Skip to main content
SpringerLink
Log in

A Local Branching MIP Heuristic for a Real-World Curriculum-Based Course Timetabling Problem

  • Conference paper
  • First Online:
Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

Automated timetabling is a challenging area in the timetabling and scheduling theory and practice, intensively addressed in research papers in the last two decades. There are three main classes of problems, which are usually studied: school timetabling, course timetabling and examination timetabling. In this report, we address a case study of the Curriculum-Based Course Timetabling (CB-CTT) problem, arising at Engineering Department of Sannio University. In general, the problem consists of finding a feasible weekly assignment of course lectures to rooms and time periods while respecting a wide range of constraints, which have to be either strictly satisfied (hard constraints) or satisfied as much as possible (soft constraints). The case study here addressed here has many special requirements due to local organizational rules. We were able to model the complex requirements by an Integer Programming formulation. The solution approach consists of using an MIP solver, integrated with two local branching heuristics tailored for the problem. The effectiveness of the proposed approach is illustrated by the computational results on two real instances.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://www.ibm.com/products/ilog-cplex-optimization-studio.

  2. 2.

    https://julialang.org/.

References

  1. Avella, P., Boccia, M., Mannino, C., Vasilyev, I.: Time-indexed formulations for the runway scheduling problem. Transp. Sci. 51(4), 1196–1209 (2017). https://doi.org/10.1287/trsc.2017.0750

    Article  Google Scholar 

  2. Avella, P., Boccia, M., Vasilyev, I.: A branch-and-cut algorithm for the multilevel generalized assignment problem. IEEE Access 1, 475–479 (2013). https://doi.org/10.1109/ACCESS.2013.2273268

    Article  Google Scholar 

  3. Avella, P., Vasil’ev, I.: A computational study of a cutting plane algorithm for university course timetabling. J. Sched. 8(6), 497–514 (2005). https://doi.org/10.1007/s10951-005-4780-1

    Article  MathSciNet  MATH  Google Scholar 

  4. Babaei, H., Karimpour, J., Hadidi, A.: A survey of approaches for university course timetabling problem. Comput. Ind. Eng. 86, 43–59 (2015). https://doi.org/10.1016/j.cie.2014.11.010. Applications of computational intelligence and fuzzy logic to manufacturing and service systems

    Article  Google Scholar 

  5. Bagger, N.C.F., Sørensen, M., Stidsen, T.R.: Benders’ decomposition for curriculum-based course timetabling. Comput. Oper. Res. 91, 178–189 (2018). https://doi.org/10.1016/j.cor.2017.10.009

    Article  MathSciNet  MATH  Google Scholar 

  6. Bellio, R., Ceschia, S., Di Gaspero, L., Schaerf, A., Urli, T.: A simulated annealing approach to the curriculum-based course timetabling problem. In: Proceedings of the 6th Multidisciplinary International Conference on Scheduling: Theory and Applications, MISTA 2013, Belgium, pp. 314–317, January 2013

    Google Scholar 

  7. Bettinelli, A., Cacchiani, V., Roberti, R., Toth, P.: An overview of curriculum-based course timetabling. TOP 23(2), 313–349 (2015). https://doi.org/10.1007/s11750-015-0366-z

    Article  MathSciNet  MATH  Google Scholar 

  8. Bonutti, A., De Cesco, F., Di Gaspero, L., Schaerf, A.: Benchmarking curriculum-based course timetabling: formulations, data formats, instances, validation, visualization, and results. Ann. Oper. Res. 194(1), 59–70 (2012). https://doi.org/10.1007/s10479-010-0707-0

    Article  MATH  Google Scholar 

  9. Burke, E., Jackson, K., Kingston, J.H., Weare, R.: Automated university timetabling: the state of the art. Comput. J. 40(9), 565–571 (1997). https://doi.org/10.1093/comjnl/40.9.565

    Article  Google Scholar 

  10. Burke, E.K., Mareček, J., Parkes, A.J., Rudová, H.: Penalising patterns in timetables: novel integer programming formulations. In: Kalcsics, J., Nickel, S. (eds.) Operations Research Proceedings 2007, pp. 409–414. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-77903-2_63

    Chapter  Google Scholar 

  11. Burke, E.K., Mareček, J., Parkes, A.J., Rudová, H.: A supernodal formulation of vertex colouring with applications in course timetabling. Ann. Oper. Res. 179(1), 105–130 (2010). https://doi.org/10.1007/s10479-010-0716-z

