摘要： 研究人工鱼群算法，按候选解分量所在的区间，将搜索空间转化为离散空间，该空间中每个点即为一个人工鱼的位置状态，其能量(食物浓度)即为该点的目标函数值。分别将离散空间集合、人工鱼集合划分为若干个非空子集。在人工鱼觅食、聚群和追尾移动过程中，计算其从一个位置状态转移到任意一个位置状态的转移概率。每个位置状态对应有限Markov链的一个状态，且满足可归约随机矩阵的稳定性条件，由此证明人工鱼群算法的全局收敛性。

关键词: 先进计算, 人工鱼群算法, 全局收敛性, 有限Markov链

Abstract: This paper studies the Artificial Fish Swarm Algorithm(AFSA). The continuous search space is discretized based on the interval-value that each component of a feasible solution locates, each point in the discrete space is just a position state of an artificial fish, its energy(food density) is the objective function value at this point. The whole discrete space and the set of all artificial fishes are also divided into a series of non-empty subsets. During preying, swarming or following activities of artificial fishes, each artificial fish’s transition probability from a position to another position can be simply calculated. Each position state corresponds to a state of a finite Markov chain, then the stability condition of a reducible stochastic matrix can be satisfied. In conclusion, the global convergence of AFSA is proved.

Key words: advanced computing, Artificial Fish Swarm Algorithm(AFSA), global convergence, finite Markov chain

中图分类号: 

• TP18