论文标题
理论框架和一些有前途的灰狼优化器的发现，第一部分：采样分布和稳定性分析的分析模型
A theoretical framework and some promising findings of grey wolf optimizer, part I: analytical model of sampling distribution and stability analysis
论文作者
论文摘要
本文提出了基于几个有趣的理论发现的灰狼优化器（GWO）的理论框架，涉及采样分布，顺序1和订单-2稳定性以及全球收敛分析。在本文的第一部分中，根据众所周知的停滞假设仔细讨论了新解的采样分布和GWO的概率稳定性的特征。首先，在更新之前的原始解决方案是恒定的假设下，讨论了新溶液的采样分布的特征，主要与关节概率密度函数（PDF）的形状相关。然后，取消原始溶液是恒定的假设以执行采样分布分析，该假设提供了新溶液的几个特征，其中包含关节PDF的形状和任何正整数阶的中央矩。最后，引入并证明了GWO在停滞假设下的顺序1和2稳定性，并证明是上述结论的推断，这些结论均通过数值模拟验证。
This paper proposes a theoretical framework of the grey wolf optimizer (GWO) based on several interesting theoretical findings, involving sampling distribution, order-1 and order-2 stability, and global convergence analysis. In the part I of the paper, the characteristics of the sampling distribution of the new solution and the probabilistic stability of the GWO are carefully discussed based on the well-known stagnation assumption for simplification purposes. Firstly, the characteristics of the sampling distribution of the new solution, mainly related to the shape of the joint probability density function (PDF), are discussed under the assumption that the original solution before updating is constant. Then, the assumption that the original solution is constant is eliminated to perform the sampling distribution analysis, based on which several characteristics of the new solution are provided, containing the shape of the joint PDF and central moments of any positive integer order. Finally, the order-1 and order-2 stability of the GWO under stagnation assumption is introduced and proved as the inference of conclusions above, which are all verified by numerical simulations.
