We present a novel formulation of structural design optimization problems specifically tailored to be solved by quantum annealing (QA). Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is QA. This approach requires the optimization problem to be present, e.g., as a quadratic unconstrained binary optimization (QUBO) model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a QUBO problem that can be immediately solved by QA. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware and find that the presented formulation is suitable for solving structural design optimization problems through QA and, for small-scale problems, already works on today's hardware.

翻译：我们提出了一种专门适用于量子退火求解的结构设计优化问题的新公式。结构设计优化旨在寻找最佳（即材料高效且性能优越）的结构构型。为此，可采用计算优化策略，其中一种基于量子力学效应的新兴策略即为量子退火。该方法要求优化问题以二次无约束二元优化模型等形式呈现。因此，我们开发了该优化问题的新公式。后者通常涉及部件的分析模型。本文采用控制结构在载荷作用下行为的能量最小化原理，从而将优化问题表述为一个全局最小化问题。接着，我们将其映射为可直接通过量子退火求解的二次无约束二元优化问题。通过自重加载下复合杆件的尺寸优化问题验证了所提方法。为此，我们制定了应对当前硬件局限性的策略，并发现所提出的公式适用于通过量子退火求解结构设计优化问题，且对于小规模问题，该方案已在当前硬件上实现运行。