  Ising formulations are widely utilized to solve combinatorial optimization
problems, and a variety of quantum or semiconductor-based hardware has recently
been made available. In combinatorial optimization problems, the existence of
local minima in energy landscapes is problematic to use to seek the global
minimum. We note that the aim of the optimization is not to obtain exact
samplings from the Boltzmann distribution, and there is thus no need to satisfy
detailed balance conditions. In light of this fact, we develop an algorithm to
get out of the local minima efficiently while it does not yield the exact
samplings. For this purpose, we utilize a feature that characterizes locality
in the current state, which is easy to obtain with a type of specialized
hardware. Furthermore, as the proposed algorithm is based on a rejection-free
algorithm, the computational cost is low. In this work, after presenting the
details of the proposed algorithm, we report the results of numerical
experiments that demonstrate the effectiveness of the proposed feature and
algorithm.
