iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/S11704-020-9102-4
Mathematical model and simulated annealing algorithm for Chinese high school timetabling problems under the new curriculum innovation | Frontiers of Computer Science Skip to main content
Springer Nature Link
Log in

Mathematical model and simulated annealing algorithm for Chinese high school timetabling problems under the new curriculum innovation

  • Research Article
  • Published:
Frontiers of Computer Science Aims and scope Submit manuscript

Abstract

As the first attempt, this paper proposes a model for the Chinese high school timetabling problems (CHSTPs) under the new curriculum innovation which was launched in 2014 by the Chinese government. According to the new curriculum innovation, students in high school can choose subjects that they are interested in instead of being forced to select one of the two study directions, namely, Science and Liberal Arts. Meanwhile, they also need to attend compulsory subjects as traditions. CHSTPs are student-oriented and involve more student constraints that make them more complex than the typical “Class-Teacher model”, in which the element “Teacher” is the primary constraint. In this paper, we first describe in detail the mathematical model of CHSTPs and then design a new two-part representation for the candidate solution. Based on the new representation, we adopt a two-phase simulated annealing (SA) algorithm to solve CHSTPs. A total number of 45 synthetic instances with different amounts of classes, teachers, and levels of student constraints are generated and used to illustrate the characteristics of the CHSTP model and the effectiveness of the designed representation and algorithm. Finally, we apply the proposed model, the designed two-part representation and the two-phase SA on10 real high schools.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kristiansen S, Stidsen T R. A comprehensive study of educational timetabling-a survey Department of Management Engineering, Technical University of Denmark, DTU Management Engineering Report, Denmark, 2013

  2. Pillay N. A survey of school timetabling research. Annals of Operations Research, 2014, 218(1): 261–293

    MathSciNet  MATH  Google Scholar 

  3. Al-Yakoob S M, Sherali H D. Mathematical models and algorithms for a high school timetabling problem. Computers & Operations Research, 2015, 61: 56–68

    MathSciNet  MATH  Google Scholar 

  4. Kwok L F, Kong S C, Kam Y Y. Timetabling in Hong Kong secondary schools. Computers & Education, 1997, 28(3): 173–183

    Google Scholar 

  5. Santos H G, Ochi L S, Souza M J F. An efficient tabu search heuristic for the school timetabling problem. In: Proceedings of International Workshop on Experimental and Efficient Algorithms. 2004, 468–481

  6. Santos H G, Ochi L S, Souza M J F. A tabu search heuristic with efficient diversification strategies for the class/teacher timetabling problem. Journal of Experimental Algorithmics, 2005, 10: 2–9

    MATH  Google Scholar 

  7. Beligiannis G N, Moschopoulos C N, Kaperonis G P, Likothanassis S D. Applying evolutionary computation to the school timetabling problem: the Greek case. Computers & Operations Research, 2008, 35(4): 1265–1280

    MATH  Google Scholar 

  8. Beligiannis G N, Moschopoulos C, Likothanassis S D. A genetic algorithm approach to school timetabling. Journal of the Operational Research Society, 2009, 60(1): 23–42

    MATH  Google Scholar 

  9. Zhang D, Liu Y, M’Hallah R, Leung S C H. A simulated annealing with a new neighborhood structure based algorithm for high school timetabling problems. European Journal of Operational Research, 2010, 203(3): 550–558

    MATH  Google Scholar 

  10. Katsaragakis IV, Tassopoulos I X, Beligiannis G N. A comparative study of modern heuristics on the school timetabling problem. Algorithms, 2015, 8(3): 723–742

    MathSciNet  MATH  Google Scholar 

  11. Skoullis V I, Tassopoulos I X, Beligiannis G N. Solving the high school timetabling problem using a hybrid cat swarm optimization based algorithm. Applied Soft Computing, 2017, 52: 277–289

    Google Scholar 

  12. Raghavjee R, Pillay N. An informed genetic algorithm for the high school timetabling problem. In: Proceedings of the 2010 Annual Research Conference of the South African Institute of Computer Scientists and Information Technologists. 2010, 408–412

  13. Raghavjee R, Pillay N. Evolving solutions to the school timetabling problem. In: Proceedings of World Congress on Nature & Biologically Inspired Computing. 2009, 1524–1527

  14. Raghavjee R, Pillay N. A genetic algorithm selection perturbative hyper-heuristic for solving the school timetabling problem. ORiON, 2015, 31(1): 39–60

