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Continuous methods for dynamic optimization of multibody systems with discrete and mixed variables

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Abstract

Considering the manufacturing process and component specifications in engineering, it is of great significance to investigate the optimization problem with discrete design variables. However, the discreteness of the feasible set of discrete variables will result in a nonconvex and discontinuous optimization problem. It renders traditional continuous variable optimization methods inaccessible and difficult to solve. Especially for the complex multibody dynamic system described by differential-algebraic equations, it is generally high-dimensional and strongly nonlinear, and the optimization calculation is more difficult. In this paper, focusing on optimization problems with discrete variables and mixed discrete-continuous variables, the continuous method for dynamic optimization of multibody systems is proposed. It converts the original problem into a continuous variable optimization problem, avoiding the inherent discontinuity and difficulty of discrete variables, so that the optimization problem can be solved by mature nonlinear programming tools. Two calculation formulas for the continuous method and their implementation are given based on the sigmoid function and nonlinear complementary problem (NCP) function, respectively. The validity and engineering practicability of the proposed method are demonstrated using two dynamic optimization examples of multibody systems with discrete and mixed variables.

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Acknowledgements

The authors are grateful to the National Natural Science Foundation of China (U2241263); the Fundamental Research Funds for the Central Universities (DUT22ZD211, DUT22QN223).

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Authors and Affiliations

  1. Department of Engineering Mechanics, State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian, 116024, P.R. China

    Haijun Peng & Mengru Zhang

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  1. Haijun Peng
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Haijun Peng and Mengru Zhang wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Haijun Peng.

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Peng, H., Zhang, M. Continuous methods for dynamic optimization of multibody systems with discrete and mixed variables. Multibody Syst Dyn 60, 475–496 (2024). https://doi.org/10.1007/s11044-023-09918-4

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