Bond Graph Causality Assignment and Evolutionary Multi-Objective Optimization

  • Tony Wong
  • Gilles Cormier


Causality assignment is an important task in physical modeling by bond graphs. Traditional causality assignment algorithms have specific aims and particular purposes. However they may fail if a bond graph has loops or contains junction causality violations. Some of the assignment algorithms focuses on the generation of differential algebraic equations to take into account junction violations caused by nonlinear multi-port devices and is not suitable for general bond graphs. In this paper, we present a formulation of the causality assignment problem as a constrained multi-objective optimization problem. Previous solution techniques to this problem include multi-objective Branch-and-Bound and Pareto archived evolution strategy – both are highly complex and time-consuming algorithms. A new solution technique called gSEMO (global Simple Evolutionary Multi-objective Optimizer) is now used to solve the causality assignment problem with very promising results.


Causality assignment constrained optimization evolutionary algorithms multi-objective optimization physical modeling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Van Dijk, On the role of bond graph causality in modeling mechatronics systems, Ph.D. dissertation, Univ. of Twente, Enschede, The Netherlands, 1994.Google Scholar
  2. [2]
    D. C. Karnopp, D. L. Margolis, and R. C. Rosenberg, System Dynamics: A Unified Approach, 2nd ed., New York: John Wiley & Sons, 1990.Google Scholar
  3. [3]
    J. Van Dijk and P. C. Breedveld, “Relaxed causality: a bond graph oriented perspective on dae-modeling,” Proc. International Conf. on Bond Graph Modeling and Simulation, pp. 225-231, 1995.Google Scholar
  4. [4]
    B. J. Joseph and H. R. Martens, “The method of relaxed causality in the bond graph analysis of nonlinear systems,” ASME Trans. Journal of Dynamic Systems, Measurement and Control, no. 96, pp. 95-99, 1974.MATHGoogle Scholar
  5. [5]
    A. Ben-Tal, “Characterization of Pareto and lexicographic optimal solutions,” in Multiple Objective Decision Making – Methods and Applications, vol. 177, Lecture Notes on Economics and Mathematical Systems. Berlin: Springer-Verlag, pp. 1-11, 1980.Google Scholar
  6. [6]
    O. Giel, P. K. Lehre, “On the effect of populations in evolutionary multi-objective optimization,” Proc. of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 651-658, 2006.Google Scholar
  7. [7]
    O. Giel. “Expected runtimes of a simple multi-objective evolutionary algorithm,” Proc. of the 2003 Congress on Evolutionary Computation, pp. 1918-1925, 2003.Google Scholar
  8. [8]
    M. Laumanns, L. Thiele, E. Zitzler, “Running time analysis of multiobjective evolutionary algorithms on Pseudo-Boolean Functions,” IEEE Transactions on Evolutionary Computation, 8(2), pp. 170-182, 2004.CrossRefGoogle Scholar
  9. [9]
    C. M. Fonseca and P. J. Fleming, “Multiobjective optimization and multiple constraint handling with evolutionary algorithms – Part I: A unified formulation,” IEEE Transactions on Systems, Man and Cybernatics, vol. 28, no. 1, pp. 26-37, 1998.CrossRefGoogle Scholar
  10. [10]
    C. A Coello, “Constraint-handling using an evolutionary multiobjective optimization technique,” Civil Engineering Systems, Gordon and Breach Science Publishers, vol. 17, pp. 319-346, 2000.Google Scholar
  11. [11]
    C. A. Coello, “Constraint handling through a multiobjective optimization technique,” in Annie S. Wu, editor, Proc. of the Genetic and Evolutionary Computation Conference, pp. 117-118, 1999.Google Scholar
  12. [12]
    M. A. Atherton, R. A. Bates, “Bond graph analysis in robust engineering design,” Quality and Reliability Engineering International, vol. 16, pp. 325-335, 2000.CrossRefGoogle Scholar
  13. [13]
    M. Laumanns, L. Thiele, E. Zitzler, “Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem,” Natural Computing, vol. 3, pp. 37-51, 2004.MATHCrossRefGoogle Scholar
  14. [14]
    F. Neumann, “Expected runtimes of a simple evolutionary algorithm for the multi-objective minimum spanning tree problem,” Proc. of the 8th Conference on Parallel Problem Solving from Nature, pp. 80-89, 2004.Google Scholar
  15. [15]
    R. Kumar, N. Banerjee, “Running time analysis of a multiobjective evolutionary algorithm on simple and hard problems,” in Alden H. et al. (editors), Foundations of Genetic Algorithms. 8th International Workshop, pp. 112–131, 2005.Google Scholar
  16. [16]
    K. Deb, Multi-Objective Optimization using Evolutionary Algorithms, Chichester, UK: Wiley, 2001.MATHGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Tony Wong
    • 1
  • Gilles Cormier
    • 1
  1. 1.Department of automated manufacturing engineering École de technologie supérieureUniversity of QuébecMontréalCanada

Personalised recommendations