GWO算法收敛性证明与优化能力验证

The Convergence Proof and the Optimization Capability Verification of the GWO

灰狼优化算法(Grey Wolf Optimizer,GWO)是一种优秀的群智能算法,现已被广泛应用于各行各业中。以灰狼优化算法为研究对象,主要分析其对狼群社会等级、包围猎物行为、狩猎行为等的模拟,给出了算法的伪代码及算法步骤。从灰狼优化算法狩猎行为的模拟中推导出该算法具有收敛性,通过定义灰狼状态、灰狼群状态、灰狼状态转移及灰狼状态转移概率,证明了灰狼群状态序列是有限的Markov链,进一步证明了在一定条件下灰狼群状态在有限状态空间具有遍历性,再依据基本的遍历性定理得出灰狼优化算法具有全局收敛性。通过实验验证了灰狼优化算法具有较强的竞争能力。

Grey Wolf Optimizer(GWO)is an excellent swarm intelligence algorithm,which has been widely used in all walks of life.Taken as the research object in this paper,the GWO algorithm is mainly used to analyze the simulation of wolf pack social hierarchy,encircling the prey behavior,hunting behavior and so on,and then the pseudo-code and the steps of the algorithm are given.The convergence of the GWO is deduced from the simulation of hunting behavior,and by defining the state of the grey wolf,the state of the wolf pack,the state transition of the grey wolf and the state transition probability.It is proved that the state sequence of the grey wolves is a finite Markov chain.It is further proved that the state of the wolf pack is ergodic in the finite state space under a certain condition.Then according to the basic ergodicity theorem,it is proved that the GWO has the global convergence.Finally,it is verified through experiments that the GWO has strong competitive ability.