滤子填充函数方法在单目标与多目标优化问题中的运用

发布时间：2018-10-14 14:09

【摘要】：填充函数算法是求解全局优化问题的有效方法之一,而滤子技术以其良好的数值效果广泛应用于局部优化算法中。为优化填充函数方法,本文首先提出一个基于滤子技术的填充函数算法用于求解带箱式约束的非凸单目标全局优化问题,主要应用滤子来监控迭代过程。文章给出一个新的填充函数并讨论了其特性,在此基础上提出了理论算法及算法性质。最后列出数值实验结果以说明算法的有效性。然后,文章定义了多目标优化问题中的局部Pareto有效解和全局Pareto有效解,将基于滤子技术的填充函数算法运用到求解非凸多目标全局优化问题中。同时,文章提出三个新的填充函数并研究了它们的性质,然后结合多目标优化算法中的理想点法、评价系数法以及最速下降法,提出了理想点的填充函数算法、和函数的填充函数算法以及直接法的填充函数算法。最后,通过数值算例验证三个算法的可行性。
[Abstract]:Filling function algorithm is one of the effective methods for solving global optimization problems, and filter technique is widely used in local optimization algorithm with its good numerical effect. In order to optimize the filling function method, a filter-based filling function algorithm is proposed to solve the non-convex single-objective global optimization problem with box constraints. The filter is mainly used to monitor the iterative process. In this paper, a new filling function is given and its properties are discussed. On this basis, a theoretical algorithm and its properties are proposed. Finally, the numerical results are given to illustrate the effectiveness of the algorithm. Then, the local Pareto efficient solution and global Pareto efficient solution of multi-objective optimization problem are defined, and the filling function algorithm based on filter technique is applied to solve the non-convex multi-objective global optimization problem. At the same time, three new filling functions are proposed and their properties are studied. Then, an ideal point method, an evaluation coefficient method and a steepest descent method are proposed, and an ideal point filling function algorithm is proposed. And the filling function algorithm of the function and the filling function algorithm of the direct method. Finally, the feasibility of the three algorithms is verified by numerical examples.
【学位授予单位】：华东理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

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