Multibody System Dynamics

, Volume 1, Issue 1, pp 47–64 | Cite as

Multibody Dynamic Response Optimization with ALM and Approximate Line Search

  • Min-Soo Kim
  • Dong-Hoon Choi


This paper presents an efficient approach for dynamic responseoptimization based on the ALM method. In this approach, an approximateaugmented Lagrangian is employed for line searches while an exactaugmented Lagrangian is used for finding search directions. An importantfeature of this study is that the approximate augmented Lagrangian forline search is composed of the linearized cost and constraint functionsprojected on the search direction. The quality of this approximationshould be good since an approximate penalty term is found to have almostsecond-order accuracy near the optimum. Quasi-Newton and conjugategradient algorithms are used to find exact search directions and a goldensection method followed by a cubic polynomial approximation is employedfor line search. The numerical performance of the proposed approach isinvestigated by solving eight typical dynamic response optimizationproblems and comparing the results with those in the literature. Thiscomparison shows that the suggested approach is robust and efficient.

dynamic response optimization approximate line search ALM method constrained optimization dynamic system 


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  1. 1.
    Barthelemy, J.-F.M. and Haftka, R.T., ‘Approximation concepts for optimum structural design–A review’, Structural Optimization 5, 1993, 129–144.Google Scholar
  2. 2.
    Fleury, C. and Braibant, V., ‘Structural optimization–Anew dualmethod using mixed variables’, International Journal for Numerical Methods in Engineering 23, 1986, 409–428.Google Scholar
  3. 3.
    Hansen, S.R. and Vanderplaats, G.N., ‘Approximation method for configuration optimization of trusses’, AIAA Journal 28(1), 1990, 161–168.Google Scholar
  4. 4.
    Cassis, J.H. and Schmit, L.A., ‘Optimum structural design with dynamic constraints’, Journal of Structural Division, ASCE ST10, 1976, 2053–2071.Google Scholar
  5. 5.
    Sepulveda, A.E. and Thomas, H.L., ‘New approximation for steady-state response of general damped systems’, AIAA Journal 33(6), 1995, 1127–1133.Google Scholar
  6. 6.
    Sepulveda, A.E. and Thomas, H.L., ‘Improved transient response approximation for general damped systems’, AIAA Journal 34(6), 1996, 1261–1269.Google Scholar
  7. 7.
    Haug, E.J. and Arora, J.S., Applied Optimal Design, Wiley-Interscience, New York, 1979, 329–386.Google Scholar
  8. 8.
    Hsieh, C.C. and Arora, J.S., ‘Design sensitivity analysis and optimization of dynamic response’, Computer Methods in Applied Mechanics and Engineering 43, 1984, 195–219.Google Scholar
  9. 9.
    Hsieh, C.C. and Arora, J.S., ‘Hybrid formulation for treatment of point-wise state variable constraints in dynamic response optimization’, Computer Methods in Applied Mechanics and Engineering 48, 1985, 171–189.Google Scholar
  10. 10.
    Paeng, J.K. and Arora, J.S., ‘Dynamic response optimization of mechanical systems with multiplier methods’, ASME Journal of Mechanism, Transmission, and Automation in Design 111, 1985, 73–80.Google Scholar
  11. 11.
    Chahande, A. and Arora, J.S., ‘Optimization of large structure subjected to dynamic loads with the multiplier method’, International Journal for Numerical Methods in Engineering 37, 1994, 413–430.Google Scholar
  12. 12.
    Choi, D.-H. and Kim, M.-S., ‘A new approach to themin-max dynamic response optimization’, in IUTAM Symposium on Optimization of Mechanical Systems, D. Bestle and W. Schiehlen (eds.), Kluwer Academic Publishers, Dordrecht, 1996, 65–72.Google Scholar
  13. 13.
    Luenberger, D.G., Linear and Nonlinear Programming, 2nd edn., Addison-Wesley, Reading, MA, 1984, 406–415.Google Scholar
  14. 14.
    Gill, P.E., Murray, W. and Wright, M.H., Practical Optimization, Academic Press, London, 1981, 225–230.Google Scholar
  15. 15.
    Bertsekas, D.P., Constrained Optimization and Lagrange Multiplier Methods, Academic Press, London, 1982.Google Scholar
  16. 16.
    Rockafella, R.T., ‘The multiplier method of Hestenes and Powell applied to convex programming’, Journal of Optimization Theory and Applications 12(6), 1973, 555–562.Google Scholar
  17. 17.
    Kim, M.-S. and Choi, D.-H., ‘Astudy on the penalty parameter update rule for AL Malgorithms in dynamic response optimization’, Technical Report OPT-9503, AMOD Lab. Hanyang University, 1995.Google Scholar
  18. 18.
    Kim, M.-S. and Choi, D.-H., ‘Integrated design optimization library 3.0 for advanced design’, Technical Report OPT-9601, AMOD Lab. Hanyang University, 1996.Google Scholar
  19. 19.
    Fletcher, R., Practical Methods of Optimization, John Wiley & Sons, Chichester, 1987, 44–96.Google Scholar
  20. 20.
    Haftka, R.T., Gürdal, Z. and Kamat, M.P., Elements of Structural Optimization, Kluwer Academic Publishers, Dordrecht, 1992, 136–137.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Min-Soo Kim
    • 1
  • Dong-Hoon Choi
    • 1
  1. 1.Department of Mechanical Design and Production EngineeringHanyang UniversitySungdong-Ku, SeoulKorea

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