Optimization via Rejection-Free Partial Neighbor Search

Abstract

Simulated Annealing using Metropolis steps at decreasing temperatures is widely used to solve complex combinatorial optimization problems (Kirkpatrick et al, 1983). To improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm which avoids the inefficiency of rejections by considering all the neighbors at each step (Rosenthal et al, 2021). To avoid the algorithm getting stuck in a local extreme area, we propose an enhanced version of Rejection-Free called Partial Neighbor Search, which only considers random part of the neighbors while applying the Rejection-Free technique. In this paper, we apply these methods to several examples such as quadratic unconstrained binary optimization (QUBO) problems to demonstrate superior performance of the Rejection-Free Partial Neighbor Search algorithm.