求非线性规划问题全局最优解的辅助函数方法
发布时间：2018-09-17 13:30
【摘要】：全局最优化是一门应用非常广泛的学科，它构造求解目标函数最优解的计算方法，，研究这些方法的理论性质及实际应用，并讨论决策问题的最优选择。许多经济管理、科学技术和工程设计等问题都可以归结为全局最优化问题，求解这些实际问题的全局最优化方法的研究取得了很大的进展。现在全局最优化已发展成为最优化学科领域中一个独立的研究方向。近几十年，产生了许多关于全局最优化的算法，例如：区间算法、积分水平集算法、填充函数算法和打洞函数算法。由于填充函数方法和打洞函数方法是利用一个辅助变换函数来实现求解全局最优解的过程，因此我们统称它们为辅助函数方法。本文研究的核心内容是非线性全局最优化的辅助函数方法。 本文结构如下：第一章介绍了非线性全局最优化的一些概念和性质，并概述了求解全局最优化问题的几种常见的算法。第二章对于离散型非线性规划问题，改进了文献[29]中定义，构造了相应的填充函数并设计了新的算法，给出了数值实验结果。第三章，在n维空间中，对于非线性约束全局最优化问题构造了一个新的填充-打洞函数，我们证明了此辅助函数同时具有填充函数和打洞函数的性质，根据这个填充-打洞函数设计了新的算法并进行了数值试验，最后还给出了一个供应链的实际问题进行求解，说明我们的算法是有效的。第四章是本文总的结论。
[Abstract]:Global optimization is a widely used subject. It constructs the calculation methods for solving the optimal solution of objective functions, studies the theoretical properties and practical applications of these methods, and discusses the optimal choice of decision problems. Many problems such as economic management, science and technology and engineering design can be reduced to global optimization problems, and great progress has been made in the study of global optimization methods for solving these practical problems. Now global optimization has developed into an independent research direction in the field of optimization. In recent decades, many global optimization algorithms have been developed, such as interval algorithm, integral level set algorithm, fill function algorithm and hole function algorithm. Because the filling function method and the hole function method are the process of solving the global optimal solution by using an auxiliary transformation function, we call them the auxiliary function method. The core of this paper is the auxiliary function method for nonlinear global optimization. The structure of this paper is as follows: in the first chapter, some concepts and properties of nonlinear global optimization are introduced, and several common algorithms for solving global optimization problems are summarized. In chapter 2, the definition of discrete nonlinear programming is improved, the corresponding filling function is constructed and a new algorithm is designed, and the numerical results are given. In chapter 3, we construct a new filling hole function for the nonlinear constrained global optimization problem in n-dimensional space. We prove that the auxiliary function has the properties of both filling function and drilling function. A new algorithm is designed according to the padding-hole function and a numerical experiment is carried out. Finally, a practical problem of the supply chain is solved, which shows that our algorithm is effective. The fourth chapter is the general conclusion of this paper.
【学位授予单位】：河南科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O221.2
本文编号：2246066
[Abstract]:Global optimization is a widely used subject. It constructs the calculation methods for solving the optimal solution of objective functions, studies the theoretical properties and practical applications of these methods, and discusses the optimal choice of decision problems. Many problems such as economic management, science and technology and engineering design can be reduced to global optimization problems, and great progress has been made in the study of global optimization methods for solving these practical problems. Now global optimization has developed into an independent research direction in the field of optimization. In recent decades, many global optimization algorithms have been developed, such as interval algorithm, integral level set algorithm, fill function algorithm and hole function algorithm. Because the filling function method and the hole function method are the process of solving the global optimal solution by using an auxiliary transformation function, we call them the auxiliary function method. The core of this paper is the auxiliary function method for nonlinear global optimization. The structure of this paper is as follows: in the first chapter, some concepts and properties of nonlinear global optimization are introduced, and several common algorithms for solving global optimization problems are summarized. In chapter 2, the definition of discrete nonlinear programming is improved, the corresponding filling function is constructed and a new algorithm is designed, and the numerical results are given. In chapter 3, we construct a new filling hole function for the nonlinear constrained global optimization problem in n-dimensional space. We prove that the auxiliary function has the properties of both filling function and drilling function. A new algorithm is designed according to the padding-hole function and a numerical experiment is carried out. Finally, a practical problem of the supply chain is solved, which shows that our algorithm is effective. The fourth chapter is the general conclusion of this paper.
【学位授予单位】：河南科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O221.2
【参考文献】
相关期刊论文 前1条
1 ;NONLINEAR INTEGER PROGRAMMING AND GLOBALOPTIMIZATION[J];Journal of Computational Mathematics;1999年02期
本文编号：2246066
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