: a computerized application. Omega 19(1):37–41
Batenburg KJ, Palenstijn WJ (2003) A new exam timetabling algorithm. In: Proceedings of the Belgian-Dutch artificial intelligence conference (BNAIC 2003), pp 19–26
Birattari M, Sttzle T, Paquete L, Varrentrapp K (2002) A racing algorithm for configuring metaheuristics. In: Langdon WB, Mathias K, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter MA, Schultz AC, Miller JF, Burke E, Jonoska N (eds) The genetic and evolutionary computation conference (GECCO) 2002. Morgan Kaufmann Publishers Inc, New York, pp 11–18
Boizumault P, Delon Y, Peridy L (1996) Logic programming for examination timetabling. Logic Program 26:217–233
Burke E, Newall JP (1999) A multi-stage evolutionary algorithm for the timetable problem. IEEE Trans Evol Comput 3(1):63–74
Burke E, Petrovic M (2002) Recent research directions in automated timetabling. Eur J Oper Res 140(2):266–280
Burke E, Elliman D, Weare R (1995a) The automation of the timetabling process in higher education. J Educ Technol Syst 23:257–266
Burke E, Elliman D, Weare R (1995b) A hybrid genetic algorithm for highly constrained timetabling problems. In: Eshelman L (ed) Genetic algorithms: proceedings of the sixth international conference (ICGA95). Morgan Kaufmann, pp 605–610
Burke E, Elliman D, Weare R (1995c) Specialised recombinative operators for timetabling problems. In: The artificial intelligence and simulated behaviour workshop on evolutionary computing, vol 993. Springer, Berlin, pp 75–85
Burke E, Elliman DG, Ford PH, Weare R (1996a) Examination timetabling in british universities: a survey. In: Burke E, Ross P (eds) Practice and theory of automated timetabling (PATAT) I, vol 1153. Springer, Berlin, pp 76–92
Burke E, Newall JP, Weare RF (1996b) A memetic algorithm for university exam timetabling. In: Burke E, Ross P (eds) Practice and theory of automated timetabling (PATAT) I, vol 1153. Springer, Berlin, pp 241–250
Burke E, Bykov Y, Petrovic M (2001) A multicriteria approach to examination timetabling. In: Burke E, Erben E (eds) practice and theory of automated timetabling (PATAT) III, vol 2070. Springer, Berlin, pp 118–131
Burke E, Bykov Y, Newall JP, Petrovic S (2003a) A time-defined approach to course timetabling. Yugoslav J Oper Res (YUJOR) 13(2):139–151
Burke E, Kendall G, Soubeiga E (2003b) A tabu-search hyperheuristic for timetabling and rostering. J Heuristics 9(6):451–470
Burke E, McCollum B, Meisels A, Petrovic S, Qu R (2007) A graph-based hyper heuristic for timetabling problems. Eur J Oper Res 176
Carrasco M, Pato M (2001) A multiobjective genetic algorithm for the class/teacher timetabling problem. In: Burke E, Erben W (eds) Practice and theory of automated timetabling (PATAT) III, vol 2079. Springer, Berlin, pp 3–17
Carrasco M, Pato M (2004) Metaheuristics: computer decision-making, chapter A Potts neural network heuristic for the class/teacher timetabling problem. Kluwer, Norwell, pp 173–186
Carter M (1986a) A langarian relaxation approach to the classroom assignment problem. INFOR 27(2):230–246
Carter M (1986b) A survey of practical applications of examination timetabling algorithms. Oper Res 34(2):193–202
Carter M, Laporte G (1998) Recent developments in practical course timetabling. In: Burke E, Carter M (eds) Practice and theory of automated timetabling (PATAT) II, vol 1408. Springer, Berlin, pp 3–19
Carter M, Laporte G, Lee SY (1996) Examination timetabling: algorithmic strategies and applications. J Oper Res Soc 47:373–383
Casey S, Thompson J (2002) Grasping the examination scheduling problem. In: Burke E, De Causmaecker P (eds) Practice and theory of automated timetabling (PATAT) IV, vol 2740. Springer, Berlin, pp 233–244
Chiarandini M, Socha K, Birattari M, Rossi-Doria O (2003) An effective hybrid approach for the university course timetabling problem. Technical Report AIDA-2003-05, FG Intellektik, FB Informatik, TU Darmstadt, Germany
Colorni A, Dorigo M, Maniezzo V (1991) Genetic algorithms and highly constrained problems: the time-table case. In: Schwefel H-P, Manner R (eds) Parallel problem solving from nature (PPSN) I, vol 496. Springer, Berlin, pp 55–59
Colorni A, Dorigo M, Maniezzo V (1992) A genetic algorithm to solve the timetable problem. Technical Report 90-060 revised, Politecnico di Milano, Italy 1992
Colorni A, Dorigo M, Maniezzo V (1997) Metaheuristics for high-school timetabling. Comput Optim Appl 9(3):277–298
Cooper T, Kingston J (1996) The complexity of timetable construction problems. In: Burke E, Ross P (eds) Practice and theory of automated timetabling (PATAT) I, vol 1153. Springer, Berlin, pp 283–295
