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

• 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
• DOI: 10.1007/s00158-019-02396-3

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.