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Answer set programming as a modeling language for course timetabling

Published online by Cambridge University Press:  25 September 2013

MUTSUNORI BANBARA ,
TAKEHIDE SOH ,
NAOYUKI TAMURA ,
KATSUMI INOUE  and
TORSTEN SCHAUB
MUTSUNORI BANBARA
Affiliation:
Kobe University, 1-1 Rokko-dai, Nada-ku, Kobe, Hyogo 657-8501, Japan (e-mail: banbara@kobe-u.ac.jp, soh@lion.kobe-u.ac.jp, tamura@kobe-u.ac.jp)
TAKEHIDE SOH
Affiliation:
Kobe University, 1-1 Rokko-dai, Nada-ku, Kobe, Hyogo 657-8501, Japan (e-mail: banbara@kobe-u.ac.jp, soh@lion.kobe-u.ac.jp, tamura@kobe-u.ac.jp)
NAOYUKI TAMURA
Affiliation:
Kobe University, 1-1 Rokko-dai, Nada-ku, Kobe, Hyogo 657-8501, Japan (e-mail: banbara@kobe-u.ac.jp, soh@lion.kobe-u.ac.jp, tamura@kobe-u.ac.jp)
KATSUMI INOUE
Affiliation:
National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan (e-mail: inoue@nii.ac.jp)
TORSTEN SCHAUB
Affiliation:
University of Potsdam, August-Bebel-Strasse 89, D-14482 Potsdam, Germany (e-mail: torsten@cs.uni-potsdam.de)
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Abstract

The course timetabling problem can be generally defined as the task of assigning a number of lectures to a limited set of timeslots and rooms, subject to a given set of hard and soft constraints. The modeling language for course timetabling is required to be expressive enough to specify a wide variety of soft constraints and objective functions. Furthermore, the resulting encoding is required to be extensible for capturing new constraints and for switching them between hard and soft, and to be flexible enough to deal with different formulations. In this paper, we propose to make effective use of ASP as a modeling language for course timetabling. We show that our ASP-based approach can naturally satisfy the above requirements, through an ASP encoding of the curriculum-based course timetabling problem proposed in the third track of the second international timetabling competition (ITC-2007). Our encoding is compact and human-readable, since each constraint is individually expressed by either one or two rules. Each hard constraint is expressed by using integrity constraints and aggregates of ASP. Each soft constraint S is expressed by rules in which the head is the form of penalty(S,V,C), and a violation V and its penalty cost C are detected and calculated respectively in the body. We carried out experiments on four different benchmark sets with five different formulations. We succeeded either in improving the bounds or producing the same bounds for many combinations of problem instances and formulations, compared with the previous best known bounds.

Keywords

answer set programmingeducational timetablingcourse timetabling

Information

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 13 , Special Issue 4-5: 29th International Conference on Logic Programming , July 2013 , pp. 783 - 798
Copyright
Copyright © 2013 [MUTSUNORI BANBARA, TAKEHIDE SOH, NAOYUKI TAMURA, KATSUMI INOUE and TORSTEN SCHAUB] 

