Matsumori Tadayoshi, Taki Masato, Kadowaki Tadashi
DENSO CORPORATION, 500-1, Minamiyama, Komenoki-cho, Nisshin, Aichi, 470-0111, Japan.
Sci Rep. 2022 Jul 15;12(1):12143. doi: 10.1038/s41598-022-16149-8.
Quadratic unconstrained binary optimization (QUBO) solvers can be applied to design an optimal structure to avoid resonance. QUBO algorithms that work on a classical or quantum device have succeeded in some industrial applications. However, their applications are still limited due to the difficulty of transforming from the original optimization problem to QUBO. Recently, black-box optimization (BBO) methods have been proposed to tackle this issue using a machine learning technique and a Bayesian treatment for combinatorial optimization. We propose a BBO method based on factorization machine to design a printed circuit board for resonance avoidance. This design problem is formulated to maximize natural frequency and simultaneously minimize the number of mounting points. The natural frequency, which is the bottleneck for the QUBO formulation, is approximated to a quadratic model in the BBO method. For the efficient approximation around the optimum solution, in the proposed method, we probabilistically generate the neighbors of the optimized solution of the current model and update the model. We demonstrated that the proposed method can find the optimum mounting point positions in shorter calculation time and higher success probability of finding the optimal solution than a conventional BBO method. Our results can open up QUBO solvers' potential for other applications in structural designs.
二次无约束二进制优化（QUBO）求解器可用于设计避免共振的最优结构。在经典或量子设备上运行的QUBO算法已在一些工业应用中取得成功。然而，由于从原始优化问题转换为QUBO存在困难，它们的应用仍然有限。最近，已提出黑盒优化（BBO）方法，使用机器学习技术和贝叶斯处理来解决组合优化问题。我们提出一种基于因子分解机的BBO方法，用于设计避免共振的印刷电路板。该设计问题被设定为最大化固有频率，同时最小化安装点数量。固有频率是QUBO公式的瓶颈，在BBO方法中被近似为二次模型。为了在最优解附近进行有效近似，在所提出的方法中，我们以概率方式生成当前模型优化解的邻域并更新模型。我们证明，与传统BBO方法相比，所提出的方法能够在更短的计算时间内找到最优安装点位置，并且找到最优解的成功概率更高。我们的结果可以开拓QUBO求解器在结构设计中其他应用的潜力。
