求解TSP问题的多级归约算法.PDF

1000-9825/2003/14(01)0035 ©2003 Journal of Software 软 件 学 报 Vol.14, No.1 ∗ 求解 TSP 问题的多级归约算法 1,2+ 1,2 1,2 1,2,3 邹 鹏 , 周 智 , 陈国良 , 顾 钧 1( 中国科学技术大学 计算机科学技术系,安徽 合肥 230026) 2( 国家高性能计算中心(合肥),安徽 合肥 230026) 3(香港科技大学 计算机科学与技术系,香港) A Multilevel Reduction Algorithm to TSP ZOU Peng1,2+, ZHOU Zhi1,2, CHEN Guo-Liang1,2, GU Jun1,2,3 1(Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230026, China) 2(Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230026, China) 3(Department of Computer Science and Technology, Hong Kong University of Science and Technology, Hong Kong, China) + Corresponding author: Phn: 86-551-3603747, Fax: 86-551-3601013, E-mail: zouchar@ /~zouchar Received 2001-07-17; Accepted 2001-12-27 Zou P, Zhou Z, Chen GL, Gu J. A multilevel reduction algorithm to TSP. Journal of Soft ware, 2003,14(1): 35~42. Abstract: The TSP (traveling salesman problem) is one of the typical NP-hard problems in combinatorial optimization problem. The fast and effective approximate algorithms are needed to solve the large-scale problem in reasonable computing time. The known approximate algorithm can not give a good enough tour for the larger instance in reasonable time. So an algorithm called multilevel reduction algorithm is proposed, which is based on the analysis of the relation of local optimal tour and global optimal tour of the TSP. The partial tour of the global optimal tour is obtained by a very high probability through simply intersecting the local optimal tours. Using these partial tours it could contract the searching space