基于微分动态系统的填充函数方法

发布时间：2018-06-24 22:26

本文选题：填充函数 + 微分动态系统　；参考：《华东理工大学》2015年硕士论文

【摘要】：本文提出了两个基于微分动态系统的填充函数方法,用于求解多极值带约束的全局最优化问题。文章提出了两个新的填充函数,在适当的假设下证明了它的填充性质。在Kennedy and Chua的基础上分别构造了两个微分动态系统并讨论了它们的稳定性,将微分动态系统分别和目标函数以及填充函数结合起来,用两阶段法求解全局最优解。第一阶段：用目标函数及其约束函数建立微分动态系统,通过求解系统,求得原问题的一个局部极小点；第二阶段：在当前局部极小点处构造填充函数和关于填充函数的微分动态系统,在理论上证明了此阶段得到的稳定点一定是在低水平集上。通过两阶段不断循环迭代最终得到原问题的全局极小点。本文根据理论分析,设计相关算法,并进行数值试验。数值结果说明算法是有效的。
[Abstract]:In this paper, two filling function methods based on differential dynamic systems are proposed to solve global optimization problems with multi-extremum constraints. In this paper, two new filling functions are proposed and their filling properties are proved under proper assumptions. On the basis of Kennedy and Chua, two differential dynamic systems are constructed and their stability is discussed. The differential dynamic system is combined with objective function and filling function respectively, and the global optimal solution is solved by two-stage method. In the first stage, the differential dynamic system is established by using the objective function and its constraint function, and a local minimal point of the original problem is obtained by solving the system. In the second stage, the filling function and the differential dynamic system about the filling function are constructed at the current local minima. It is proved theoretically that the stable points obtained in this stage must be on the low level set. Finally, the global minima of the original problem is obtained by two stage continuous iteration. Based on the theoretical analysis, this paper designs relevant algorithms and carries out numerical experiments. Numerical results show that the algorithm is effective.
【学位授予单位】：华东理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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