  The Metropolis algorithm involves producing a Markov chain to converge to a
specified target density $\pi$. In order to improve its efficiency, we can use
the Rejection-Free version of the Metropolis algorithm, which avoids the
inefficiency of rejections by evaluating all neighbors. Rejection-Free can be
made more efficient through the use of parallelism hardware. However, for some
specialized hardware, such as Digital Annealing Unit, the number of units will
limit the number of neighbors being considered at each step. Hence, we propose
an enhanced version of Rejection-Free known as Partial Neighbor Search, which
only considers a portion of the neighbors while using the Rejection-Free
technique. This method will be tested on several examples to demonstrate its
effectiveness and advantages under different circumstances.
