  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.
