Dynamic Graph Drawing with a Hybridized Genetic Algorithm

  • Bruno Pinaud
  • Pascale Kuntz
  • RØmi Lehn


Automatic graph drawing algorithms, especially those for hierarchical digraphs, have an important place in computer‐aided design software or more generally in software programs where an ef cient visualization tool for complex structure is required. In these cases, aesthetics plays a major role for generating readable and understandable layouts. Besides, in an interactive approach, the program must preserve the mental map of the user between time t 1 and t. In this paper we introduce a dynamic drawing procedure for hierarchical digraph drawing. It tends to minimize arc‐crossing thanks to a hybridized genetic algorithm. The hybridization consists of a local optimization step based on averaging heuristics and two problem‐based crossover operators. A stability constraint based on a similarity measure is used to preserve the likeness between the layouts at time t 1 and t. Computational experiments have been done with an adapted random graph generator to simulate the construction process of 90 graphs. They confirm that, because of the actual algorithm, the arc crossing number of the selected layout is close to the best layout found. We show that computation of the similarity measure tends to preserve the likeness between the two layouts.


Genetic Algorithm Hybridize Genetic Algorithm Stability Constraint Graph Drawing Vertex Pair 


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  1. [1]
    G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph drawing-Algorithms for the visualization of graphs. Prentice Hall, 1999.Google Scholar
  2. [2]
    H. Purchase. Effective information visualization: a study of graph drawing aesthetics and algorithms. Interacting with computers, 13(2), 2000.Google Scholar
  3. [3]
    P. Eades and N. Wormald. Edge crossings in drawings of bipartite graphs. Algo-rithmica, 11:379–403, 1994.MathSciNetMATHGoogle Scholar
  4. [4]
    A. Papakostas, J. M. Six, and I. G. Tollis. Experimental and theoretical results in interactive orthogonal graph drawing. In Proc. of Graph Drawing’96, volume 1190 of Lecture Notes in Computer Sciences, pages 371–386. Springer Verlag, 1997.CrossRefGoogle Scholar
  5. [5]
    P. Eades, W. Lai, K. Misue, and K. Sugiyama. Preserving the mental map of a diagram. In Proc. of Compugraphics, pages 24–33, 1991.Google Scholar
  6. [6]
    L. J. Groves, Z. Michalewicz, P. V. Elia, and C. Z. Janikow. Genetic algorithms for drawing directed graphs. In Proc. of the 5 st Int. Symp. on Methodologies for Intelligent Systems, pages 268–276. Elsevier, 1990.Google Scholar
  7. [7]
    A. Ochoa-Rodr guez and A. Rosete-Suarez. Automatic graph drawing by genetic search. In Proc. of the 11 st Int. Conf. on CAD, CAM, Robotics and Manufactories of the Future, pages 982–987, 1995.Google Scholar
  8. [8]
    J. Utech, J. Branke, H. Schmeck, and P. Eades. An evolutionary algorithm for drawing directed graphs. In Proc. of the Int. Conf. on Imaging Science, Systems and Technology, pages 154–160. CSREA Press, 1998.Google Scholar
  9. [9]
    P. Kuntz, B. Pinaud, and R. Lehn. Elements for the description of tness landscapes associated with local operators for layered drawings of directed graphs. In M. G. C. Resende and J. P. de Sousa, editors, Metaheuristics: Computer Decision-Making, volume 86 of Applied optimization, pages 405–420. Kluwer Academic Publishers, 2004. ISBN 1-4020-7653-2.Google Scholar
  10. [10]
    M. Laguna, R. Marti, and V. Valls. Arc crossing minimization in hierarchical digraphs with tabu search. Computers and Operation Research, 24(12):1175–1186, 1997.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    K. Sugiyama, S. Tagawa, and M. Toda. Methods for visual understanding of hierarchical systems. IEEE Trans. Syst., Man, Cybern., 11(2):109–125, 1981.MathSciNetCrossRefGoogle Scholar
  12. [12]
    R. Marti. Arc crossing minimization in graphs with GRASP. IIE Trans., 33(10):913–919, 2001.MathSciNetGoogle Scholar
  13. [13]
    J. Branke. Dynamic graph drawing. In D. Wagner M. Kaufmann, editor, Drawing Graphs: methods and models, pages 228–246. Springer, 2001.Google Scholar
  14. [14]
    K. F. B hringer and F. N. Paulisch. Using constraints to achieve stability in automatic graph layout algorithms. In Proc. of CHI’90, pages 43–51. ACM, 1990.Google Scholar
  15. [15]
    S. C. North. Incremental layout in DynaDAG. In Proc. of Graph Drawing’95, volume 1027 of Lecture Notes in Computer Science, pages 409–418. SpringerVerlag, 1996.CrossRefGoogle Scholar
  16. [16]
    S. Bridgeman and R. Tamassia. A user study in similarity measures for graph drawing. J. of Graph Algorithms and Applications, 6(3):225–254, 2002.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    D. Whitley and N. Yoo. Modeling simple genetic algorithms for permutation problems. In L. D. Whitley and M. D. Vose, editors, Fundations of Genetic Algorithms III, pages 163–184. Morgan Kaufmann, 1995.Google Scholar
  18. [18]
    Carlos A. Coello Coello. A comprehensive survey of evolutionary-based multiob-jective optimization techniques. Knowledge and information systems, 1(3):269–308, 1999.Google Scholar

Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • Bruno Pinaud
    • 1
  • Pascale Kuntz
    • 1
  • RØmi Lehn
    • 1
  1. 1.Ecole plytechnique de l’universitØde NantesNantes Cedex 3France

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