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Decomposition and Parallelization of Multi-resource Timetabling Problems

  • Petr Šlechta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3616)

Abstract

This paper presents a model of generalized timetabling problem and a decomposition algorithm which can decompose large problems into independent smaller subproblems—the search for a feasible solution can then be easily parallelized. The timetabling problem consists in fixing a sequence of meetings between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types [9]. Course timetabling is a multi-dimensional NP-complete problem [4]. In this paper we present the multi-resource timetabling problem (MRTP), our model for the generalized high-school timetabling problem. The MRTP is a search problem—a feasible solution is searched. The main contribution of this paper is the Decomposition Algorithm for MRTP to parallelize the search, so the whole MRTP can be easily distributed and parallelized. Our approach was applied to real-life instances of high-school timetabling problems. Results are discussed at the end of this paper and parallelized search is compared with the centralized one.

Keywords

Decomposition Algorithm Timetabling Problem Color Marking Independent Subproblem School Timetabling Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bárta, J., Štepánková, O., Pechoucek, M.: Distributed Branch and Bound Algorithm in Coalition Planning. In: Mařík, V., Štěpánková, O., Krautwurmová, H., Luck, M. (eds.) ACAI 2001, EASSS 2001, AEMAS 2001, and HoloMAS 2001. LNCS (LNAI), vol. 2322, p. 159. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Burke, E.K., Newall, J.P.: A Multi-Stage Evolutionary Algorithm for the Timetable Problem. IEEE Trans. on Evolutionary Computation 3, 63–74 (1999)Google Scholar
  3. 3.
    Carter, M.W.: A Decomposition Algorithm for Practical Timetabling Problems. Technical Paper 83-06. Department of Industrial Engineering, University of Toronto (1983)Google Scholar
  4. 4.
    Carter, M.W., Laporte, G.: Recent Developments in Practical Course Timetabling. In: Burke, E.K., Carter, M. (eds.) PATAT 1997. LNCS, vol. 1408, pp. 3–19. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Friha, L., Queloz, P., Pellegrini, C.: A Decomposition Method for Hospital Scheduling Problems. In: Workshop on Industrial Constraint-Directed Scheduling (1997)Google Scholar
  6. 6.
    Goltz, H.-J., John, U.: Methods for Solving Practical Problems of Job-Shop Scheduling Modelled in CLP(FD). In: Proc. Practical Application of Constraint Technology (PACT 1996) (1996)Google Scholar
  7. 7.
    Hansen, P., Mladenovic, N., Perez-Brito, D.: Variable Neighborhood Decomposition Search. J. Heuristics 7, 335–350 (2001)Google Scholar
  8. 8.
    Marík, V., Štepánková, O., Lažanský, J., et al.: Umelá Intelligence, vol. 3. Academia, Praha (2001)Google Scholar
  9. 9.
    Schaerf, A.: A Survey of Automated Timetabling. CWI Report (1995) ISSN 0169-118X Google Scholar
  10. 10.
    The Source for Java Technology. Sun Microsystems, Inc. (2003), http://java.sun.com
  11. 11.
    Souza, M.J.F., Maculan, N., Ochi, L.S.: A GRASP-Tabu Search Algorithm to Solve a School Timetabling Problem. In: 4th Metaheuristics Int. Conf. (MIC 2001) (2001)Google Scholar
  12. 12.
    de Werra, D.: An Introduction to Timetabling. Eur. J. Oper. Res. 19, 151–162 (1985)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Petr Šlechta
    • 1
  1. 1.Department of CyberneticsCzech Technical University in PraguePrague 6Czech Republic

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