This paper presents a MATLAB code with the implementation of the Topology Optimization of Binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49–61, 2018). The TOBS is a gradient-based topology optimization method that employs binary design variables and formal mathematical programming. Besides its educational purposes, the 101-line code is provided to show that topology optimization with integer linear programming can be efficiently carried out, contrary to the previous reports in the literature. Compliance minimization subject to a volume constraint is first solved to highlight the main features of the TOBS method. The optimization parameters are discussed. Then, volume minimization subject to a compliance constraint is solved to illustrate that the method can efficiently deal with different types of constraints. Finally, simultaneous volume and displacement constraints are investigated in order to expose the capabilities of the optimizer and to serve as a tutorial of multiple constraints. The 101-line MATLAB code and some simple enhancements are elucidated, keeping only the integer programming solver unmodified so that it can be tested and extended to other numerical examples of interest.

本文介绍了一种MATLAB代码，该代码实现了Sivapuram和Picelli首次发布的二元结构拓扑优化（TOBS）方法（Finite Elem Anal Des 139：第49–61页，2018年）。TOBS是一种基于梯度的拓扑优化方法，采用二进制设计变量和形式化数学程序设计。除了其教学目的之外，还提供了101行代码，以表明可以有效地执行具有整数线性规划的拓扑优化，这与文献中先前的报道相反。首先解决受体积约束的合规性最小化问题，以突出TOBS方法的主要特征。讨论了优化参数。然后，解决了服从约束条件下的体积最小化问题，以说明该方法可以有效处理不同类型的约束条件。最后，对同时存在的体积和位移约束进行了研究，以揭示优化器的功能并用作多个约束的教程。阐明了101行MATLAB代码和一些简单的增强功能，仅使整数编程求解器保持不变，以便可以对其进行测试并将其扩展到其他感兴趣的数值示例。