【作者】 梁玉梅；

【导师】 张连生；

【作者基本信息】 上海大学 ， 运筹学与控制论， 2006， 博士

【摘要】 最优化是一门应用相当广泛的学科，它讨论决策问题的最优选择，构造寻求最优解的计算方法并研究这些方法的理论性质及实际计算表现。由于社会的进步和科学技术的发展，最优化问题广泛见于经济计划，工程设计，生产管理，交通运输，国防军事等重要领域，因此受到高度重视。伴随着计算机的高速发展和最优化工作者的努力，最优化的理论分析和计算方法得到了极大提高。 求解一般函数的全局最优解问题是热点课题之一。对全局最优化问题有两个困难需要解决：一是如何从一个局部极小解出发找到更好的局部极小解，另一个是全局最优解的判定问题。全局最优化算法，从算法的构造上大体可以分为确定型算法和随机型算法。其中，填充函数法就是随之出现的一种确定型算法，它是解决第一个困难的实用方法之一。 填充函数的主要思想是：如果已经找到了一个局部极小x~*，但它不是全局最小，我们可以在x~*处构造一个填充函数使迭代点列离开x~*所在的谷域，找到更好的点x′(即x′处的目标函数值比x~*处的目标函数值更小)。然后以x′为初始点极小化原问题找到更优的局部极小点。 填充函数法只需应用成熟的局部极小化算法，因此受到理论以及实际工作者的欢迎。但是由于填充函数是目标函数的复合函数，且目标函数本身可能很复杂，所以构造的填充函数形式也可能很复杂。再就是参数过多，难于调节。还有早期提出的填充函数法是沿着线方向搜索方法，使得在实际计算时工作量很大。构造形式简单以及较少参数的填充函数并使其具有好的性质，以便节约许多冗长的计算步骤及调整参数的时间，提高算法的效率，是理论和实际工作者继续研究填充函数的目的。 本论文的主要工作是：在已有填充函数算法的基础上，对三类连续全局最优化问题尝试提出一些改进和创新。力图在算法效果方面有所提高，在理论方面有所深化。其内容详细情况如下： 本文包含五章内容，第一章主要介绍了目前国内外主要的几种全局最优化问题和算法，以及他们的特点。这包括：填充函数法、打洞函数法、分支定界法等。更多还原

【Abstract】 The optimization is a widely used discipline, which discusses the characters of optimal choice on decision problems and constructs computing approaches to find the optimal solution. Due to the advancement of society and the development of science and technology, the optimization problems are often discovered in the field of economic planning administration, engineering design, production management, traffic transportation, national defence and so on. They are so important that meet with much recognition With the speedy development of computer and the hard work of scientists, the theoretic analysis and computational methods on optimization have been highly improved.To find the effective methods for finding the global optimal solutions of a general multi-minimizers function is one of the hot topics. There two difficulties in global optimization. One is how to leave from a local minimizer to a smaller one and the other is how to judge that the current minimizer is global. Global optimization methods can be classified into two groups: stochastic and deterministic methods. The filled function algorithm introduced by Ge and Qin (1987) is one of the well-known and practical methods for settling the first difficulty The main idea of filled function method is: If a local minimizer x* has been found, we can make a filled function, such that iterative sequential points leave the valley in which x* lies to find a better point x’ in the lower valley (i.e. f(x’) < f(x~*)). Then let x’ be a new initial point to search for a better minimizer.In recent years, many kinds of filled functions with parameters have been presented. However, those parameters are too hard to adjust and it is most probable that global optimizers are lost or fake better minimizers are found. Therefore, further research is worthy of continuing on how we can construct filled functions with simple forms, better properties and more efficient algorithms.This paper mainly consists of five chapters. In the first chapter, some methods for global optimization problems are briefly presented, including the new filled function methods and the branch - and - bound methods, the modified tunnelling methods and the integral function methods, and so on.Chapter 2, a new filled function with one parameter is suggested for finding a global minimum point for a general class of nonlinear programming problems with a closed bounded domain. Without the Lipschitz continuous condition, a new algorithm is presented according to the theoretical analysis. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.Chapter 3, a novel filled function with one parameter is suggested in this paper for finding a global minimum point for a general class of nonlinear programming problems with a closed bounded domain. Two algorithms are presented according to the theoretical analysis. The implementation of the algorithms on several test更多还原