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Constraint Programming for High School Timetabling: A Scheduling-Based Model with Hot Starts

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10848))

Abstract

High School Timetabling (HSTT) is a well-known and wide-spread problem. It consists of coordinating resources (e.g. teachers, rooms), times, and events (e.g. classes) with respect to a variety of constraints. In this paper, we study the applicability of constraint programming (CP) for high school timetabling. We formulate a novel CP model for HSTT using a scheduling-based point of view. We show that a drastic improvement in performance over the baseline CP model can be achieved by including solution-based phase saving, which directs the CP solver to first search in close proximity to the best solution found, and our hot start approach, where we use existing heuristic methods to produce a starting point for the CP solver. The experiments demonstrate that our approach outperforms the IP and maxSAT complete methods and provides competitive results when compared to dedicated heuristic solvers.

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References

  1. Abío Roig, I.: Solving hard industrial combinatorial problems with SAT (2013)

    Google Scholar 

  2. Global Constraint Catalog: all_equal constraint. http://www.emn.fr/x-info/sdemasse/gccat/Call_equal.html

  3. Chu, G.: Improving combinatorial optimization. Ph.D. thesis, The University of Melbourne (2011). http://hdl.handle.net/11343/36679

  4. Chu, G., Stuckey, P.J.: LNS = restarts + dynamic search + phase saving. Technical draft

    Google Scholar 

  5. Demirović, E., Musliu, N.: Modeling high school timetabling as partial weighted maxSAT. In: The 4th Workshop on Logic and Search (LaSh 2014) (2014)

    Google Scholar 

  6. Demirović, E., Musliu, N.: Solving high school timetabling with satisfiability modulo theories. In: Proceedings of the International Conference of the Practice and Theory of Automated Timetabling (PATAT 2014), pp. 142–166 (2014)

    Google Scholar 

  7. Demirović, E., Musliu, N.: MaxSAT based large neighborhood search for high school timetabling. Comput. Oper. Res. 78, 172–180 (2017)

    Article  MathSciNet  Google Scholar 

  8. Demirović, E., Musliu, N.: Modeling high school timetabling as partial weighted maxSAT. In: Technical Draft - Extended LaSh 2014 Workshop Paper (2017)

    Google Scholar 

  9. Global Constraint Catalog: disjunctive constraint. http://www.emn.fr/x-info/sdemasse/gccat/Cdisjunctive.html

  10. Dorneles, Á.P., de Araujo, O.C.B., Buriol, L.S.: A fix-and-optimize heuristic for the high school timetabling problem. Comput. Oper. Res. 52, 29–38 (2014)

    Article  MathSciNet  Google Scholar 

  11. Fonseca, G.H.G., Santos, H.G.: Variable neighborhood search based algorithms for high school timetabling. Comput. Oper. Res. 52, 203–208 (2014)

    Article  MathSciNet  Google Scholar 

  12. da 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. Ann. Oper. Res. 239(1), 77–97 (2016). https://doi.org/10.1007/s10479-014-1685-4

    Article  MathSciNet  MATH  Google Scholar 

  13. Jacobsen, F., Bortfeldt, A., Gehring, H.: Timetabling at German secondary schools: tabu search versus constraint programming. In: Proceedings of the International Conference of the Practice and Theory of Automated Timetabling (PATAT 2006) (2006)

    Google Scholar 

  14. Kheiri, A., Ozcan, E., Parkes, A.J.: HySST: hyper-heuristic search strategies and timetabling. In: Proceedings of the International Conference of the Practice and Theory of Automated Timetabling (PATAT 2012), pp. 497–499 (2012)

    Google Scholar 

  15. Kingston, J.: KHE14: an algorithm for high school timetabling. In: Proceedings of the International Conference of the Practice and Theory of Automated Timetabling (PATAT 2014), pp. 498–501 (2014)

    Google Scholar 

  16. Kristiansen, S., Sørensen, M., Stidsen, T.R.: Integer programming for the generalized high school timetabling problem. J. Sched. 18(4), 377–392 (2015)

    Article  MathSciNet  Google Scholar 

  17. Lahrichi, A.: Scheduling: the notions of hump, compulsory parts and their use in cumulative problems. C. R. Acad. Sci. Paris 294, 209–211 (1982)

    Google Scholar 

  18. Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. Inf. Process. Lett. 47(4), 173–180 (1993)

