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

arXiv: https://arxiv.org/abs/2204.04906 · HTML: https://mlsanity.com/paper/2204.04906/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 11 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Bayesian Optimization of Combinatorial Structures](https://mlsanity.com/paper/1806.08838/) (2018)
- [Traffic flow optimization using a quantum annealer](https://mlsanity.com/paper/1708.01625/) (2017)
- [Control of automated guided vehicles without collision by quantum annealer and digital devices](https://mlsanity.com/paper/1812.01532/) (2018)
- [Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer](https://mlsanity.com/paper/1508.06182/) (2015)
- [Quadratization in discrete optimization and quantum mechanics](https://mlsanity.com/paper/1901.04405/) (2019)
- [Continuous black-box optimization with quantum annealing and random subspace coding](https://mlsanity.com/paper/2104.14778/) (2021)

## Built on by (most cited first, 17 of 17)

- [Lossy compression of matrices by black-box optimisation of mixed integer nonlinear programming](https://mlsanity.com/paper/2204.10579/) (2022)
- [Implementation of Trained Factorization Machine Recommendation System on Quantum Annealer](https://mlsanity.com/paper/2210.12953/) (2022)
- [Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machine](https://mlsanity.com/paper/2303.14993/) (2023)
- [SWIFT-FMQA: Enhancing Factorization Machine with Quadratic-Optimization Annealing via Sliding Window](https://mlsanity.com/paper/2507.21024/) (2025)
- [Effectiveness of Binary Autoencoders for QUBO-Based Optimization Problems](https://mlsanity.com/paper/2602.10037/) (2026)
- [Random Postprocessing for Combinatorial Bayesian Optimization](https://mlsanity.com/paper/2309.02842/) (2023)
- [Function Smoothing Regularization for Precision Factorization Machine Annealing in Continuous Variable Optimization Problems](https://mlsanity.com/paper/2407.04393/) (2024)
- [Real-Time Black-Box Optimization for Dynamic Discrete Environments Using Embedded Ising Machines](https://mlsanity.com/paper/2506.16924/) (2025)
- [Efficient Bit Labeling in Factorization Machines with Annealing for Traveling Salesman Problem](https://mlsanity.com/paper/2407.02091/) (2024)
- [Subsampling Factorization Machine Annealing](https://mlsanity.com/paper/2508.08778/) (2025)
- [High-Order Epistasis Detection Using Factorization Machine with Quadratic Optimization Annealing and MDR-Based Evaluation](https://mlsanity.com/paper/2601.01860/) (2026)
- [Factorization Machine with Quadratic-Optimization Annealing for RNA Inverse Folding and Evaluation of Binary-Integer Encoding and Nucleotide Assignment](https://mlsanity.com/paper/2602.16643/) (2026)
- [Initialization Method for Factorization Machine Based on Low-Rank Approximation for Constructing a Corrected Approximate Ising Model](https://mlsanity.com/paper/2410.12747/) (2024)
- [Standardization of Multi-Objective QUBOs](https://mlsanity.com/paper/2504.12419/) (2025)
- [Quantum Computing and AI: Perspectives on Advanced Automation in Science and Engineering](https://mlsanity.com/paper/2505.10012/) (2025)
- [Binarizing Physics-Inspired GNNs for Combinatorial Optimization](https://mlsanity.com/paper/2507.13703/) (2025)
- [Stage-dependent integer-binary encoding in factorization-machine black-box optimization](https://mlsanity.com/paper/2606.23188/) (2026)

## Abstract (arXiv)

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.