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References

Achá, R. A. and Nieuwenhuis, R. 2012. Curriculum-based course timetabling with SAT and MaxSAT. Annals of Operations Research (February 2012), 1–21.Google Scholar
Andres, B., Kaufmann, B., Matheis, O. and Schaub, T. 2012. Unsatisfiability-based optimization in clasp. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12), Dovier, A. and Costa, V. S., Eds. Leibniz International Proceedings in Informatics (LIPIcs), vol. 17, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 211–221.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.CrossRefGoogle Scholar
Bonutti, A., Cesco, F. D., Gaspero, L. D. and Schaerf, A. 2012. Benchmarking curriculum-based course timetabling: formulations, data formats, instances, validation, visualization, and results. Annals of Operations Research 194, 1, 59–70.CrossRefGoogle Scholar
Burke, E. K., Marecek, J., Parkes, A. J. and Rudová, H. 2010a. Decomposition, reformulation, and diving in university course timetabling. Computers & Operations Research 37, 3, 582–597.CrossRefGoogle Scholar
Burke, E. K., Marecek, J., Parkes, A. J. and Rudová, H. 2010b. A supernodal formulation of vertex colouring with applications in course timetabling. Annals of Operations Research 179, 1, 105–130.CrossRefGoogle Scholar
Burke, E. K., Marecek, J., Parkes, A. J. and Rudová, H. 2012. A branch-and-cut procedure for the udine course timetabling problem. Annals of Operations Research 194, 1, 71–87.CrossRefGoogle Scholar
Burke, E. K. and Petrovic, S. 2002. Recent research directions in automated timetabling. European Journal of Operational Research 140, 2, 266–280.CrossRefGoogle Scholar
Carter, M. W. 2001. A comprehensive course timetabling and student scheduling system at the university of waterloo. In Proceedings of the 3th International Conference on the Practice and Theory of Automated Timetabling (PATAT 2000), Burke, E. K. and Erben, W., Eds. Lecture Notes in Computer Science, vol. 2079, Springer, 64–84.Google Scholar
Daskalaki, S. and Birbas, T. 2005. Efficient solutions for a university timetabling problem through integer programming. European Journal of Operational Research 160, 1, 106–120.CrossRefGoogle Scholar
Faber, W., Leone, N. and Pfeifer, G. 1998. Representing school timetabling in a disjunctive logic programming language. In Proceedings of the 13th Workshop on Logic Programming (WLP'98), Egly, U. and Tompits, H., Eds. 43–52.Google Scholar
Gaspero, L. D., McCollum, B. and Schaerf, A. 2007. The second international timetabling competition (ITC-2007): Curriculum-based course timetabling (track 3). Technical report, Queen's University, Belfast, United Kingdom. URL: http://www.cs.qub.ac.uk/itc2007/curriculmcourse/report/curriculumtechreport.pdf.Google Scholar
Gaspero, L. D. and Schaerf, A. 2003. Multi-neighbourhood local search with application to course timetabling. In Proceedings of the 4th International Conference on the Practice and Theory of Automated Timetabling (PATAT 2002), Burke, E. K. and Causmaecker, P. D., Eds. Lecture Notes in Computer Science, vol. 2740, Springer, Berlin Heidelberg, 262–275.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2012. Answer Set Solving in Practice, Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T., Schneider, M. T. and Ziller, S. 2011. A portfolio solver for answer set programming: Preliminary report. In Proceedings of the 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2011), Delgrande, J. P. and Faber, W., Eds. Lecture Notes in Computer Science, vol. 6645, Springer, 352–357.CrossRefGoogle Scholar
Gebser, M., Kaufmann, B., Neumann, A. and Schaub, T. 2007. Conflict-driven answer set solving. In Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), MIT Press, 386–392.Google Scholar
Gebser, M., Kaufmann, B. and Schaub, T. 2009. The conflict-driven answer set solver clasp: Progress report. In Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2009), Erdem, E., Lin, F. and Schaub, T., Eds. Lecture Notes in Computer Science, vol. 5753. Springer, 509–514.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proceedings of the Fifth International Conference and Symposium on Logic Programming, MIT Press, 1070–1080.Google Scholar
Gotlieb, C. C. 1962. The construction of class-teacher time-tables. In Proceedings of IFIP Congress 62, Popplewell, C. M., Ed. North-Holland, 73–77.Google Scholar
Lach, G. and Lübbecke, M. E. 2012. Curriculum based course timetabling: New solutions to udine benchmark instances. Annals of Operations Research 194, 1, 255–272.CrossRefGoogle Scholar
Lewis, R. 2007. A survey of metaheuristic-based techniques for university timetabling problems. OR Spectrum 30, 1, 167–190.CrossRefGoogle Scholar
McCollum, B. 2007. A perspective on bridging the gap between theory and practice in university timetabling. In Proceedings of the 6th International Conference on the Practice and Theory of Automated Timetabling (PATAT 2006), Revised Selected Papers, Burke, E. K. and Rudová, H., Eds. Lecture Notes in Computer Science, vol. 3867, Springer, 3–23.Google Scholar
McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., Gaspero, L. D., Qu, R. and Burke, E. K. 2010. Setting the research agenda in automated timetabling: The second international timetabling competition. INFORMS Journal on Computing 22, 1, 120–130.CrossRefGoogle Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241–273.CrossRefGoogle Scholar
Qualizza, A. and Serafini, P. 2005. A column generation scheme for faculty timetabling. In Proceedings of the 5th international conference on the practice and theory of automated timetabling (PATAT 2004), Burke, E. K. and Trick, M. A., Eds. Lecture Notes in Computer Science, vol. 3616, Springer, 161–173.Google Scholar
Schaerf, A. 1999. A survey of automated timetabling. Artificial Intelligence Review 13, 2, 87–127.CrossRefGoogle Scholar
Schimmelpfeng, K. and Helber, S. 2007. Application of a real-world university-course timetabling model solved by integer programming. OR Spectrum 29, 4, 783–803.CrossRefGoogle Scholar
Schutt, A., Feydy, T., Stuckey, P. J. and Wallace, M. G. 2011. Explaining the cumulative propagator. Constraints 16, 3, 250–282.CrossRefGoogle Scholar
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