    Google Scholar 

  15. Cerdeira-Pena A, Carpente L, Farina A, Seco D. New approaches for the school timetabling problem. In: Proceedings of the 7th Mexican International Conference on Artificial Intelligence. 2008, 261–267

  16. Odeniyi O A, Omidiora E O, Olabiyisi S O, Aluko J O. Development of a modified simulated annealing to school timetabling problem. International Journal of Applied Information Systems, 2015, 8(1): 16–24

    Google Scholar 

  17. Boland N, Hughes B D, Merlot L T G, Stuckey P J. New integer linear programming approaches for course timetabling. Computers & Operations Research, 2008, 35(7): 2209–2233

    MATH  Google Scholar 

  18. Kingston J H. A tiling algorithm for high school timetabling. In: Proceedings of International Conference on the Practice and Theory of Automated Timetabling. 2004, 208–225

  19. Merlot L. Techniques for academic timetabling. PhD Thesis, University of Melbourne, Australia, 2005

    Google Scholar 

  20. Ribeiro F G, Lorena L A N. A constructive evolutionary approach to school timetabling. In: Proceedings of Workshops on Applications of Evolutionary Computation. 2001, 130–139

  21. Willemen R J R. School Timetable Construction: Algorithms and Complexity. Eindhoven: Technische Universiteit Eindhoven, 2002

    Google Scholar 

  22. Bello G S, Rangel M C, Boeres M C S. An approach for the class/teacher timetabling problem using graph coloring. In: Proceedings of the International Conference on the Practice and Theory of Automated Timetabling. 2008

  23. Moura A V, Scaraficci R A. A GRASP strategy for a more constrained school timetabling problem. International Journal of Operational Research, 2010, 7(2): 152–170

    MATH  Google Scholar 

  24. Santos H G, Uchoa E, Ochi L S, Maculan N. Strong bounds with cut and column generation for class-teacher timetabling. Annals of Operations Research, 2012, 194(1): 399–412

    MathSciNet  MATH  Google Scholar 

  25. Brito S S, Fonseca G H G, Toffolo T A M, Santos H G, Souza M J F. A SA-VNS approach for the high school timetabling problem. Electronic Notes in Discrete Mathematics, 2012, 39: 169–176

    MATH  Google Scholar 

  26. Lach G, Lübbecke M E. Curriculum based course timetabling: new solutions to Udine benchmark instances. Annals of Operations Research, 2012, 194(1): 255–272

    MathSciNet  MATH  Google Scholar 

  27. Sørensen M, Dahms F H W. A two-stage decomposition of high school timetabling applied to cases in Denmark. Computers & Operations Research, 2014, 43: 36–49

    MathSciNet  MATH  Google Scholar 

  28. Birbas T, Daskalaki S, Housos E. Timetabling for Greek high schools. Journal of the Operational Research Society, 1997, 48(12): 1191–1200

    MATH  Google Scholar 

  29. Valouxis C, Housos E. Constraint programming approach for school timetabling. Computers & Operations Research, 2003, 30(10): 1555–1572

    MATH  Google Scholar 

  30. Papoutsis K, Valouxis C, Housos E. A column generation approach for the timetabling problem of Greek high schools. Journal of the Operational Research Society, 2003, 54(3): 230–238

    MATH  Google Scholar 

  31. Moschopoulos C N, Alexakos C E, Dosi C, Beligiannis G N, Likothanassis S D. A user-friendly evolutionary tool for high-school timetabling. Tools and Applications with Artificial Intelligence, 2009, 166: 149–162

    Google Scholar 

  32. Birbas T, Daskalaki S, Housos E. School timetabling for quality student and teacher schedules. Journal of Scheduling, 2009, 12(2): 177–197

    MATH  Google Scholar 

  33. Valouxis C, Gogos C, Alefragis P, Housos E. Decomposing the high school timetable problem. In: Proceedings of International Conference on the Practice and Theory of Automated Timetabling. 2012, 29–31

  34. Colorni A, Dorigo M, Maniezzo V. Metaheuristics for high school timetabling. Computational Optimization and Applications, 1998, 9(3): 275–298

    MATH  Google Scholar 

  35. Schaerf A. Local search techniques for large high school timetabling problems. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 1999, 29(4): 368–377

    Google Scholar 

  36. Avella P, D’Auria B, Salerno S, Vasil’ev I. A computational study of local search algorithms for Italian high-school timetabling. Journal of Heuristics, 2007, 13(6): 543–556

    MATH  Google Scholar 

  37. Fernandes C, Caldeira J P, Melicio F, Rosa A. High school weekly timetabling by evolutionary algorithms. In: Proceedings of the ACM Symposium on Applied Computing. 1999, 344–350

