最優(yōu)化理論與方法是工科研究生學(xué)習(xí)的一門主干課。該課程主要教授研究生一些實用的最優(yōu)化理論和方法，使其在今后的研究中能夠運用這些理論和方法，在設(shè)計、制造和選材等方面獲得結(jié)構(gòu)、電路和過程的最優(yōu)解。
以往大多數(shù)的最優(yōu)化方法課程和書籍專業(yè)性較強，常被分為生產(chǎn)規(guī)劃類的線性規(guī)劃、機械類的優(yōu)化設(shè)計、計算機類的智能優(yōu)化和電子類的最優(yōu)控制等不同課程。隨著科學(xué)技術(shù)的發(fā)展，各學(xué)科間的交叉與融合越來越緊密，一項科學(xué)研究需要應(yīng)用不同學(xué)科的理論與方法已經(jīng)是極為普遍的，因此這也對最優(yōu)化理論與方法的研究生教學(xué)提出了新的要求。為了適應(yīng)學(xué)科發(fā)展現(xiàn)狀，我們在多年實踐的基礎(chǔ)上，編寫了本書，以介紹成熟的最優(yōu)化理論與方法為主，適當介紹最優(yōu)化理論的新的研究成果和發(fā)展趨勢，為研究生將來開展的論文研究提供最優(yōu)化方面的理論基礎(chǔ)與實用方法。
本書較系統(tǒng)地介紹了在工科中常用的最優(yōu)化理論與方法，分為線性規(guī)劃與整數(shù)規(guī)劃、非線性規(guī)劃、智能優(yōu)化方法、變分法和動態(tài)規(guī)劃4個篇次，共15章。第1篇包含最優(yōu)化基本要素、線性規(guī)劃和整數(shù)規(guī)劃3章。線性規(guī)劃在工業(yè)、農(nóng)業(yè)、商業(yè)、交通運輸、軍事和科學(xué)研究的各個領(lǐng)域有廣泛應(yīng)用。例如，在資源有限的情況下，如何合理使用人力、物力和資金等資源，以獲取最大效益； 如何組織生產(chǎn)、合理安排工藝流程或調(diào)整產(chǎn)品成分等，使所消耗的資源（人力、設(shè)備臺時、資金、原材料等）為最少等。在介紹了最優(yōu)化的基本內(nèi)容后，討論了線性規(guī)劃求解的基本原理和最常用的單純形方法，并給出了用于整數(shù)線性規(guī)劃的求解方法。第2篇所述內(nèi)容是20世紀中期形成的一個方向，隨著計算機技術(shù)的發(fā)展，出現(xiàn)了許多有效的算法，并得到了快速發(fā)展。非線性規(guī)劃廣泛應(yīng)用于機械設(shè)計、工程管理、經(jīng)濟生產(chǎn)、科學(xué)研究和軍事等方面。這一篇的主要內(nèi)容包含非線性規(guī)劃數(shù)學(xué)基礎(chǔ)、一維最優(yōu)化方法、無約束多維非線性規(guī)劃方法、約束問題的非線性規(guī)劃方法和多目標最優(yōu)化5章，這些內(nèi)容是非線性規(guī)劃中最基本也是最重要的，可以為優(yōu)化設(shè)計等提供有力的工具。第3篇是智能優(yōu)化方法。智能優(yōu)化算法有別于一般的按照圖靈機進行精確計算的程序，是對計算機模型的一種新的詮釋，它模擬自然過程、生物或人類思維等方式來求解最優(yōu)化問題。例如，模擬退火法源于物質(zhì)的退火過程，遺傳算法借鑒了生物進化思想，神經(jīng)網(wǎng)絡(luò)模擬了人腦的思維等。其中一些方法可以解決組合優(yōu)化或較有效處理“局部極值”和“全局極值”等問題。智能優(yōu)化方法很多，本書選取了啟發(fā)式搜索方法、Hopfield神經(jīng)網(wǎng)絡(luò)優(yōu)化方法、模擬退火法與均場退火法、遺傳算法4章內(nèi)容。第4篇包括變分法及其在最優(yōu)控制中的應(yīng)用、最大（�。┲翟�理和動態(tài)規(guī)劃共3章，這些內(nèi)容是解決最優(yōu)控制問題的主要方法。最優(yōu)控制廣泛應(yīng)用于控制系統(tǒng)、燃料控制系統(tǒng)、能耗控制系統(tǒng)、線性調(diào)節(jié)器等最優(yōu)綜合和設(shè)計場合。
本書介紹的最優(yōu)化理論與方法范圍較寬，包括了目前各工程類專業(yè)在科學(xué)研究與應(yīng)用時常用的和主要的方法與手段，這些是作為一名工科研究生需要學(xué)習(xí)和掌握的。另外，為了兼顧不同學(xué)科的特點，在某些內(nèi)容上具有一定的理論深度。但是本書的重點是讓學(xué)生掌握這些內(nèi)容的基本理論和基本方法�？紤]到教學(xué)時數(shù)的限制，書中給出了適當?shù)乃憷�，而具體的工程應(yīng)用實例有待于學(xué)生在今后的研究中進一步學(xué)習(xí)和領(lǐng)會。本書各章均配備了習(xí)題，可作為高等院校機械工程一級學(xué)科各專業(yè)的最優(yōu)化理論與方法課程的研究生教材和教師的教學(xué)和科研參考書，也可作為其他相關(guān)專業(yè)的教學(xué)用書，以及作為從事生產(chǎn)規(guī)劃、優(yōu)化設(shè)計和最優(yōu)控制方面工作的工程技術(shù)與科研人員的參考用書。
本書主編為黃平，副主編為孟永鋼。具體參加本書各章內(nèi)容編寫工作的是： 李旻（第1~5章）、孟永鋼（第6，7章），黃平（第8，9，13章）、胡廣華（第10，11章）、邱志成（第12章）、劉旺玉（第14章）、孫建芳（第15章）。在本書編寫工作中，我們參考和引用了許多國內(nèi)外的書籍和文獻等材料，為此我們向這些作者表示衷心的感謝，這些參考文獻都列在本書各章的后面。另外，由于作者的水平所限，難免存在不足和錯誤，希望讀者給予批評指正。
編者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 “l(fā)ocal 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