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

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.