    Article  MathSciNet  MATH  Google Scholar 

  12. Burke, E.K., Mareček, J., Parkes, A.J., Rudová, H.: A branch-and-cut procedure for the Udine Course Timetabling problem. Ann. Oper. Res. 194(1), 71–87 (2012). https://doi.org/10.1007/s10479-010-0828-5

    Article  MathSciNet  MATH  Google Scholar 

  13. Burke, E.K., Marečdek, J., Parkes, A.J., Rudová, H.: Decomposition, reformulation, and diving in university course timetabling. Comput. Oper. Res. 37(3), 582–597 (2010). https://doi.org/10.1016/j.cor.2009.02.023. Hybrid metaheuristics

    Article  MathSciNet  MATH  Google Scholar 

  14. Burke, E.K., Petrovic, S.: Recent research directions in automated timetabling. Eur. J. Oper. Res. 140(2), 266–280 (2002). https://doi.org/10.1016/S0377-2217(02)00069-3

    Article  MATH  Google Scholar 

  15. Cacchiani, V., Caprara, A., Roberti, R., Toth, P.: A new lower bound for curriculum-based course timetabling. Comput. Oper. Res. 40(10), 2466–2477 (2013). https://doi.org/10.1016/j.cor.2013.02.010

    Article  MathSciNet  MATH  Google Scholar 

  16. Clark, M., Henz, M., Love, B.: QuikFix-a repair-based timetable solver. In: Proceedings of the 7th International Conference on the Practice and Theory of Automated Timetabling (2009). http://www.comp.nus.edu.sg/ henz/publications/ps/PATAT2008.pdf

  17. Di Gaspero, L., Schaerf, A., Mccollum, B.: The 2nd International Timetabling Competition (itc2007): Curriculum-based course timetabling (track 3. Technical report, School of Electronics, Electrical Engineering and Computer Science, Queens University, Belfast (UK), ITC-2007 (2007). http://www.cs.qub.ac.uk/itc2007/

  18. Dunning, I., Huchette, J., Lubin, M.: JuMP: a modeling language for mathematical optimization. SIAM Rev. 59(2), 295–320 (2017)

    Article  MathSciNet  Google Scholar 

  19. Fischetti, M., Lodi, A.: Local branching. Math. Program. 98(1), 23–47 (2003). https://doi.org/10.1007/s10107-003-0395-5

    Article  MathSciNet  MATH  Google Scholar 

  20. Geiger, M.J.: Applying the threshold accepting metaheuristic to curriculum based course timetabling. Ann. Oper. Res. 194(1), 189–202 (2012). https://doi.org/10.1007/s10479-010-0703-4

    Article  MathSciNet  MATH  Google Scholar 

  21. Hao, J.K., Benlic, U.: Lower bounds for the ITC-2007 curriculum-based course timetabling problem. Eur. J. Oper. Res. 212(3), 464–472 (2011). https://doi.org/10.1016/j.ejor.2011.02.019

    Article  Google Scholar 

  22. Kiefer, A., Hartl, R.F., Schnell, A.: Adaptive large neighborhood search for the curriculum-based course timetabling problem. Ann. Oper. Res. 252(2), 255–282 (2017). https://doi.org/10.1007/s10479-016-2151-2

    Article  MathSciNet  MATH  Google Scholar 

  23. Kristiansen, S., Stidsen, T.: A Comprehensive Study of Educational Timetabling - A Survey. Department of Management Engineering, Technical University of Denmark, Lyngby (2013)

    Google Scholar 

  24. Lach, G., Lübbecke, M.E.: Curriculum based course timetabling: new solutions to Udine benchmark instances. Ann. Oper. Res. 194(1), 255–272 (2012). https://doi.org/10.1007/s10479-010-0700-7

    Article  MathSciNet  MATH  Google Scholar 

  25. Lewis, R.: A survey of metaheuristic-based techniques for university timetabling problems. OR Spectr. 30(1), 167–190 (2008). https://doi.org/10.1007/s00291-007-0097-0

    Article  MathSciNet  MATH  Google Scholar 

  26. Lindahl, M., Mason, A.J., Stidsen, T., Srensen, M.: A strategic view of university timetabling. Eur. J. Oper. Res. 266(1), 35–45 (2018). https://doi.org/10.1016/j.ejor.2017.09.022

