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书  名:最优化理论与方法
  • 作  者: 黄平、孟永钢
  • 出版时间: 2009-02-01
  • 出 版 社: 清华大学出版社
  • 字  数: 469 千字
  • 印  次: 1-1
  • 印  张: 19
  • 开  本: 16开
  • ISBN: 9787302191537
  • 装  帧: 平装
  • 定  价:¥36.00
电子书价:¥25.20 折扣:70折 节省:¥10.80 vip价:¥25.20 电子书大小:19.59M
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内容简介
   本书系统地介绍了在机械工程学科中常用的最优化理论与方法,分为线性规划与整数规划、非线性规划、智能优化方法、变分法与动态规划4个篇次,共15章。第1篇包含最优化基本要素、线性规划和整数规划。在介绍优化变量、目标函数、约束条件和数学建模等最优化的基本内容后,讨论了线性规划求解基本原理和最常用的单纯形方法,然后给出了两种用于整数线性规划的求解方法。在第2篇的非线性规划中,包含了非线性规划数学分析基础、一维最优化方法、无约束多维最优化方法、约束非线性规划方法等。第3篇的智能优化方法包括启发式搜索方法Hopfield神经网络优化方法、模拟退火法与均场退火法、遗传算法等内容。在第4篇中,介绍了变分法、最大(小)值原理和动态规划等内容。各章都配备了习题。
本书可作为高等院校机械工程一级学科各专业的最优化理论与方法课程的研究生教材和教师的教学和科研参考书,也可作为其他相关专业的教学用书,以及从事生产规划、优化设计和最优控制方面工作的工程技术与科研人员的参考用书。
前言
  
最优化理论与方法是工科研究生学习的一门主干课。该课程主要教授研究生一些实用的最优化理论和方法,使其在今后的研究中能够运用这些理论和方法,在设计、制造和选材等方面获得结构、电路和过程的最优解。
以往大多数的最优化方法课程和书籍专业性较强,常被分为生产规划类的线性规划、机械类的优化设计、计算机类的智能优化和电子类的最优控制等不同课程。随着科学技术的发展,各学科间的交叉与融合越来越紧密,一项科学研究需要应用不同学科的理论与方法已经是极为普遍的,因此这也对最优化理论与方法的研究生教学提出了新的要求。为了适应学科发展现状,我们在多年实践的基础上,编写了本书,以介绍成熟的最优化理论与方法为主,适当介绍最优化理论的新的研究成果和发展趋势,为研究生将来开展的论文研究提供最优化方面的理论基础与实用方法。
本书较系统地介绍了在工科中常用的最优化理论与方法,分为线性规划与整数规划、非线性规划、智能优化方法、变分法和动态规划4个篇次,共15章。第1篇包含最优化基本要素、线性规划和整数规划3章。线性规划在工业、农业、商业、交通运输、军事和科学研究的各个领域有广泛应用。例如,在资源有限的情况下,如何合理使用人力、物力和资金等资源,以获取最大效益; 如何组织生产、合理安排工艺流程或调整产品成分等,使所消耗的资源(人力、设备台时、资金、原材料等)为最少等。在介绍了最优化的基本内容后,讨论了线性规划求解的基本原理和最常用的单纯形方法,并给出了用于整数线性规划的求解方法。第2篇所述内容是20世纪中期形成的一个方向,随着计算机技术的发展,出现了许多有效的算法,并得到了快速发展。非线性规划广泛应用于机械设计、工程管理、经济生产、科学研究和军事等方面。这一篇的主要内容包含非线性规划数学基础、一维最优化方法、无约束多维非线性规划方法、约束问题的非线性规划方法和多目标最优化5章,这些内容是非线性规划中最基本也是最重要的,可以为优化设计等提供有力的工具。第3篇是智能优化方法。智能优化算法有别于一般的按照图灵机进行精确计算的程序,是对计算机模型的一种新的诠释,它模拟自然过程、生物或人类思维等方式来求解最优化问题。例如,模拟退火法源于物质的退火过程,遗传算法借鉴了生物进化思想,神经网络模拟了人脑的思维等。其中一些方法可以解决组合优化或较有效处理“局部极值”和“全局极值”等问题。智能优化方法很多,本书选取了启发式搜索方法、Hopfield神经网络优化方法、模拟退火法与均场退火法、遗传算法4章内容。第4篇包括变分法及其在最优控制中的应用、最大(小)值原理和动态规划共3章,这些内容是解决最优控制问题的主要方法。最优控制广泛应用于控制系统、燃料控制系统、能耗控制系统、线性调节器等最优综合和设计场合。
本书介绍的最优化理论与方法范围较宽,包括了目前各工程类专业在科学研究与应用时常用的和主要的方法与手段,这些是作为一名工科研究生需要学习和掌握的。另外,为了兼顾不同学科的特点,在某些内容上具有一定的理论深度。但是本书的重点是让学生掌握这些内容的基本理论和基本方法。考虑到教学时数的限制,书中给出了适当的算例,而具体的工程应用实例有待于学生在今后的研究中进一步学习和领会。本书各章均配备了习题,可作为高等院校机械工程一级学科各专业的最优化理论与方法课程的研究生教材和教师的教学和科研参考书,也可作为其他相关专业的教学用书,以及作为从事生产规划、优化设计和最优控制方面工作的工程技术与科研人员的参考用书。
本书主编为黄平,副主编为孟永钢。具体参加本书各章内容编写工作的是: 李旻(第1~5章)、孟永钢(第6,7章),黄平(第8,9,13章)、胡广华(第10,11章)、邱志成(第12章)、刘旺玉(第14章)、孙建芳(第15章)。在本书编写工作中,我们参考和引用了许多国内外的书籍和文献等材料,为此我们向这些作者表示衷心的感谢,这些参考文献都列在本书各章的后面。另外,由于作者的水平所限,难免存在不足和错误,希望读者给予批评指正。
编者2008年10月30日

