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Numerical comparison of nonlinear programming algorithms for structural optimization

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Abstract

For FE-based structural optimization systems, a large variety of different numerical algorithms is available, e.g. sequential linear programming, sequential quadratic programming, convex approximation, generalized reduced gradient, multiplier, penalty or optimality criteria methods, and combinations of these approaches. The purpose of the paper is to present the numerical results of a comparative study of eleven mathematical programming codes which represent typical realizations of the mathematical methods mentioned. They are implemented in the structural optimization system MBB-LAGRANGE, which proceeds from a typical finite element analysis. The comparative results are obtained from a collection of 79 test problems. The majority of them are academic test cases, the others possess some practicalreal life background. Optimization is performed with respect to sizing of trusses and beams, wall thicknesses, etc., subject to stress, displacement, and many other constraints. Numerical comparison is based on reliability and efficiency measured by calculation time and number of analyses needed to reach a certain accuracy level.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany

    K. Schittkowski

  2. IWR, Universität Heidelberg, D-69120, Heidelberg, Germany

    C. Zillober

  3. CAP debis Division Industrie, D-80992, München, Germany

    R. Zotemantel

Authors
  1. K. Schittkowski
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  2. C. Zillober
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  3. R. Zotemantel
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The research project was sponsored by the Deutsche Forschungsgemeinschaft under research contract DFG-Schi 173/6-1

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Schittkowski, K., Zillober, C. & Zotemantel, R. Numerical comparison of nonlinear programming algorithms for structural optimization. Structural Optimization 7, 1–19 (1994). https://doi.org/10.1007/BF01742498

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