Optimization via Rejection-Free Partial Neighbor Search

• Published in: Statistics and computing Vol. 33; no. 6
• Main Authors: Chen, Sigeng, Rosenthal, Jeffrey S., Dote, Aki, Tamura, Hirotaka, Sheikholeslami, Ali
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2023; Springer Nature B.V
• Subjects: Artificial Intelligence; Combinatorial analysis; Computer Science; Knapsack problem; Optimization; Original Paper; Probability and Statistics in Computer Science; Quadratic programming; Rejection; Search algorithms; Simulated annealing; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Partial Neighbor Search; Simulated Annealing; Rejection-Free; QUBO
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-023-10300-9

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.