Corne D, Ross P, Fang H (1995) Evolving timetables. In: Lance C. Chambers (ed) The practical handbook of genetic algorithms, vol 1. CRC, Florida, pp 219–276
Costa D (1994) A tabu search algorithm for computing an operational timetable. Eur J Oper Res 79:98–110
Cote P, Wong T, Sabourin R (2005) Application of a hybrid multi-objective evolutionary algorithm to the uncapacitated exam proximity problem. In: Burke E, Trick M (eds) Practice and theory of automated timetabling (PATAT) V, vol 3616. Springer, Berlin, pp 294–312
Daskalaki S, Birbas T, Housos E (2004) An integer programming formulation for a case study in university timetabling. Eur J Oper Res 153:117–135
De Werra D (1985) An introduction to timetabling. Eur J Oper Res 19(2):151–162
Deris B, Omatu S, Ohta H, Samat D (1997) University timetabling by constraint-based reasoning: a case study. J Oper Res Soc 48(12):1178–1190
Di Gaspero L, Schaerf A (2001) Tabu search techniques for examination timetabling. In: Burke E, Erben E (eds) Practice and theory of automated timetabling (PATAT) III, vol 2079. Springer, Berlin, pp 104–117
Di Gaspero L, Schaerf A (2002) Multi-neighbourhood local search with application to course timetabling. In: Burke E, De Causmaecker P (eds) Practice and theory of automated timetabling (PATAT) IV, vol 2740. Springer, Berlin, pp 263–287
Dueck G (1993) New optimization heuristics: the great deluge algorithm and the record-to-record travel. J Comput Phys 104:86–92
Elmohamed S, Fox G, Coddington P (1998) A comparison of annealing techniques for academic course scheduling. In: Burke E, Carter M (eds) Practice and theory of automated timetabling (PATAT) II, vol 1408. Springer, Berlin, pp 146–166
Erben E (2001) A grouping genetic algorithm for graph colouring and exam timetabling. In: Burke E, Erben W (eds), Practice and theory of automated timetabling (PATAT) III, vol 2079. Springer, Berlin, pp 132–158
Even S, Itai A, Shamir A (1976) On the complexity of timetable and multicommodity flow problems. SIAM J Comput 5(4):691–703
Falkenauer E (1994) A new representation and operators for genetic algorithms applied to grouping problems. Evol Comput 2(2):123–144
Falkenauer E (1998) Genetic algorithms and grouping problems. Wiley, London
Garey MR, Johnson DS (1979) Computers and intractability—a guide to NP-completeness, 1st edn. W. H. Freeman and Company, San Francisco
Garey MR, Johnson DS, Stockmeyer L (1976) Some simplified np-complete graph problems. Theor Comput Sci 1:237–267
Gislen L, Peterson C, Soderberg B (1989) Teachers and classes with neural networks. Int J Neural Syst 1:167–176
Goltz H-J, Matzke D (1999) University timetabling using constraint logic programming. In: Practical aspects of declarative languages, vol 1511 of Lecture notes in computer science, Springer, Heidelberg, pp 320–334
Guéret C, Jussien N, Boizumault P, Prins C (1996) Building university timetables using constraint logic programming. In: Practice and theory of automated timetabling I (PATAT I), vol 1153 of Lecture notes in computer science. Springer, Heidelberg, pp 130–145
Hertz A (1991) Tabu search for large scale timetabling problems. Eur J Oper Res 54(1):39–47
Kirkpatrick S, Gelatt C, Vecchi M (1983) Optimization by simulated annealing. Science 4598:671–680
Kostuch P (2005) The university course timetabling problem with a 3-phase approach. In: Burke E, Trick M (eds) Practice and theory of automated timetabling (PATAT) V, vol 3616. Springer, Berlin, pp 109–125
Kovacic M (1993) Timetable construction using markovian neural network. Eur J Oper Res 69:92–96
Lajos G (1996) Complete university modular timetabling using constraint logic programming. In: Burke E, Ross P (eds) Practice and theory of automated timetabling (PATAT) I, vol 1153. Springer, Berlin, pp 146–161
Lewis R (2006) Metaheuristics for University course timetabling. PhD thesis, School of Computing, Napier University, Edinburgh, October
Lewis R, Paechter B (2004) New crossover operators for timetabling with evolutionary algorithms. In: Lofti A (ed) The fifth international conference on recent advances in soft computing RASC2004. Nottingham, England, pp 189–194
Lewis R, Paechter B (2007) Finding feasible timetables using group based operators. IEEE Trans Evol Comput 11(3):397–413
Melicio F, Caldeira J (1998) Timetabling implementation aspects by simulated annealing. In: Jifa Gu (ed) IEEE systems science and systems engineering. Beijing. Aceite, pp 553–557
