To efficiently find an optimum parameter combination in a large-scale problem, it is a key to convert the parameters into available variables in actual machines. Specifically, quadratic unconstrained binary optimization problems are solved with the help of machine learning, e.g., factorization machines with annealing, which convert a raw parameter to binary variables. This work investigates the dependence of the convergence speed and the accuracy on binary labeling method, which can influence the cost function shape and thus the probability of being captured at a local minimum solution. By exemplifying traveling salesman problem, we propose and evaluate Gray labeling, which correlates the Hamming distance in binary labels with the traveling distance. Through numerical simulation of traveling salesman problem up to 15 cities at a limited number of iterations, the Gray labeling shows less local minima percentages and shorter traveling distances compared with natural labeling.

翻译：为在大规模问题中高效寻找最优参数组合，关键在于将参数转换为实际机器可用的变量。具体而言，二次无约束二进制优化问题可借助机器学习方法求解，例如采用退火因子分解机将原始参数转换为二进制变量。本研究探讨了收敛速度和精度对二进制标记方法的依赖性，该方法会影响代价函数的形态，从而影响陷入局部最优解的概率。以旅行商问题为例，我们提出并评估了格雷标记法，该方法将二进制标签的汉明距离与旅行距离相关联。通过对多达15个城市、有限迭代次数的旅行商问题进行数值模拟，结果表明：与自然标记法相比，格雷标记法具有更低的局部最优解比例和更短的旅行距离。