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A Grouping Genetic Algorithm for Graph Colouring and Exam Timetabling

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Book cover Practice and Theory of Automated Timetabling III (PATAT 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2079))

Abstract

It has frequently been reported that pure genetic algorithms for graph colouring are in general outperformed by more conventional methods. There is every reason to believe that this is mainly due to the choice of an unsuitable encoding of solutions. Therefore, an alternative representation, based on the grouping character of the graph colouring problem, was chosen. Furthermore, a fitness function defined on the set of partitions of vertices, guiding the Grouping Genetic Algorithm well in the search, was developed. This algorithm has been applied to a choice of hard-to-colour graph examples, with good results. It has also been extended to the application to real-world timetabling problems. As a by-product, phase transition regions of a class of randomly generated graphs have been located.

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References

  1. Brelaz, D.: New Methods to Color the Vertices of a Graph. Commun. of the ACM 22 (1979) 251–256

    Article  MATH  MathSciNet  Google Scholar 

  2. Burke, E., Newall, J., Weare, R.: A Memetic Algorithm for University Exam Timetabling. In: Burke, E., Ross, P. (eds.): Practice and Theory of Automated Timetabling, 1st International Conference (Edinburgh, August/September 1995), Selected Papers. Lecture Notes in Computer Science, Vol. 1153. Springer-Verlag, Berlin Heidelberg New York (1996) 241–250

    Google Scholar 

  3. Burke, E., Newall, J.: A Multi-stage Evolutionary Algorithm for the Timetable Problem. IEEE Trans. Evol. Comput. 3 (1999) 63–74

    Article  Google Scholar 

  4. Carter, M., Laporte, G., Lee, S.Y.: Examination Timetabling: Algorithmic Strategies and Applications. J. Oper. Res. Soc. 47 (1996) 373–383

    Article  Google Scholar 

  5. Carter, M.: ftp://ie.utoronto.ca/pub/carter/testprob

  6. Cheeseman, P., Kanefsky, B., Taylor, W.: Where the Really Hard Problems Are. In: Mylopoulos, J., Reiter, R. (eds.): Proc. 12th IJCAI-91, Vol. 1. Kaufmann, San Francisco, CA (1991) 331–337

    Google Scholar 

  7. Clearwater, S., Hogg, T.: Problem Structure Heuristics and Scaling Behavior for Genetic Algorithms. Artif. Intell. 81 (1996) 327–347

    Article  MathSciNet  Google Scholar 

  8. Culberson, J., Luo, F.: Exploring the k-colorable Landscape with Iterated Greedy. In: Trick, M., Johnson, D. (eds.): Cliques, Colors, and Satisfiability: 2nd DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26. American Mathematical Society (1996) 245–284

    Google Scholar 

  9. Culberson, J.: Graph Coloring:http://www.cs.ualberta.ca/~joe/Coloring/index.html (1995)

  10. Dorne, R., Hao, J.: A New Genetic Local Search Algorithm for Graph Coloring. In: Eiben, A., Bäck, T., Schoenauer, M., Schwefel, H—P. (eds.): Parallel Problem Solving from Nature-PPSN V, Proc. 5th Int. Conf. (Amsterdam, September 1998). Lecture Notes in Computer Science, Vol. 1498. Springer-Verlag, Berlin Heidelberg New York (1998) 745–754

    Chapter  Google Scholar 

  11. Eiben, A., Van der Hauw, J., Van Hemert, J.: Graph Coloring with Adaptive Evolutionary Algorithms. J. Heuristics 4 (1998) 25–46

    Article  MATH  Google Scholar 

  12. Falkenauer, E.: Genetic Algorithms and Grouping Problems. Wiley, Chichester (1998)

    Google Scholar 

  13. Fleurent, Ch.; Ferland, J.: Genetic and Hybrid Algorithms for Graph Coloring. Ann. Oper. Res. 63 (1995) 437–463

    Article  Google Scholar 

  14. Hertz, A., De Werra, D.: Using Tabu Search Techniques for Graph Coloring. Computing 39 (1987) 345–351

    Article  MATH  MathSciNet  Google Scholar 

  15. Johnson, D., Aragon, C., McGeoch, L., Schevon, C.: Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning. Oper. Res. 39 (1991) 378–406

