Application of QUBO solver using black-box optimization to structural design for resonance avoidance

TL;DR

This paper demonstrates how black-box optimization methods, specifically using factorization machines, can effectively apply QUBO solvers to structural design problems like resonance avoidance, overcoming transformation challenges.

Contribution

It introduces a novel approach combining BBO with QUBO for structural design, enabling efficient resonance avoidance without complex problem reformulation.

Findings

BBO with factorization machines performs well in calculation time.

The method successfully finds optimal resonance avoidance solutions.

Potential for broader application in structural design optimization.

Abstract

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 employed the BBO methods 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. We demonstrated that BBO using a factorization machine shows good performance in both the calculation time and the success probability of finding the optimal solution. Our results can open up QUBO solvers' potential for other applications in structural designs.