This paper proposes a novel weighted graph representation for structural topology optimization. Based on the graph theory, a weighted adjacency matrix is first introduced to collect the connectivity information and the corresponding width value of the edges. Accordingly, each edge with different width is symbolized as a rectangle to represent the mapped topology for a regular meshed design domain. To reduce the computational cost, an improved differential evolution (DE) process with a dual self-adaptive mutation operator which is named as the DSADE is proposed to utilize as an optimizer. Finally, three classical numerical tests are carried out. The results indicate that the present method can effectively deal with a series of structural topology optimization problem with different boundary constraints. In addition, by comparing with the related methods in literatures, it is found that the present method can achieve an optimized solution without complex initial definitions.

本文提出了一种用于结构拓扑优化的新型加权图表示。基于图论，首先引入加权邻接矩阵，以收集连通性信息和相应的边缘宽度值。因此，将具有不同宽度的每个边缘符号化为一个矩形，以表示规则网格设计域的映射拓扑。为了降低计算成本，提出了一种具有双重自适应变异算子（称为DSADE）的改进的差分进化（DE）过程，该过程称为优化器。最后，进行了三个经典的数值测试。结果表明，该方法可以有效地解决一系列具有不同边界约束的结构拓扑优化问题。此外，