    Article  MathSciNet  Google Scholar 

  19. Marte, M.: Towards constraint-based school timetabling. Ann. Oper. Res. (ANOR) 155(1), 207–225 (2007)

    Article  MathSciNet  Google Scholar 

  20. Martins, R., Manquinho, V., Lynce, I.: Open-WBO: a modular MaxSAT solver’. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 438–445. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_33

    Chapter  Google Scholar 

  21. Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: towards a standard CP modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74970-7_38

    Chapter  Google Scholar 

  22. Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 482–495. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30201-8_36

    Chapter  MATH  Google Scholar 

  23. Pipatsrisawat, K., Darwiche, A.: A lightweight component caching scheme for satisfiability solvers. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 294–299. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72788-0_28

    Chapter  Google Scholar 

  24. Post, G., Ahmadi, S., Daskalaki, S., Kingston, J., Kyngas, J., Nurmi, C., Ranson, D.: An XML format for benchmarks in high school timetabling. Ann. Oper. Res. 194(1), 385–397 (2012)

    Article  Google Scholar 

  25. Post, G., Kingston, J.H., Ahmadi, S., Daskalaki, S., Gogos, C., Kyngäs, J., Nurmi, C., Musliu, N., Pillay, N., Santos, H., Schaerf, A.: XHSTT: an XML archive for high school timetabling problems in different countries. Ann. Oper. Res. 218(1), 295–301 (2014)

    Article  MathSciNet  Google Scholar 

  26. Santos, H.G., Uchoa, E., Ochi, L.S., Maculan, N.: Strong bounds with cut and column generation for class-teacher timetabling. Ann. Oper. Res. 194(1), 399–412 (2012)

    Article  MathSciNet  Google Scholar 

  27. Sørensen, M.: A matheuristic for high school timetabling. In: Timetabling at High Schools, Ph.D. thesis, pp. 137–153. Department of Management Engineering, Technical University of Denmark (2013)

    Google Scholar 

  28. Sørensen, M., Dahms, F.H.: A two-stage decomposition of high school timetabling applied to cases in Denmark. Comput. Oper. Res. 43, 36–49 (2014)

    Article  MathSciNet  Google Scholar 

  29. Sørensen, M., Kristiansen, S., Stidsen, T.R.: International timetabling competition 2011: an adaptive large neighborhood search algorithm. In: Proceedings of the International Conference on the Practice and Theory of Automated Timetabling (PATAT 2012), pp. 489–492 (2012)

    Google Scholar 

  30. Sørensen, M., Stidsen, T.R.: Hybridizing integer programming and metaheuristics for solving high school timetabling. In: Proceedings of the International Conference of the Practice and Theory of Automated Timetabling (PATAT 2014), pp. 557–560 (2014)

    Google Scholar 

  31. Sørensen, M., Stidsen, T.R., Kristiansen, S.: Integer programming for the generalized (high) school timetabling problem. In: Proceedings of the International Conference of the Practice and Theory of Automated Timetabling (PATAT 2014), pp. 498–501 (2014)

    Google Scholar 

  32. Sørensen, M., Stidsen, T.R.: High school timetabling: modeling and solving a large number of cases in Denmark. In: Proceedings of the International Conference of the Practice and Theory of Automated Timetabling (PATAT 2012), pp. 359–364 (2012)

    Google Scholar 

  33. Sørensen, M., Stidsen, T.R.: Comparing solution approaches for a complete model of high school timetabling. Technical report, DTU Management Engineering (2013)

    Google Scholar 

  34. Valouxis, C., Housos, E.: Constraint programming approach for school timetabling. Comput. Oper. Res. 30(10), 1555–1572 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Computing and Information Systems, University of Melbourne, Melbourne, Australia

    Emir Demirović & Peter J. Stuckey

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  1. Emir Demirović
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  2. Peter J. Stuckey
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Correspondence to Emir Demirović or Peter J. Stuckey .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

    Willem-Jan van Hoeve

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Demirović, E., Stuckey, P.J. (2018). Constraint Programming for High School Timetabling: A Scheduling-Based Model with Hot Starts. In: van Hoeve, WJ. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2018. Lecture Notes in Computer Science(), vol 10848. Springer, Cham. https://doi.org/10.1007/978-3-319-93031-2_10

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  • DOI: https://doi.org/10.1007/978-3-319-93031-2_10

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