Merlot L, Boland N, Hughes B, Stuckey P (2003) A hybrid algorithm for the examination timetabling problem. In: Burke E, De. Causmaeker P (eds) The practice and theory of automated timetabling (PATAT) IV, vol 2740. Springer, Berlin, pp 207–231
Morgenstern C (1989) Algorithms for general graph coloring. PhD thesis, University of New Mexico
Morgenstern C, Shapiro H (1990) Coloration neighborhood structures for general graph coloring. In: Proceedings of the first annual ACM-SIAM symposium on discrete algorithms. San Francisco, California, USA, Society for Industrial and Applied Mathematics, pp 226–235
Paechter B, Rankin R, Cumming A, Fogarty T (1998) Timetabling the classes of an entire university with an evolutionary algorithm. In: Baeck T, Eiben A, Schoenauer M, Schwefel H (eds) Parallel problem solving from nature (PPSN) V, vol 1498. Springer, Berlin, pp 865–874
Paquete L, Fonseca C (2001) A study of examination timetabling with multiobjective evolutionary algorithms. In: 4th metaheuristics international conference (MIC 2001). Porto, pp 149–154
Petrovic S, Bykov Y (2003) A multiobjective optimisation approach for exam timetabling based on trajectories. In: Burke E, De Causmaecker P (eds) The paractice and theory of automated timetabling (PATAT) IV, vol 2740. Springer, Berlin, pp 181–194
Richardson JT, Palmer MR, Liepins G, Hilliard M (1989) Some guidelines for genetic algorithms with penalty functions. In: Schaffer JD (ed) The third international conference on genetic algorithms. Morgan Kaufmann Publishers Inc, San Francisco, pp 191–197
Ross P, Hart E, Corne D (2003) Genetic algorithms and timetabling. In: Ghosh A, Tsutsui K (eds) Advances in evolutionary computing: theory and applications. Springer, New York, pp 755–771
Rossi-Doria O, Knowles J, Sampels M, Socha K, Paechter B (2002) A local search for the timetabling problem. In: Burke E, Causmaecker P (eds) Practice and theory of automated timetabling (PATAT) IV. Gent, Belgium, pp 124–127
Schaerf A (1996) Tabu search techniques for large high-school timetabling problems. In: Proceedings of the thirteenth national conference on artificial intelligence. AAAI Press/MIT Press, Portland (OR), pp 363–368
Schaerf A (1999) Local search techniques for large high-school timetabling problems. IEEE Trans Syst Man Cyber Part A 29(4):368–377
Schaerf A (1999) A survey of automated timetabling. Artif Intell Rev 13(2):87–127
Schimmelpfeng K, Helber S (2007) Application of a real-world university-course timetabling model solved by integer programming. OR Spect 29(4)
Smith K, Abramson D, Duke D (2003) Hopfield neural networks for timetabling: formulations, methods, and comparative results. Comput Ind Eng 44(2):283–305
Socha K, Samples M (2003) Ant algorithms for the university course timetabling problem with regard to the state-of-the-art. In: Evolutionary computation in combinatorial optimization (EvoCOP 2003), vol 2611. Springer, Berlin, pp 334–345
Socha K, Knowles J, Samples M (2002) A max-min ant system for the university course timetabling problem. In: Dorigo M, Di Caro G, Samples M (eds) Proceedings of ants 2002—third international workshop on ant algorithms (Ants’2002), vol 2463. Springer, Berlin, pp 1–13
Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2:221–248
Thompson JM, Dowsland KA (1998) A robust simulated annealing based examination timetabling system. Comput Oper Res 25(7/8):637–648
Tripathy A (1984) School timetabling—a case in large binary linear integer programming. Manag Sci 30:1473–1489
White G, Chan W (1979) Towards the construction of optimal examination schedules. INFOR 17:219–229
Yu E, Sung K-S (2002) A genetic algorithm for a university weekly courses timetabling problem. Int Trans Oper Res 9:703–717
Zitzler E, Laumanns M, Thiele L (2001) Spea2: improving the strength pareto evolutionary algorithm for multiobjective optimization. Technical Report 103, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland
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The author would like to give thanks to Ben Paechter at Napier University, Edinburgh, and Barry McCollum of Queens University, Belfast for providing the initial motivation for the production of this work. The author is also grateful to Peter Morgan, Bruce Curry, and Jonathan Thompson at Cardiff University and also an anonymous referee for their helpful comments and insights.
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Lewis, R. A survey of metaheuristic-based techniques for University Timetabling problems. OR Spectrum 30, 167–190 (2008). https://doi.org/10.1007/s00291-007-0097-0
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DOI: https://doi.org/10.1007/s00291-007-0097-0