人工鱼群算法的全局收敛性证明

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。

Global Convergence Proof of Artificial Fish Swarm Algorithm

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.