    Article  MathSciNet  MATH  Google Scholar 

  27. Lü, Z., Hao, J.K.: Adaptive tabu search for course timetabling. Eur. J. Oper. Res. 200(1), 235–244 (2010). https://doi.org/10.1016/j.ejor.2008.12.007

    Article  MATH  Google Scholar 

  28. Lü, Z., Hao, J.K., Glover, F.: Neighborhood analysis: a case study on curriculum-based course timetabling. J. Heuristics 17(2), 97–118 (2011). https://doi.org/10.1007/s10732-010-9128-0

    Article  Google Scholar 

  29. McCollum, B.: A perspective on bridging the gap between theory and practice in university timetabling. In: Burke, E.K., Rudová, H. (eds.) PATAT 2006. LNCS, vol. 3867, pp. 3–23. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77345-0_1

    Chapter  Google Scholar 

  30. McCollum, B.: Setting the research agenda in automated timetabling: the second international timetabling competition. INFORMS J. Comput. 22(1), 120–130 (2010). https://doi.org/10.1287/ijoc.1090.0320

    Article  MathSciNet  MATH  Google Scholar 

  31. Müller, T.: ITC 2007 solver description: a hybrid approach. Ann. Oper. Res. 172(1), 429 (2009). https://doi.org/10.1007/s10479-009-0644-y

    Article  MATH  Google Scholar 

  32. Phillips, A.E., Waterer, H., Ehrgott, M., Ryan, D.M.: Integer programming methods for large-scale practical classroom assignment problems. Comput. Oper. Res. 53, 42–53 (2015). https://doi.org/10.1016/j.cor.2014.07.012

    Article  MathSciNet  MATH  Google Scholar 

  33. Pillay, N.: A review of hyper-heuristics for educational timetabling. Ann. Oper. Res. 239(1), 3–38 (2016). https://doi.org/10.1007/s10479-014-1688-1

    Article  MathSciNet  MATH  Google Scholar 

  34. Schaerf, A.: A survey of automated timetabling. Artif. Intell. Rev. 13(2), 87–127 (1999). https://doi.org/10.1023/A:1006576209967

    Article  Google Scholar 

  35. Shaker, K., Abdullah, S., Alqudsi, A., Jalab, H.: Hybridizing meta-heuristics approaches for solving university course timetabling problems. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013. LNCS (LNAI), vol. 8171, pp. 374–384. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41299-8_36

    Chapter  Google Scholar 

  36. Tarawneh, H., Ayob, M., Ahmad, Z.: A hybrid simulated annealing with solutions memory for curriculum-based course timetabling problem. J. Appl. Sci. 13, 262–269 (2013). https://doi.org/10.3923/jas.2013.262.269

    Article  Google Scholar 

  37. Vasilyev, I., Klimentova, X., Boccia, M.: Polyhedral study of simple plant location problem with order. Oper. Res. Lett. 41(2), 153–158 (2013). https://doi.org/10.1016/j.orl.2012.12.006

    Article  MathSciNet  MATH  Google Scholar 

  38. Vasilyev, I., Avella, P., Boccia, M.: A branch and cut heuristic for a runway scheduling problem. Autom. Remote Control 77(11), 1985–1993 (2016). https://doi.org/10.1134/S0005117916110084

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DING – Dipartimento di Ingegneria, Università del Sannio, Piazza Roma 21, 82100, Benevento, Italy

    Pasquale Avella & Sandro Viglione

  2. DIETI – Dipartimento di Ingegneria Elettrica e delle Tecnologie dell’Informazione, Universitá degli Studi di Napoli “Federico II”, Naples, Italy

    Maurizio Boccia

  3. Matrosov Institute of System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Lermontov str. 134, 664033, Irkutsk, Russia

    Igor Vasilyev

Authors
  1. Pasquale Avella
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maurizio Boccia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sandro Viglione
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Igor Vasilyev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Igor Vasilyev .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Avella, P., Boccia, M., Viglione, S., Vasilyev, I. (2019). A Local Branching MIP Heuristic for a Real-World Curriculum-Based Course Timetabling Problem. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-33394-2_34

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33393-5

  • Online ISBN: 978-3-030-33394-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation