Further elaborations on topology optimization via sequential integer programming and Canonical relaxation algorithm and 128-line MATLAB code

This paper provides further elaborations on discrete variable topology optimization via sequential integer programming and Canonical relaxation algorithm. Firstly, discrete variable topology optimization problem for minimum compliance subject to a material volume constraint is formulated and approxi...

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Published in:	Structural and multidisciplinary optimization Vol. 61; no. 1; pp. 411 - 431
Main Authors:	Liang, Yuan, Cheng, Gengdong
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020 Springer Nature B.V
Subjects:	Algorithms Computational Mathematics and Numerical Analysis Continuity (mathematics) Educational Paper Engineering Engineering Design Integer programming Integers Matlab Optimization Sensitivity Theoretical and Applied Mechanics Topology optimization Discrete variable topology optimization Sequential approximate programming (SAP) Canonical relaxation algorithm MATLAB
ISSN:	1615-147X, 1615-1488
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Abstract	This paper provides further elaborations on discrete variable topology optimization via sequential integer programming and Canonical relaxation algorithm. Firstly, discrete variable topology optimization problem for minimum compliance subject to a material volume constraint is formulated and approximated by a sequence of discrete variable sub-programming with the discrete variable sensitivity. The differences between continuous variable sensitivity and discrete variable sensitivity are discussed. Secondly, the Canonical relaxation algorithm designed to solve this sub-programming is presented with a discussion on the move limit strategy. Based on the discussion above, a compact 128-line MATLAB code to implement the new method is included in Appendix 1 . As shown by numerical experiments, the 128-line code can maintain black-white solutions during the optimization process. The code can be treated as the foundation for other problems with multiple constraints.
AbstractList	This paper provides further elaborations on discrete variable topology optimization via sequential integer programming and Canonical relaxation algorithm. Firstly, discrete variable topology optimization problem for minimum compliance subject to a material volume constraint is formulated and approximated by a sequence of discrete variable sub-programming with the discrete variable sensitivity. The differences between continuous variable sensitivity and discrete variable sensitivity are discussed. Secondly, the Canonical relaxation algorithm designed to solve this sub-programming is presented with a discussion on the move limit strategy. Based on the discussion above, a compact 128-line MATLAB code to implement the new method is included in Appendix 1. As shown by numerical experiments, the 128-line code can maintain black-white solutions during the optimization process. The code can be treated as the foundation for other problems with multiple constraints. This paper provides further elaborations on discrete variable topology optimization via sequential integer programming and Canonical relaxation algorithm. Firstly, discrete variable topology optimization problem for minimum compliance subject to a material volume constraint is formulated and approximated by a sequence of discrete variable sub-programming with the discrete variable sensitivity. The differences between continuous variable sensitivity and discrete variable sensitivity are discussed. Secondly, the Canonical relaxation algorithm designed to solve this sub-programming is presented with a discussion on the move limit strategy. Based on the discussion above, a compact 128-line MATLAB code to implement the new method is included in Appendix 1 . As shown by numerical experiments, the 128-line code can maintain black-white solutions during the optimization process. The code can be treated as the foundation for other problems with multiple constraints.
Author	Liang, Yuan Cheng, Gengdong
Author_xml	– sequence: 1 givenname: Yuan surname: Liang fullname: Liang, Yuan organization: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology – sequence: 2 givenname: Gengdong surname: Cheng fullname: Cheng, Gengdong email: chenggd@dlut.edu.cn organization: State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology
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SubjectTerms	Algorithms Computational Mathematics and Numerical Analysis Continuity (mathematics) Educational Paper Engineering Engineering Design Integer programming Integers Matlab Optimization Sensitivity Theoretical and Applied Mechanics Topology optimization
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Title	Further elaborations on topology optimization via sequential integer programming and Canonical relaxation algorithm and 128-line MATLAB code
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