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38626 results in Cambridge Textbooks

Page 1501 of 1932

  • 14 - Discrete Optimization

  • from PART V - MORE ADVANCED TOPICS IN OPTIMIZATION
  • Achille Messac, Mississippi State University
  • Book:
    Optimization in Practice with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    19 March 2015, pp 335-354

  • Summary

    Overview

    In most previous chapters, continuous optimization problems were considered where the design variables were assumed to be continuous; that is, design variables assume real values within given ranges. In many practical engineering problems, the acceptable values of the design variables do not form a continuous set. These problems are referred to as discrete optimization problems. For example, the number of rivets required in a riveted joint has to be an integer (such as 1, 2, 3). Another example is when the feasible region of the design variable is a set of given discrete numbers, such as {6.25, 6.95, 7.65}, which may be the available standardized sizes of nuts. The basics of discrete optimization were introduced in Chapter 9, where some pertinent elementary methods were presented. This chapter introduces more advanced approaches. The reader is advised to first review Chapter 9 as preparation for the current chapter.

    This chapter is organized as follows. The next section (Sec. 14.2) provides the problem classes, examples, and definition (along with the notion of computational complexity of the solution algorithms). Section 14.3 discusses the basics of some popular techniques used to solve integer programming problems, with examples. The methods studied will be: the exhaustive search method (Sec. 14.3.1), the graphical method (Sec. 14.3.2), the relaxation method (Sec. 14.3.3), the branch and bound method (Sec. 14.3.4), and the cutting plane method (Sec. 14.3.5). Popular current software options (Sec. 14.3.7) are also discussed. The chapter concludes with a summary in Sec. 14.4.

    Problem Classes, Examples and Definition

    This section presents discrete optimization problem classes, problem examples, and problem definition. Computational complexity of the solution algorithms is also briefly addressed in connection with the discrete optimization problem definition.

  • 19 - Evolutionary Algorithms

  • from PART V - MORE ADVANCED TOPICS IN OPTIMIZATION
  • Achille Messac, Mississippi State University
  • Book:
    Optimization in Practice with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    19 March 2015, pp 445-460

  • Summary

    Overview

    This book has presented various algorithms and applications where the optimizer was primarily gradient-based (i.e., the search direction is governed by gradient and/or Hessian information). This chapter introduces an entirely different class of optimization algorithms called the evolutionary algorithms (EA). Evolutionary algorithms imitate natural selection processes to develop powerful computational algorithms to select optimal solutions. Genetic algorithms (GA), simulated annealing (SA), ant colony optimization (ACO), particle swarm optimization (PSO), and tabu search (TS) are some of the popular techniques that fall under the umbrella of evolutionary algorithms.

    The motivation for using biologically-inspired computational approaches stems from two key observation. First, the mathematical optimization algorithms in solving complex problems in engineering, computing, and other fields suffer strong limitations. The common challenges in these areas revolve around the lack of mathematical models that define the physical phenomena, discontinuous functions, and high nonlinearity. Second, many complex problems encountered in engineering already exist in nature in some relevant form. Optimization is inherent in nature, such as in the process of adaptation performed by biological organisms in order to survive. Engineers and scientists continue to explore the various efficient problem-solving techniques employed by nature to optimize natural systems.

    The relative advantages and limitations of EAs vs. traditional optimization methods are as follows:

  • Traditional algorithms typically generate a single candidate optimum at each iteration that progresses toward the optimal solution. Evolutionary algorithms generate a population of points at each iteration. The best point in the population approaches an optimal solution.

  • Traditional algorithms calculate the candidate optimal point at the next iteration by a deterministic computation. EAs usually select the next population by a combination of operations that use random number generators.

  • Traditional algorithms require gradient and/or Hessian information to proceed, while EAs usually require only function values. As a result, EAs can solve a variety of optimization problems in which the objective function is not smooth and potentially discontinuous.[…]

  • 6 - Multiobjective Optimization

  • from PART III - USING OPTIMIZATION—PRACTICAL ESSENTIALS
  • Achille Messac, Mississippi State University
  • Book:
    Optimization in Practice with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    19 March 2015, pp 123-157

  • Summary

    Overview

    In Part I of this book, we reviewed preparatory knowledge needed to start learning optimization: Matlab, and elementary mathematics. In Part II, we were exposed to the world of optimization and its potentially powerful role in our lives as engineers or professionals in quantitative fields. We then delved into the specific activities of analysis, design, and optimization, their links and distinctions. In the previous chapter, we then began addressing the fundamental aspects of computational optimization. These included single objective optimization, and the different approaches to optimization (analytical, numerical, experimental, and graphical). This was followed by a discussion of software options.

