The phase-transition niche for evolutionary algorithms in timetabling

  • Peter Ross
  • David Corne
  • Hugo Terashima-Marín
Complexity Issues
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1153)


Constraint satisfaction problems tend to display phase transitions with respect to the effort required by specific problem solving strategies. So far, little is known concerning the causes of phase transitions, or the relative differences between performance of different algorithms around them, especially with respect to stochastic iterative methods such as evolutionary search. Also, work so far on phase transitions concentrates on homogeneous random problems, rather than problems displaying elements of structure typical of more realistic problems. We investigate some of these issues, and uncover some new phase transition regions on timetabling style problems, occurring in the context of varying degrees of problem homogenity as well as (the more standard) graph connectivity. Further, we find that a simple evolutionary algorithm outperforms a simple Stochastic Hillclimber in regions strongly associated with certain phase transitions, and not others. Finally, we discuss various clues to the underlying causes of these phase transitions.


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  1. 1.
    D. Abramson and J. Abela, ‘A parallel genetic algorithm for solving the school timetabling problem', Technical report, Division of Information Technology, C.S.I.R.O., (April 1991).Google Scholar
  2. 2.
    B. Bollobas, Random Graphs, Academic Press, 1985.Google Scholar
  3. 3.
    P. Cheeseman, B. Kenefsky, and W.M. Taylor, ‘Where the really hard problems are', in Proceedings of IJCAI-91, pp. 331–337, (1991).Google Scholar
  4. 4.
    Robert J. Collins and David R. Jefferson, ‘Selection in massively parallel genetic algorithms', in Proceedings of the Fourth International Conference on Genetic Algorithms, eds., R.K. Belew and L.B. Booker, pp. 249–256. San Mateo: Morgan Kaufmann, (1991).Google Scholar
  5. 5.
    Dave Corne, Hsiao-Lan Fang, and Chris Mellish, 'solving the module exam scheduling problem with genetic algorithms', in Proceedings of the Sixth International Conference in Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, eds., Paul W.H. Chung, Gillian Lovegrove, and Moonis Ali, 370–373, Gordon and Breach Science Publishers, (1993).Google Scholar
  6. 6.
    A. Juels and M. Wattenberg, ‘Stochastic hillclimbing as a baseline method for evaluating genetic algorithms', Technical Report UCB Technical Report CSD-94-834, Department of Computer Science, University of California at Berkeley, (1994).Google Scholar
  7. 7.
    U-M. O'Reilly and F. Oppacher, ‘Program search with a hierarchical variable length representation: genetic programming, simulated annealing and stochastic hill climbing', in Parallel Problem Solving from Nature — PPSN III, eds., Y. Davidor, H-P. Schwefel, and R. Manner, number 866 in Lecture Notes in Computer Science. Springer-Verlag, (1994).Google Scholar
  8. 8.
    Patrick Prosser, ‘Binary constraint satisfaction problems: Some are harder than others', in Proceedings of the 11th European Conference on Artificial Intelligence, ed., A. Cohn, pp. 95–99. John Wiley & Sons, Ltd., (1994).Google Scholar
  9. 9.
    Peter Ross, Dave Corne, and Hsiao-Lan Fang, ‘Improving evolutionary timetabling with delta evaluation and directed mutation', in Parallel Problem Solving from Nature III, ed., Y. Davidor, Springer-Verlag, (1994).Google Scholar
  10. 10.
    Barbara Smith, ‘Phase transition and the mushy region in constraint satisfaction problems', in Proceedings of the 11th European Conference on Artificial Intelligence, ed., A. Cohn, pp. 100–104. John Wiley & Sons, Ltd., (1994).Google Scholar
  11. 11.
    H. Terashima-Marin, ‘A comparison of ga-based methods and graph-colouring methods for solving the timetabling problem', Technical Report Technical Report AIGA-94-15, University of Edinburgh Department of Artificial Intelligence, (1994).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter Ross
    • 1
  • David Corne
    • 2
  • Hugo Terashima-Marín
    • 3
  1. 1.Department of Artificial IntelligenceUniversity of EdinburghEdinburghUK
  2. 2.Parallel Emergent & Distributed Architectures Laboratory, Department of Computer ScienceUniversity of ReadingReadingUK
  3. 3.Centre for Artificial IntelligenceITESMMonterreyMexico

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