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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brelaz, D.: New Methods to Color the Vertices of a Graph. Commun. of the ACM 22 (1979) 251–256
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
Burke, E., Newall, J.: A Multi-stage Evolutionary Algorithm for the Timetable Problem. IEEE Trans. Evol. Comput. 3 (1999) 63–74
Carter, M., Laporte, G., Lee, S.Y.: Examination Timetabling: Algorithmic Strategies and Applications. J. Oper. Res. Soc. 47 (1996) 373–383
Carter, M.: ftp://ie.utoronto.ca/pub/carter/testprob
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
Clearwater, S., Hogg, T.: Problem Structure Heuristics and Scaling Behavior for Genetic Algorithms. Artif. Intell. 81 (1996) 327–347
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
Culberson, J.: Graph Coloring:http://www.cs.ualberta.ca/~joe/Coloring/index.html (1995)
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
Eiben, A., Van der Hauw, J., Van Hemert, J.: Graph Coloring with Adaptive Evolutionary Algorithms. J. Heuristics 4 (1998) 25–46
Falkenauer, E.: Genetic Algorithms and Grouping Problems. Wiley, Chichester (1998)
Fleurent, Ch.; Ferland, J.: Genetic and Hybrid Algorithms for Graph Coloring. Ann. Oper. Res. 63 (1995) 437–463
Hertz, A., De Werra, D.: Using Tabu Search Techniques for Graph Coloring. Computing 39 (1987) 345–351
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
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
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
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
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
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)
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
Turner, J.: Almost All k-colorable Graphs are Easy to Color. J. Algorithms 9 (1988) 63–82
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Sringer-Verlag Berlin Hrdelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-44629-X_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42421-5
Online ISBN: 978-3-540-44629-3
eBook Packages: Springer Book Archive