Preface
Theories and methods of optimization is one of the main subjects for engineering graduate students. The purpose of this subject is to teach graduate students some common and useful theories and methods of optimization so that they can use the knowledge in design, manufacturing and material selection to obtain the optimal solution of a structure, a circuit or a process.
Most of the traditional text books on optimization are discipline oriented, usually dividing into different courses of operation research, optimal machine design, intelligent optimization and optimal control. Along with the development of science and technology, interdisciplinary merging and fusion become closer and tighter. Nowadays it is quite often to apply theories and methods in different fields to solve problems in scientific researches. To meet the demands of scientific development, the education of theories and methods of optimization for graduate students should be improved. Based on the teaching practice in the past several years, the authors have compiled this new text book, which mainly covers the welldeveloped theories and methods of optimization, adding a few topics of advances in optimization theory. The book provides the knowledge of basic theories and practical methods of optimization for graduate students to carry out their research work.
The subject matters of this book are grouped into 4 parts in total 15 chapters, linear programming and integer linear programming,nonlinear programming, intelligent optimization methods, calculus of variations and dynamic programming, collecting most of the theories and methods of optimization commonly used in engineering. In the first part of linear programming, 3 chapters of basic elements of optimization, linear programming and integer linear programming are included. Linear programming is of wide applications in industry, agriculture, business, transportation, military operations and scientific researches. For an example, under the condition of finite resources, linear programming can be used to make a plan of the distribution of human, material and financial resources for getting the maximum gain. Meanwhile, consumption of resources can be reduced to minimum by production planning, process rationalization and/or ingredient modification with the optimization method. At first fundamentals of optimization theories are introduced. Then the principles of linear programming and the simplex method are discussed. In addition, the scheme of integer linear programming is described in this part. The second part is on the nonlinear programming which is a branch formed in the middle of the 20th century. Accompanying with the development of digital computers, nonlinear programming has been growing rapidly, and many effective algorithms has appeared. Nowadays, nonlinear programming has been widely used in machine design, project management, production, scientific research activities and military affairs. In this part there are 5 chapters, including basic mathematics of nonlinear optimization, optimization methods for single argument problems, unconstrained multivariate problems and constrained nonlinear programming, which are the most fundamental and important contents of nonlinear programming, and powerful tools for optimal design. The third part is on intelligent optimization methods, which provide new interpretation of computing, differing from the precise calculation programs of Turing machines. Intelligent optimization methods are inspired from nature, and mimic of natural evolution and biological thinking processes to find optimal solutions. Simulated annealing method, for instance, mimics the annealing process of substances, while genetic algorithm refers to the evolution of organisms, and neural network is a model of human brain. Some of the intelligent optimization methods can effectively solve the problem of “local maxima” or “whole maxima”. Among many intelligent optimization methods, the heuristic search method, Hopfield neural network optimization method, the simulated annealing method and mean field annealing method, and the genetic algorithm are selected and included in the book. The last part of the book consists of 3 chapters of calculus of variations and its applications in optimal control, maximum principle and dynamic programming, which are the major methods for solving optimal control problems. Optimal control is widely applied in the fields of system control, fuel consumption control, energy consumption control and linear adjustors.
The major feature of this book is the broadness of its contents, covering most of the common optimization methods used in different engineering disciplines, which are necessary knowledge for engineering graduate students to be mastered. Considering the different requirements for the students in different fields, the book puts emphasis on the fundamentals of theories and methods of optimization although a part of them more theoretical are also included. Because of the limited course time in one semester, practical engineering problems are not discussed much in the book, leaving them for students to study in the future, while giving some relative simple examples. In the end of each chapter, exercises are prepared for students to do. This book can be used as a textbook for postgraduates majoring in mechanical engineering. It can also serve as a reference book for university teachers and students in their teaching and research work as well as for the researchers and engineers who work on operation research, optimal design or optimal control.
The author in chief of this book is Huang Ping, and the associate author is Meng Yonggang. The following authors took part in the following compilations of the book, Li Min (Chapter 15), Meng Yonggang (Chapter 6 and 7), Huang Ping (Chapter 8, 9 and 13), Hu Guanghua (Chapter 10 and 11), Qiu Zhicheng (Chapter 12), Liu Wangyu (Chapter 14), and Sun Jianfang (Chapter 15). During the compilation of the book, we have referred and cited many publications which are listed in the references. To all of the authors of the references, we extend our most sincere thanks. The authors welcome hearing from readers about any errors of fact or omission that may undoubtedly existed in the book.
AuthorsOctober 30, 2008
目录
第1篇线性规划与整数规划

