Optimization via Rejection-Free Partial Neighbor Search

Simulated Annealing using Metropolis steps at decreasing temperatures is widely used to solve complex combinatorial optimization problems (Kirkpatrick et al. in Science 220(4598):671–680, 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 every step (Rosenthal et al. in Comput Stat 36(4):2789–2811, 2021). To prevent the algorithm from becoming stuck in local extreme areas, we propose an enhanced version of Rejection-Free called Partial Neighbor Search, which only considers random parts of the neighbors while applying Rejection-Free. We demonstrate the superior performance of the Rejection-Free Partial Neighbor Search algorithm compared to the Simulation Annealing and Rejection-Free with several examples, such as the QUBO question, the Knapsack problem, the 3R3XOR problem, and the quadratic programming.