  38. Melício F, Calderia J P, Rosa A. THOR: a tool for school timetabling. In: Proceedings of International Conference on the Practice and Teaching of Automated Timetabling. 2006, 532–535

  39. Alvarez-Valdés R, Parreño F, Tamarit J M. A tabu search algorithm for assigning teachers to courses. Top, 2002, 10(2): 239–259

    MathSciNet  MATH  Google Scholar 

  40. Nurmi K, Kyngas J. A framework for school timetabling problem. In: Proceedings of the 3rd Multidisciplinary International Scheduling Conference: Theory and Applications. 2007, 386–393

  41. Post G F, Ruizenaar H W A, Post G, Ruizenaar H. Clusterschemes in Dutch secondary schools. Department of Applied Mathematics, University of Twente, The Netherlands, 2004

    Google Scholar 

  42. De H P, Landman R, Post G, Ruizenaar H. A case study for timetabling in a Dutch secondary school. In: Proceedings of International Conference on the Practice and Theory of Automated Timetabling. 2006, 267–279

  43. Post G, Ahmadi S, Geertsema F. Cyclic transfers in school timetabling. OR Spectrum, 2012, 34(1): 133–154

    MathSciNet  MATH  Google Scholar 

  44. Hartog J. Timetabling on dutch high schools. PhD Thesis, The Netherland: Technische Universiteit Delft, 2007

    Google Scholar 

  45. Bufé M, Fischer T, Gubbels H, Hacker C, Hasprich O, Scheibel C, Weicker K, Weicker N, Wenig M, Wolfangel C. Automated solution of a highly constrained school timetabling problem-preliminary results. In: Proceedings of Workshops on Applications of Evolutionary Computation. 2001, 431–440

  46. Wilke P, Gröbner M, Oster N. A hybrid genetic algorithm for school timetabling. In: Proceedings of Australian Joint Conference on Artificial Intelligence. 2002, 455–464

  47. Jacobsen F, Bortfeldt A, Gehring H. Timetabling at German secondary schools: tabu search versus constraint programming. In: Proceedings of International Conference on the Practice and Theory of Automated Timetabling. 2006, 439–442

  48. Löhnertz M. A timetabling system for the German gymnasium. In: Proceedings of International Conference on the Practice and Theory of Automated Timetabling. 2002

  49. Marte M. Models and algorithms for school timetabling-a constraint-programming approach. Dissertation, Ludwig-Maximilians-Universitat Munchen, 2002

  50. Wood J, Whitaker D. Student centred school timetabling. Journal of the Operational Research Society, 1998, 49(11): 1146–1152

    MATH  Google Scholar 

  51. Wilke P, Ostler J. Solving the school time tabling problem using tabu search, simulated annealing, genetic and branch & bound algorithms. In: Proceedings of the 7th International Conference on the Practice and Theory of Automated Timetabling. 2008, 3–6

  52. Wilke P, Killer H. Comparison of algorithms solving school and course time tabling problems using the erlangen advanced time tabling system (EATTS). In: Proceedings of the 8th International Conference on the Practice and Theory of Automated Timetabling. 2010, 427–439

  53. Paper C, Shambour M K, Khader A T, Ozcan E. A two stage approach for high school timetabling. In: Proceedings of International Conference on Neural Information Processing. 2013, 66–73

  54. Fonseca G H G, Santos H G, Toffolo T Â M, Brito S S, Souza M J F. GOAL solver: a hybrid local search based solver for high school timetabling. Annals of Operations Research, 2016, 239(1): 77–97

    MathSciNet  MATH  Google Scholar 

  55. Fonseca G H G, Santos H G. Variable neighborhood search based algorithms for high school timetabling. Computers & Operations Research, 2014, 52: 203–208

    MathSciNet  MATH  Google Scholar 

  56. Fonseca G H G, Santos H G, Carrano E G. Late acceptance hill-climbing for high school timetabling. Journal of Scheduling, 2016, 19(4): 453–465

    MathSciNet  MATH  Google Scholar 

  57. Kristiansen S, Sørensen M, Stidsen TR. Integer programming for the generalized high school timetabling problem. Journal of Scheduling, 2015, 18(4): 377–392

    MathSciNet  MATH  Google Scholar 

  58. Post G, Kingston J H, Ahmadi S, Daskalaki S, Gogos C, Kyngas J, Nurmi C, Musliu N, Pillay N, Santos H, Schaerf A. XHSTT: an XML archive for high school timetabling problems in different countries. Annals of Operations Research, 2014, 218(1): 295–301