    Article  MATH  Google Scholar 

  16. Paechter, B., Cumming, A., Norman, M., Luchian, H.: Extensions to a Memetic Timetabling System. In: Burke, E., Ross, P. (eds.): Practice and Theory of Automated Timetabling, 1st International Conference (Edinburgh, August/September 1995), Selected Papers. Lecture Notes in Computer Science, Vol. 1153. Springer-Verlag, Berlin Heidelberg New York (1996) 251–265

    Google Scholar 

  17. Ross, P., Corne, D., Terashima-Marìn, H.: The Phase-Transition Niche for Evolutionary Algorithms in Timetabling. In: Burke, E., Ross, P. (eds.): Practice and Theory of Automated Timetabling, 1st International Conference (Edinburgh, August/September 1995), Selected Papers. Lecture Notes in Computer Science, Vol. 1153. Springer-Verlag, Berlin Heidelberg New York (1996) 309–324

    Google Scholar 

  18. Ross, P., Hart, E., Corne, D.: Some Observations about GA-Based Exam Timetabling. In: Burke, E., Carter, M. (eds.): Practice and Theory of Automated Timetabling II, 2nd International Conference (PATAT’97, Toronto, August 1997), Selected Papers. Lecture Notes in Computer Science, Vol. 1408. Springer-Verlag, Berlin Heidelberg New York (1998) 115–129

    Chapter  Google Scholar 

  19. Ross, P., Hart, E.: An Adaptive Mutation Scheme for a Penalty-Based Graph-Colouring GA. In: Eiben, A., Bìck, T., Schoenauer, M., Schwefel, H.-P. (eds.): Parallel Problem Solving from Nature-PPSN V, Proc. 5th International Conference (Amsterdam, September 1998). Lecture Notes in Computer Science, Vol. 1498. Springer-Verlag, Berlin Heidelberg New York (1998) 795–802

    Chapter  Google Scholar 

  20. Terashima-Marìn, H.: A Comparison of GA-Based Methods and Graph-Colouring Methods for Solving the Timetabling Problem. Master’s Thesis, Department of AI, University of Edinburgh (1994)

    Google Scholar 

  21. Terashima-Marìn, H., Ross, P., Valenzuela-Rendón, M.: Evolution of Constraint Satisfaction Strategies in Examination Timetabling. Proc. Genetic and Evolutionary Conference 1999, Orlando, FL., July 13-17 (1999) 635–642

    Google Scholar 

  22. Turner, J.: Almost All k-colorable Graphs are Easy to Color. J. Algorithms 9 (1988) 63–82

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, FH Konstanz, University of Applied Sciences, 78462, Konstanz, Germany

    Wilhelm Erben

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  1. Wilhelm Erben
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Editor information

Editors and Affiliations

  1. School of Computer Science and Information Technology Automated Scheduling, Optimisation and Planning Research Group, University of Nottingham, Jubilee Campus,Wollaton Road, NG8 1BB, Nottingham, UK

    Edmund Burke

  2. Department of Computer Science, FH Konstanz, University of Applied Science, Brauneggerstr. 55, 78462, Konstanz, Germany

    Wilhelm Erben

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© 2001 Sringer-Verlag Berlin Hrdelberg

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Erben, W. (2001). A Grouping Genetic Algorithm for Graph Colouring and Exam Timetabling. In: Burke, E., Erben, W. (eds) Practice and Theory of Automated Timetabling III. PATAT 2000. Lecture Notes in Computer Science, vol 2079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44629-X_9

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  • DOI: https://doi.org/10.1007/3-540-44629-X_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42421-5

  • Online ISBN: 978-3-540-44629-3

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