Skip to main content
×
×
Home

Answer set programming as a modeling language for course timetabling

  • MUTSUNORI BANBARA (a1), TAKEHIDE SOH (a1), NAOYUKI TAMURA (a1), KATSUMI INOUE (a2) and TORSTEN SCHAUB (a3)...
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.

Copyright
References
Hide All
Achá, R. A. and Nieuwenhuis, R. 2012. Curriculum-based course timetabling with SAT and MaxSAT. Annals of Operations Research (February 2012), 1–21.
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, 211221.
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.
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, 5970.
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, 582597.
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, 105130.
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, 7187.
Burke, E. K. and Petrovic, S. 2002. Recent research directions in automated timetabling. European Journal of Operational Research 140, 2, 266280.
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, 6484.
Daskalaki, S. and Birbas, T. 2005. Efficient solutions for a university timetabling problem through integer programming. European Journal of Operational Research 160, 1, 106120.
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. 4352.
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.
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, 262275.
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.
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, 352357.
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, 386392.
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, 509514.
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, 10701080.
Gotlieb, C. C. 1962. The construction of class-teacher time-tables. In Proceedings of IFIP Congress 62, Popplewell, C. M., Ed. North-Holland, 7377.
Lach, G. and Lübbecke, M. E. 2012. Curriculum based course timetabling: New solutions to udine benchmark instances. Annals of Operations Research 194, 1, 255272.
Lewis, R. 2007. A survey of metaheuristic-based techniques for university timetabling problems. OR Spectrum 30, 1, 167190.
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, 323.
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, 120130.
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241273.
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, 161173.
Schaerf, A. 1999. A survey of automated timetabling. Artificial Intelligence Review 13, 2, 87127.
Schimmelpfeng, K. and Helber, S. 2007. Application of a real-world university-course timetabling model solved by integer programming. OR Spectrum 29, 4, 783803.
Schutt, A., Feydy, T., Stuckey, P. J. and Wallace, M. G. 2011. Explaining the cumulative propagator. Constraints 16, 3, 250282.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Theory and Practice of Logic Programming
  • ISSN: 1471-0684
  • EISSN: 1475-3081
  • URL: /core/journals/theory-and-practice-of-logic-programming
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Type Description Title
PDF
Supplementary materials

Banbara et al. supplementary material
Appendix

 PDF (281 KB)
281 KB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed