This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate regularity measures for any discrete optimization algorithm. Shape regularity is quantified by scalar figures ready to evaluate design choices in the form of Pareto-frontiers. Developed metrics deal with information concerning material usage, problematic distribution, and features that complicate manufacturing. The theory is verified by several examples demonstrating the treatment of isolated islands of materials, point connections between material segments, or homogeneity.

翻译：本文处理离散拓扑优化算法中的形状不规则性问题，其中设计是通过在设计区域内自动分布材料来生成的。采用图论为任意离散优化算法推导出合适的正则性度量。形状正则性通过标量值进行量化，这些标量值可随时以帕累托前沿的形式评估设计选择。所开发的度量涉及材料使用、有问题的分布以及使制造复杂化的特征等信息。该理论通过多个示例进行验证，这些示例展示了孤立材料岛、材料片段之间的点连接或均匀性的处理。