Binary-coding-based ant colony optimization and its convergence

Ant colony optimization (ACO for short) is a meta-heuristics for hard combinatorial optimization problems. It is a population-based approach that uses exploitation of positive feedback as well as greedy search. In this paper, genetic algorithm's (GA for short) ideas are introduced into ACO to present a new binary-coding based ant colony optimization. Compared with the typical ACO, the algorithm is intended to replace the problem's parameter-space with coding-space, which links ACO with GA so that the fruits of GA can be applied to ACO directly. Furthermore, it can not only solve general combinatorial optimization problems, but also other problems such as function optimization. Based on the algorithm, it is proved that if the pheromone remainder factor ρ is under the condition of ρ≥1, the algorithm can promise to converge at the optimal, whereas if 0<ρ<1, it does not. This work is supported by the Science Foundation of Shanghai Municipal Commission of Science and Technology under Grant No.00JC14052. Tian-Ming Bu received the M.S. degree in computer software and theory from Shanghai University, China, in 2003. And now he is a Ph.D. candidate of Fudan University in the same area of theory computer science. His research interests include algorithms, especially, heuristic algorithms and heuristic algorithms and parallel algorithms, quantum computing and computational complexity. Song-Nian Yu received the B.S. degree in mathematics from Xi'an University of Science and Technology, Xi'an, China, in 1981, the Ph.D. degree under Prof. L. Lovasz's guidance and from Lorand University, Budapest, Hungary, in 1990. Dr. Yu is a professor in the School of Computer Engineering and Science at Shanghai University. He was a visiting professor as a faculty member in Department of Computer Science at Nelson College of Engineering, West Virginia University, from 1998 to 1999. His current research interests include parallel algorithms' design and analyses, graph theory, combinatorial optimization, wavelet analyses, and grid computing. Hui-Wei Guan received the B.S. degree in electronic engineering from Shanghai University, China, in 1982, the M.S. degree in computer engineering from China Textile University, China, in 1989, and the Ph.D. degree in computer science and engineering from Shanghai Jiaotong University, China, in 1993. He is an associate professor in the Department of Computer Science at North Shore Community College, USA. He is a member of IEEE. His current research interests are parallel and distributed computing, high performance computing, distributed database, massively parallel processing system, and intelligent control.