1最优化基本要素

1.1优化变量

1.2目标函数

1.3约束条件

1.4最优化问题的数学模型及分类

1.5最优化方法概述

习题

参考文献

2线性规划

2.1线性规划数学模型

2.2线性规划求解基本原理

2.3单纯形方法

2.4初始基本可行解的获取

习题

参考文献

3整数规划

3.1整数规划数学模型及穷举法

3.2割平面法

3.3分枝定界法

习题

参考文献

第2篇非线性规划

4非线性规划数学基础

4.1多元函数的泰勒展开式

4.2函数的方向导数与最速下降方向

4.3函数的二次型与正定矩阵

4.4无约束优化的极值条件

4.5凸函数与凸规划

4.6约束优化的极值条件

习题

参考文献

5一维最优化方法

5.1搜索区间的确定

5.2黄金分割法

5.3二次插值法

5.4切线法

5.5格点法

习题

参考文献

6无约束多维非线性规划方法

6.1坐标轮换法

6.2最速下降法

6.3牛顿法

6.4变尺度法

6.5共轭方向法

6.6单纯形法

6.7最小二乘法

习题

参考文献

7约束问题的非线性规划方法

7.1约束最优化问题的间接解法

7.2约束最优化问题的直接解法

习题

参考文献

8非线性规划中的一些其他方法

8.1多目标优化

8.2数学模型的尺度变换

8.3灵敏度分析及可变容差法

习题

参考文献

第3篇智能优化方法

9启发式搜索方法

9.1图搜索算法

9.2启发式评价函数

9.3A*搜索算法

习题

参考文献

10Hopfield神经网络优化方法

10.1人工神经网络模型

10.2Hopfield神经网络

10.3Hopfield网络与最优化问题

习题

参考文献

11模拟退火法与均场退火法

11.1模拟退火法基础

11.2模拟退火算法

11.3随机型神经网络

11.4均场退火

习题

参考文献

12遗传算法

12.1遗传算法实现

12.2遗传算法示例

12.3实数编码的遗传算法

习题

参考文献

第4篇变分法与动态规划

13变分法

13.1泛函

13.2泛函极值条件——欧拉方程

13.3可动边界泛函的极值

13.4条件极值问题

13.5利用变分法求解最优控制问题

习题

参考文献

14最大(小)值原理

14.1连续系统的最大(小)值原理

14.2应用最大(小)值原理求解最优控制问题

14.3离散系统的最大(小)值原理

习题

参考文献

15动态规划

15.1动态规划数学模型与算法

15.2确定性多阶段决策

15.3动态系统最优控制问题

习题

参考文献

附录A中英文索引









Part 1Linear Programming and Integer Programming

1Fundamentals of Optimization

1.1Optimal Variables

1.2Objective Function

1.3Constraints

1.4Mathematical Model and Classification of Optimization

1.5Introduction of Optimal Methods

Problems

References

2Linear Programming

2.1Mathematical Models of Linear Programming

2.2Basic Principles of Linear Programming

2.3Simplex Method

2.4Acquirement of Initial Basic Feasible Solution

Problems

References

3Integer Programming

3.1Mathematical Models of Integer Programming and Enumeration
Method

3.2Cutting Plane Method

3.3Branch and Bound Method

Problems

References

Part 2NonLinear Programming

4Mathematical Basis of NonLinear Programming

4.1Taylor Expansion of MultiVariable Function

4.2Directional Derivative of Function and Steepest Descent Direction

4.3Quadratic Form and Positive Matrix

4.4Extreme Conditions of Unconstrained Optimum

4.5Convex Function and Convex Programming

4.6Extreme Conditions of Constrained Optimum

Problems

References






5OneDimensional Optimal Methods

5.1Determination of Search Interval

