Experiments on networks of employee timetabling problems

  • Amnon Meisels
  • Natalia Lusternik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1408)


The natural representation of employee timetabling problems (ETPs), as constraint networks (CNs), has variables representing tasks and values representing employees that are assigned to tasks. In this representation, ETPs have binary constraints of non-equality (mutual exclusion), the networks are non uniform, and variables have different domains of values. There is also a typical family of non-binary constraints that represent finite capacity limits. These features differentiate the networks of ETPs from random uniform binary CNs. Much experimental work has been done in recent years on random binary constraint networks (cf. [10,11, 9]) and the so called phase transitions have been connected with certain value combinations of the parameters of random binary CNs.

This paper designs and experiments with a random testbed of ETPs that includes all of the above features and is solved by standard constraint processing techniques, such as forward checking (FC) and conflict directed backjumping (CBJ). Random ETPs are characterized by the usual parameters of constraint networks, like the density of constraints p1. One result of the experiments is that random ETPs exhibit a strong change in difficulty, as measured by consistency checks, (a phase transition). The critical parameter for the observed phase transition is the average size of domains of variables. Non binary constraints of finite capacity are part of the experimental testbed. An enhanced FC-CBJ search algorithm is used to test these random networks and the experimental results are presented.

Key words

Employee Timetabling Constraint Networks Experimental CSP Non binary constraints 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Arkin and E. B. Silverberg. Scheduling jobs with fixed start and end times. Discrete Applied Mathematics, 18:1–8, 1987.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    P. Cheeseman, B. Kanefsky, and W. M. Taylor. Where the really hard problems are. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, pages 331–337, Sydney, Australia, 1991.Google Scholar
  3. 3.
    B. Y. Choueiry and B. Faltings. Temporal abstractions and a partitioning heuristic for interactive resource allocation. In Notes of Workshop on Knowledge-based Production Planning, Scheduling and Control, IJCAI-93, pages 59–72, Chambery, France, 1993.Google Scholar
  4. 4.
    D. Corne, P. Ross, and Hsiao-Lan Fang. Fast practical evolutionary timetabling. Lecture Notes in Computer Science, 865:250–263, 1994.Google Scholar
  5. 5.
    R. Dechter. Constraint networks. In S. C. Shapiro, editor, Encyclopedia of Artificial Intelligence, 2nd Edition, pages 276–285. John Wiley & Sons, 1992.Google Scholar
  6. 6.
    R. Dechter and J. Pearl. Network-based heuristics for constraint satisfaction problems. Artificial Intelligence, 34:1–38, 1988.MathSciNetCrossRefGoogle Scholar
  7. 7.
    R. Dechter and P. vanBeek. Constraint tightness and looseness versus local and global consistency. J. of ACM, 44:549–566, 1997.MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    M. C. Golumbic. Algorithmic aspects of perfect graphs. Annals of Discrete Mathematics, 21:301–323, 1984.MATHMathSciNetGoogle Scholar
  9. 9.
    S.A. Grant and B.M. Smith. The phase transition behaviour of maintaining arc consistency. In Proceedings of the 12th European Conference on Artificial Intelligence, pages 175–179, Budapest, Hungary, 1996.Google Scholar
  10. 10.
    P. Prosser. Hybrid algorithms for the constraint satisfaction problem. Computational Intelligence, 9:268–299, 1993.Google Scholar
  11. 11.
    P. Prosser. Binary constraint satisfaction problems: some are harder than others. In Proceedings of the 11th European Conference on Artificial Intelligence, pages 95–99, Amsterdam, 1994.Google Scholar
  12. 12.
    P. Ross, D. Corne, and H. Terashima. The phase transition niche for evolutionary algorithms in timetabling. In Proceedings of the 1st Conference on Practice and Applications of Automated Timetabling, pages 269–282, Edinburgh, UK, August, 1995.Google Scholar
  13. 13.
    B. M. Smith. Phase transition and the mushy region in csp. In Proceedings of the 11th European Conference on Artificial Intelligence, pages 100–104, Amsterdam, The Netherlands, 1994.Google Scholar
  14. 14.
    G. Solotorevsky, E. Shimony, and A. Meisels. Csps with counters: a likelihood-based heuristic. In Proc. Workshop on Non Standard Constraint Processing, ECAI96, pages 107–118, Budapest, August, 1996.Google Scholar
  15. 15.
    E. Tsang. Foundations of Constraint Satisfaction. Academic Press, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Amnon Meisels
    • 1
  • Natalia Lusternik
    • 1
  1. 1.Dept. of Mathematics and Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael

Personalised recommendations