    MathSciNet  MATH  Google Scholar 

  59. Fonseca G H G, Santos H G, Carrano E G. Integrating matheuristics and metaheuristics for timetabling. Computers & Operations Research, 2016, 74: 108–117

    MathSciNet  MATH  Google Scholar 

  60. Fonseca G H G, Santos H G, Carrano E G, Stidsen T J R. Integer programming techniques for educational timetabling. European Journal of Operational Research, 2017, 262(1): 28–39

    MathSciNet  MATH  Google Scholar 

  61. Burke E K, Kendall G, Misir M, Özcan E. A study of simulated annealing hyper-heuristics. In: Proceedings of the International Conference on the Practice and Theory of Automated Timetabling. 2008

  62. Burke E K, Kendall G, Misir M, Özcan E. Monte carlo hyper-heuristics for examination timetabling. Annals of Operations Research, 2012, 196(1): 73–90

    MathSciNet  MATH  Google Scholar 

  63. Bai R, Blazewicz J, Burke E K, Kendall G, McCollum B. A simulated annealing hyper-heuristic methodology for flexible decision support. 4OR: A Quarterly Journal of Operations Research, 2012, 10(1): 43–66

    MATH  Google Scholar 

  64. Chiarandini M, Birattari M, Socha K, Rossi-Doria O. An effective hybrid algorithm for university course timetabling. Journal of Scheduling, 2006, 9(5): 403–432

    MathSciNet  MATH  Google Scholar 

  65. Jackson W G, Özcan E, John R I. Move acceptance in local search meta-heuristics for cross-domain search. Expert Systems with Applications, 2018, 109: 131–151

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Outstanding Young Scholar Program of National Natural Science Foundation of China (NSFC) (Grant No. 61522311), in part by the General Program of NSFC (Grant No. 61773300), in part by the Key Program of Fundamental Research Project of Natural Science of Shaanxi Province, China (2017JZ017), and in part by the Doctoral Students’ Short-Term Study Abroad Scholarship Fund of Xidian University.

Author information

Authors and Affiliations

  1. Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi’an, 710071, China

    Xingxing Hao, Jing Liu, Yutong Zhang & Gustaph Sanga

Authors
  1. Xingxing Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yutong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gustaph Sanga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jing Liu.

Additional information

Xingxing Hao received the BS degree in intelligent science and technology from Xidian University, China in 2014. Now, he is pursuing the PhD degree in circuits and systems from the School of Artificial Intelligence, Xidian University, China. His research interests include combinatorial optimization, evolutionary algorithms, evolutionary multitasking, and hyper-heuristics.

Jing Liu received the BS degree in computer science and technology and the PhD degree in circuits and systems from Xidian University, China in 2000 and 2004, respectively. In 2005, she joined Xidian University as a lecture, and was promoted to a full professor in 2009. From Apr. 2007 to Apr. 2008, she worked at the University of Queensland, Australia as a postdoctoral research fellow, and from Jul. 2009 to Jul. 2011, she worked at the University of New South Walesat the Australian Defence Force Academy as a research associate. Now, she is a full professor in School of Artificial Intelligence, Xidian University. Her research interests include evolutionary computation, complex networks, fuzzy cognitive maps, multiagent systems, and data mining.

Yutong Zhang received the BS degree in intelligent science and technology from Xidian University, China in 2014. Now, he is pursuing the PhD degree in circuits and systems from the School of Artificial Intelligence, Xidian University, China. His research interests include transportation problems and evolutionary algorithms.

Gustaph Sanga received BS degree in Computer Science from the University of Dar es Salaam, Tanzania. He received his Master of Engineering in Computer Science and Technology from Hunan University, China. Now he is a PhD student with the School of Artificial Intelligence, Xidian University, China. His research interest is focused on evolutionary computations, complex networks, artificial immune systems, sematic web technology, big data, and data science.

Electronic Supplementary Material

11704_2020_9102_MOESM1_ESM.pdf

Mathematical model and simulated annealing algorithm for Chinese high school timetabling problems under the new curriculum innovation

11704_2020_9102_MOESM2_ESM.pdf

Mathematical model and simulated annealing algorithm for Chinese high school timetabling problems under the new curriculum innovation

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hao, X., Liu, J., Zhang, Y. et al. Mathematical model and simulated annealing algorithm for Chinese high school timetabling problems under the new curriculum innovation. Front. Comput. Sci. 15, 151309 (2021). https://doi.org/10.1007/s11704-020-9102-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11704-020-9102-4

Keywords

Search

Navigation