This paper presents a novel design update strategy for topology optimization, as an iterative optimization. The key contribution lies in incorporating a design updater concept with quantum annealing, applicable to both truss and continuum structures. To align with density-based approaches in topology optimization, these updaters are formulated through a multiplicative relationship to represent the design material and serve as design variables. Specifically, structural analysis is conducted on a classical computer using the finite element method, while quantum annealing is utilized for topology updates. The primary objective of the framework is to minimize compliance under a volume constraint. An encoding formulation for the design variables is derived, and the penalty method along with a slack variable is employed to transform the inequality volume constraint. Subsequently, the optimization problem for determining the updater is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model. To demonstrate its performance, the developed design framework is tested on different computing platforms to perform design optimization for truss structures, as well as 2D and 3D continuum structures. Numerical results indicate that the proposed framework successfully finds optimal topologies similar to benchmark results. Furthermore, the results show the advantage of reduced time in finding an optimal design using quantum annealing compared to simulated annealing.

翻译：本文提出了一种新颖的拓扑优化设计更新策略，作为一种迭代优化方法。其核心贡献在于将设计更新器概念与量子退火技术相结合，该方法可同时应用于桁架结构和连续体结构。为了与拓扑优化中的密度法保持一致，这些更新器通过乘法关系进行公式化，以表征设计材料并作为设计变量。具体而言，结构分析在经典计算机上使用有限元法进行，而拓扑更新则利用量子退火实现。该框架的主要目标是在体积约束下最小化柔度。我们推导了设计变量的编码公式，并采用罚函数法及松弛变量来处理不等式体积约束。随后，将确定更新器的优化问题表述为二次无约束二进制优化模型。为验证其性能，所开发的设计框架在不同计算平台上进行了测试，以执行桁架结构以及二维和三维连续体结构的设计优化。数值结果表明，所提出的框架成功地找到了与基准结果相似的最优拓扑。此外，结果还显示了使用量子退火相较于模拟退火在寻找最优设计时具有时间缩短的优势。