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Modeling high school timetabling with bitvectors

Author

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  • Emir Demirović

    (Technische Universität Wien)

  • Nysret Musliu

    (Technische Universität Wien)

Abstract

High school timetabling (HSTT) is a well known and wide spread problem. The problem consists of coordinating resources (e.g. teachers, rooms), times, and events (e.g. lectures) with respect to various constraints. Unfortunately, HSTT is hard to solve and just finding a feasible solution for simple variants of HSTT has been proven to be NP-complete. We propose a new modeling approach for HSTT using bitvectors in which constraint costs of the general HSTT can be calculated using bit operations. This model allows efficient computation of constraint costs making it useful when implementing HSTT algorithms. Additionally, it can be used to solve HSTT with satisfiability modulo theory (SMT) solvers that support bitvectors. We evaluate the performance for our bitvector modeling approach and compare it to the leading engine KHE when developing local search algorithms such as hill climbing and simulated annealing. The experimental results show that our approach is useful for this problem. Furthermore, experimental results using SMT are given on instances from the ITC 2011 benchmark repository.

Suggested Citation

  • Emir Demirović & Nysret Musliu, 2017. "Modeling high school timetabling with bitvectors," Annals of Operations Research, Springer, vol. 252(2), pages 215-238, May.
    • Handle: RePEc:spr:annopr:v:252:y:2017:i:2:d:10.1007_s10479-016-2220-6
    DOI: 10.1007/s10479-016-2220-6
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    References listed on IDEAS

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    1. Gerhard Post & Samad Ahmadi & Sophia Daskalaki & Jeffrey Kingston & Jari Kyngas & Cimmo Nurmi & David Ranson, 2012. "An XML format for benchmarks in High School Timetabling," Annals of Operations Research, Springer, vol. 194(1), pages 385-397, April.
    2. Gerhard Post & Jeffrey Kingston & Samad Ahmadi & Sophia Daskalaki & Christos Gogos & Jari Kyngas & Cimmo Nurmi & Nysret Musliu & Nelishia Pillay & Haroldo Santos & Andrea Schaerf, 2014. "XHSTT: an XML archive for high school timetabling problems in different countries," Annals of Operations Research, Springer, vol. 218(1), pages 295-301, July.
    3. Barry McCollum & Edmund Burke, 2014. "The practice and theory of automated timetabling," Annals of Operations Research, Springer, vol. 218(1), pages 1-2, July.
    4. Haroldo Santos & Eduardo Uchoa & Luiz Ochi & Nelson Maculan, 2012. "Strong bounds with cut and column generation for class-teacher timetabling," Annals of Operations Research, Springer, vol. 194(1), pages 399-412, April.
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