    In this chapter, we study one of the most important aspects of optimization in practice, the notion of multiobjective optimization. Stated simply, Multiobjective optimization is the art and science of formulating how to optimize a set of competing objectives, which is almost always the case in practice. A detailed presentation of the pertinent methods is provided in such a way as to allow you to be readily productive and effective in practical design.

    The Multiobjective Problem Definition

    The identification of the right design objectives plays a crucial role in the design of any system. More often than not, in real-life design, you will find that your optimization problem contains more than one design objective. For example, wouldn't it be nice if your car dealer would tell you that the car you like happens to feature more miles per gallon and also costs less than a competitor's car? As an engineer, you would think twice before making a decision based on his interesting comments. If he were right, the other car company would probably not stay in business for very long. The point here is that while designing any product or system, you will almost always have to consider several competing design objectives. As a car designer, you would like the car to provide the most miles per gallon possible, while taking care that the car does not cost a million dollars.

  • Preface

  • Achille Messac, Mississippi State University
  • Book:
    Optimization in Practice with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    19 March 2015, pp xxv-xxx

  • Summary

    Contacting the Author Regarding this Book

    I am delighted that you are using this book in your study of, or involvement with, optimization. I would very much welcome your comments, particularly regarding this first edition, and any suggestions that you might have for the next edition. For your comments regarding this book, I will be happy to receive your direct email at OptimizationInPracticeMessac@google.com.

    Book Website

    The website www.cambridge.org/Messac will be maintained for this book. Information for instructors and students will be separately provided. Software for various problems will be provided in this website. I expect it to be a dynamic website, where the information available will evolve over time to be responsive to readers’ requests and feedback.

    Book Organization

    This book is intended to be used by undergraduate and graduate students in the classroom, or by industry practitioners learning independently. Its organization suits these objectives. Following are messages specifically tailored for students, for industry practitioners and for instructors. The book has five parts:

  • Part I Helpful Preliminaries

  • Part II Using Optimization—The Road Map

  • Part III Using Optimization—Practical Essentials

  • Part IV Going Deeper: Inside the Codes and Theoretical Aspects

  • Part V More Advanced Topics in Optimization

    • Part I has two chapters that present prerequisite material explaining how to use Matlab and some useful mathematical information. Most of this book assumes knowledge of undergraduate calculus and elementary linear algebra. The second chapter provides a brief review of the math needed. In Part II, three chapters introduce the world of optimization in the form of a road map. This part provides the basics of what should be known about optimization before attempting to use it. In Part III, there are five chapters that teach the basic use of optimization. In fact, learning the material up to Part III provides the practitioner with sufficient information for solving practical problems. In doing so, student users will not be experts on how optimization works under the hood, so to speak, but will have the ability to use optimization in general practical contexts.

  • 18 - Physical Programming for Multiobjective Optimization

  • from PART V - MORE ADVANCED TOPICS IN OPTIMIZATION
  • Achille Messac, Mississippi State University
  • Book:
    Optimization in Practice with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    19 March 2015, pp 429-444

  • Summary

    Overview

    Engineering design problems are multiobjective in nature. These problems usually optimize two or more conflicting objectives – simultaneously. An approach to multiobjective problem formulation combines the multiple objectives into a single objective function, also known as the Aggregate Objective Function (AOF). This AOF is solved to obtain one Pareto solution. One of several challenges in the area of multiobjective optimization is to judiciously construct an AOF that satisfactorily models the designer's preferences. This chapter provides a concise presentation of the Physical Programming method, which defines a framework to effectively incorporate the designer's preferences into the AOF (Ref. [1]).

    Several methods to solve multiobjective optimization problems have been discussed in Chapter 6, such as the weighted sum method, compromise programming, and goal programming. These weight-based approaches require the designer to specify numerical weights in defining the AOF. This process can be ambiguous. For example, consider the following: (1) How does the designer specify weights in weight-based approaches? (2) Do the weights reflect the designer's preferences accurately? If the designer chooses to increase the importance of a particular objective, by how much should he/she increase the weight? Is 25% adequate? Or is 200% adequate? (3) Does the AOF denote a true mathematical representation of the designer's preferences?

    The above questions begin to explain that the problem of determining “good weights” can be difficult and dubious. Because of this ambiguity, the weight selection process is often a computational bottleneck in large scale multiobjective design optimization problems. The above discussion paves the way for a multiobjective problem formulation framework that alleviates these ambiguities: Physical Programming (PP) developed by Messac [2].

    Physical Programming systematically develops an AOF that effectively reflects the designer's wishes. This approach eliminates the need for iterative weight setting, which alleviates the above discussed ambiguities. Instead of choosing weights, the designer chooses ranges of desirability for each objective. The PP method formulates the AOF from these ranges of desirability, while yielding interesting and useful properties for the AOF.

