【摘要】：全局最優(yōu)化是一門(mén)應(yīng)用非常廣泛的學(xué)科，它構(gòu)造求解目標(biāo)函數(shù)最優(yōu)解的計(jì)算方法，，研究這些方法的理論性質(zhì)及實(shí)際應(yīng)用，并討論決策問(wèn)題的最優(yōu)選擇。許多經(jīng)濟(jì)管理、科學(xué)技術(shù)和工程設(shè)計(jì)等問(wèn)題都可以歸結(jié)為全局最優(yōu)化問(wèn)題，求解這些實(shí)際問(wèn)題的全局最優(yōu)化方法的研究取得了很大的進(jìn)展�，F(xiàn)在全局最優(yōu)化已發(fā)展成為最優(yōu)化學(xué)科領(lǐng)域中一個(gè)獨(dú)立的研究方向。近幾十年，產(chǎn)生了許多關(guān)于全局最優(yōu)化的算法，例如：區(qū)間算法、積分水平集算法、填充函數(shù)算法和打洞函數(shù)算法。由于填充函數(shù)方法和打洞函數(shù)方法是利用一個(gè)輔助變換函數(shù)來(lái)實(shí)現(xiàn)求解全局最優(yōu)解的過(guò)程，因此我們統(tǒng)稱它們?yōu)檩o助函數(shù)方法。本文研究的核心內(nèi)容是非線性全局最優(yōu)化的輔助函數(shù)方法。 本文結(jié)構(gòu)如下：第一章介紹了非線性全局最優(yōu)化的一些概念和性質(zhì)，并概述了求解全局最優(yōu)化問(wèn)題的幾種常見(jiàn)的算法。第二章對(duì)于離散型非線性規(guī)劃問(wèn)題，改進(jìn)了文獻(xiàn)[29]中定義，構(gòu)造了相應(yīng)的填充函數(shù)并設(shè)計(jì)了新的算法，給出了數(shù)值實(shí)驗(yàn)結(jié)果。第三章，在n維空間中，對(duì)于非線性約束全局最優(yōu)化問(wèn)題構(gòu)造了一個(gè)新的填充-打洞函數(shù)，我們證明了此輔助函數(shù)同時(shí)具有填充函數(shù)和打洞函數(shù)的性質(zhì)，根據(jù)這個(gè)填充-打洞函數(shù)設(shè)計(jì)了新的算法并進(jìn)行了數(shù)值試驗(yàn)，最后還給出了一個(gè)供應(yīng)鏈的實(shí)際問(wèn)題進(jìn)行求解，說(shuō)明我們的算法是有效的。第四章是本文總的結(jié)論。
[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.
【學(xué)位授予單位】：河南科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：O221.2

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 ;NONLINEAR INTEGER PROGRAMMING AND GLOBALOPTIMIZATION[J];Journal of Computational Mathematics;1999年02期

本文編號(hào)：2246066