5.2Golden Section Method

5.3Quadratic Interpolation Method

5.4Tangent Method

5.5Grid Method

Problems

References

6NonConstraint NonLinear Programming

6.1Coordinate Alternation Method

6.2Steepest Descent Method

6.3Newtons Method

6.4Variable Metric Method

6.5Conjugate Gradient Algorithm

6.6Simplex Method

6.7Least Squares Method

Problems

References

7Constraint Optimal Methods

7.1Constraint Optimal Indirect Methods

7.2Constraint Optimal Direct Methods

Problems

References

8Other Methods in Non Linear Programming

8.1Multi Objectives Optimazation

8.2Metric Variation of a Mathematic Model

8.3Sensitivity Analysis and Flexible Tolerance Method

Problems

References

Part 3Intelligent Optimization Method

9Heuristic Search Method

9.1Graph Search Method

9.2Heuristic Evaluation Function

9.3A*Search Method

Problems

References

10Optimization Method Based on Hopfield Neural Networks

10.1Artificial Neural Networks Model

10.2Hopfield Neural Networks

10.3Hopfield Neural Networks and Optimization Problems

Problems

References

11Simulated Annealing Algorithm and Mean Field Annealing Algorithm

11.1Basis of Simulated Annealing Algorithm

11.2Simulated Annealing Algorithm

11.3Stochastic Neural Networks

11.4Mean Field Annealing Algorithm

Problems

References

12Genetic Algorithm

12.1Implementation Procedure of Genetic Algorithm

12.2Genetic Algorithm Examples

12.3RealNumber Encoding Genetic Algorithm

Problems

References

Part 4Variation Method and Dynamic Programming

13Variation Method

13.1Functional

13.2Functional Extreme Value Condition—Eulers Equation

13.3Functional Extreme Value for Moving Boundary

13.4Conditonal Extreme Value

13.5Solving Optimal Control with Variation Method

Problems

References

14Maximum (Minimum) Principle

14.1Maximum (Minimum) Principle for Continuum System

14.2Applications of Maximum (Minimum) Principle

14.3Maximum (Minimum) Principle for Discrete System

Problems

References

15Dynamic Programming

15.1Mathematic Model and Algorithm of Dynamic Programming

15.2Deterministic MultiStage Process Decision

15.3Optimal Control of Dynamic System

Problems

References

Appendix AChinese and English Index

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