  • Part IV - 1914–1950: Wars and revolutions

  • John Coatsworth, Columbia University, New York, Juan Cole, Michael P. Hanagan, Vassar College, New York, Peter C. Perdue, Yale University, Connecticut, Charles Tilly, Columbia University, New York, Louise Tilly, New School for Social Research, New York
  • Book:
    Global Connections
    Published online:
    28 May 2018
    Print publication:
    16 March 2015, pp 317-320

  • Summary

    The main theme of this part is the collapse and partial restoration of the liberal, capitalist, and imperial orders that allowed Europeans to dominate most of the world. For Europeans, the nineteenth century was a time of unprecedented prosperity and power. Their mastery of the new industrial technologies had given them direct control of over half of the world’s peoples and huge influence over the rest. The great global linkages created by the European empires drew in commodities and labor from all over the world to create the products that went out to consumers everywhere. The USA, too, enjoyed its Gilded Age of wealth and empire, and Japan was rising quickly to join the elite club of great powers. It seemed that this machinery of expanding production and power could continue indefinitely. Many predicted, in the words of the historian Arnold Toynbee, the coming of an age of universal peace, wealth, and justice, an “earthly paradise.”

    It was not to be. The Great War which broke out in 1914 destroyed the international imperial order, devastating all the European societies far beyond anyone’s expectations. Worse was to come. The brief, precarious stability of the 1920s fell apart in the 1930s under the impact of a savage world depression and the rise of a new, vicious mass movement: fascism. The world plunged into a new global war even more destructive than the first.

  • 10 - Simple Stress and Strain

  • H. D. Ram, A. K. Chauhan
  • Book:
    Foundations and Applications of Engineering Mechanics
    Published online:
    26 June 2025
    Print publication:
    16 March 2015, pp 514-561

  • Summary

    10.1 Introduction

    One of the major reasons for the failure of materials or components is stress. The understanding and analysis of stress is a very important step in any design. Our primary objective here is to identify the stress, and then discuss the scheme of analysis for simple and complex situations.

    10.2 Definitions

    Stress is defined as the intensity of internal reaction. The intensity is measured with respect to the area. Consider a body in equilibrium under the action of certain forces as shown in Figure 10.1a.

  • 6 - Kinematics of Particle and Rigid Body

  • H. D. Ram, A. K. Chauhan
  • Book:
    Foundations and Applications of Engineering Mechanics
    Published online:
    26 June 2025
    Print publication:
    16 March 2015, pp 340-398

  • Summary

    6.1 Introduction

    Kinematics is the study of the motion of particles and rigid bodies disregarding the forces associated with these motions.

    6.2 Kinematics of particle

    Kinematics of particle involves the study of position, velocity and acceleration of the particle without any consideration of the forces working on it. Particle can move on a straight line, on a plane or in space. We will restrict our study to plane motion only. The plane motion of the particle is classified as:

    (a) Straight line motion

    (b) Motion on curved path

    Following classification of motion on curved path is useful from application point of view

    (a) Position, velocity and acceleration in terms of Cartesian components

    (b) Position, velocity and acceleration in terms of path variables and

    (c) Position, velocity and acceleration in terms of polar coordinates

  • 15 - Decolonization, democratization, and civil wars, 1950–1980

  • from Part V - 1950–2000: Global threats and promises
  • John Coatsworth, Columbia University, New York, Juan Cole, Michael P. Hanagan, Vassar College, New York, Peter C. Perdue, Yale University, Connecticut, Charles Tilly, Columbia University, New York, Louise Tilly, New School for Social Research, New York
  • Book:
    Global Connections
    Published online:
    28 May 2018
    Print publication:
    16 March 2015, pp 447-477

  • Summary

    The lawyer Nelson Mandela (1918–2013) spent twenty-five years in jail for organizing against the South African apartheid regime, but in 1994 he was elected president of South Africa. The young Mandela was an activist against the racist policies of the white regime; only later in life did he endorse non-violent political action. In his inauguration speech, he called for the “healing of wounds” and an end to the “pernicious ideology and practice of racism and racial oppression.” His Korean counterpart, Kim Dae-jung (1925–2009), also spent time in jail under military rule, but as prime minister pursued policies of democratization and reconciliation with his colonial rulers, the Japanese. Both won the Nobel Peace Prize.

    Other anti-imperial leaders took different paths. Mao Zedong (1893–1976) and Kim Il-sung (1912–94) strongly endorsed violent struggle, isolating their countries from the world. Ho Chi Minh (1890–1969) and his Viet Minh nationalists successfully fought off both the French and the Americans during a thirtyyear struggle. The bloody contest between Palestinians and Israelis continues today, despite intensive efforts at mediation. The struggle to rid the world of imperial domination has led to many unpredicted outcomes, and it is not yet over.

Page 1501 of 1932