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Engineering Optimization: Theory and Practice, 5/Ed > 이산수학

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Engineering Optimization: Theory and Practice, 5/Ed
히트도서
판매가격 79,000원
저자 Rao
도서종류 외국도서
출판사 Wiley
발행언어 영어
발행일 2019
페이지수 880
ISBN 9781119454717
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  • 도서 정보

    도서 상세설명

    TABLE OF CONTENTS

    Preface

    Acknowledgment

    About the Companion Website

    1. Introduction to Optimization

    1.1 Introduction

    1.2 Historical Development

    1.3 Engineering Applications of Optimization

    1.4 Statement of an Optimization Problem

    1.4.1 Design Vector

    1.4.2 Design Constraints

    1.4.3 Constraint Surface

    1.4.4 Objective Function

    1.4.5 Objective Function Surfaces

    1.5 Classification of Optimization Problems

    1.5.1 Classification Based on the Existence of Constraints

    1.5.2 Classification Based on the Nature of the Design Variables

    1.5.3 Classification Based on the Physical Structure of the Problem

    1.5.4 Classification Based on the Nature of the Equations Involved

    1.5.5 Classification Based on the Permissible Values of the Design Variables

    1.5.6 Classification Based on the Deterministic Nature of the Variables

    1.5.7 Classification Based on the Separability of the Functions

    1.5.8 Classification Based on the Number of Objective Functions

    1.6 Classification Based on the Number of Objective Functions

    1.7 Engineering Optimization Literature

    References & Bibliography

    Review Questions

    Problems

    2 Classical Optimization Techniques

    2.1 Introduction

    2.2 Single-Variable Optimization

    2.3 Multivariable Optimization with No Constraints

    2.3.1 Semidefinite Case

    2.3.2 Saddle Point

    2.4 Multivariable Optimization with Equality Constraints

    2.4.1 Solution by Direct Substitution

    2.4.2 Solution by the Method of Constrained Variation

    2.4.3 Solution by the Method of Lagrange Multipliers

    2.5 Multivariable Optimization with Inequality Constraints

    2.5.1 Kuhn–Tucker Conditions

    2.5.2 Constraint Qualification

    2.6 Convex Programming Problem

    References and Bibliography

    Review Questions

    Problems

    3. Linear Programming I: Simplex Method

    3.1 Introduction

    3.2 Applications of Linear Programming

    3.3 Standard Form of a Linear Programming Problem

    3.4 Geometry of Linear Programming Problems

    3.5 Definitions and Theorems

    3.6 Solution of a System of Linear Simultaneous Equations

    3.7 Pivotal Reduction of a General System of Equations

    3.8 Motivation of the Simplex Method

    3.9 Simplex Algorithm

    3.10 Two Phases of the Simplex Method

    References and Bibliography

    Review Questions

    Problems

    4. Linear Programming II: Additional Topics and Extensions

    4.1 Introduction

    4.2 Revised Simplex Method

    4.3 Duality in Linear Programming

    4.3.1 Symmetric Primal–Dual Relations

    4.3.2 General Primal–Dual Relations

    4.3.3 Primal–Dual Relations When the Primal Is in Standard Form

    4.3.4 Duality Theorems

    4.3.5 Dual Simplex Method

    4.4 Decomposition Principle

    4.5 Sensitivity or Postoptimality Analysis

    4.5.1 Changes in the Right-Hand-Side Constants bi

    4.5.2 Changes in the Cost Coefficients cj

    4.5.3 Addition of New Variables

    4.5.4 Changes in the Constraint Coefficients aij

    4.5.5 Addition of Constraints

    4.6 Transportation Problem

    4.7 Karmarkar’s Interior Method

    4.7.1 Statement of the Problem

    4.7.2 Conversion of an LP Problem into the Required Form

    4.7.3 Algorithm

    4.8 Quadratic Programming

    Solutions Using Matlab

    References and Bibliography

    Review Questions

    Problems

    5. Nonlinear Programming I: One-Dimensional Minimization Methods

    5.1 Introduction

    5.2 Unimodal Function

    5.3 Unrestricted Search

    5.4 Exhaustive Search

    5.5 Dichotomous Search

    5.6 Interval Halving Method

    5.7 Fibonacci Method

    5.8 Golden Section Method

    5.9 Comparison of Elimination Methods

    5.10 Quadratic Interpolation Method

    5.11 Cubic Interpolation Method

    5.12 Direct Root Methods

    5.12.1 Newton Method

    5.12.2 Quasi-Newton Method

    5.12.3 Secant Method

    5.13 Practical Considerations

    5.13.1 How to Make the Methods Efficient and More Reliable

    5.13.2 Implementation in Multivariable Optimization Problems

    5.13.3 Comparison of Methods

    Solutions Using Matlab

    References and Bibliography

    Review Questions

    Problems

    6. Nonlinear Programming II: Unconstrained Optimization Techniques

    6.1 Introduction

    6.1.1 Classification of Unconstrained Minimization Methods

    6.1.2 General Approach

    6.1.3 Rate of Convergence

    6.1.4 Scaling of Design Variables

    6.2 Random Search Methods

    6.2.1 Random Jumping Method

    6.2.2 Random Walk Method

    6.2.3 Random Walk Method with Direction Exploitation

    6.2.4 Advantages of Random Search Methods

    6.3 Grid Search Method

    6.4 Univariate Method

    6.5 Pattern Directions

    6.6 Powell’s Method

    6.6.1 Conjugate Directions

    6.6.2 Algorithm

    6.7 Simplex Method

    6.7.1 Reflection

    6.7.2 Expansion

    6.7.3 Contraction

    6.8 Gradient of a Function

    6.8.1 Evaluation of the Gradient

    6.8.2 Rate of Change of a Function along a Direction

    6.9 Steepest Descent (Cauchy) Method

    6.10 Conjugate Gradient (Fletcher–Reeves) Method

    6.10.1 Development of the Fletcher–Reeves Method

    6.10.2 Fletcher–Reeves Method

    6.11 Newton’s Method

    6.12 Marquardt Method

    6.13 Quasi-Newton Methods

    6.13.1 Rank 1 Updates

    6.14 Davidon–Fletcher–Powell Method

    6.15 Broyden–Fletcher–Goldfarb–Shanno Method

    6.16 Test Functions

    Solutions Using Matlab

    References and Bibliography

    Review Questions

    Problems

    7. Nonlinear Programming III: Constrained Optimization Techniques

    7.1 Introduction

    7.2 Characteristics of a Constrained Problem

    7.3 Random Search Methods

    7.4 Complex Method

    7.5 Sequential Linear Programming

    7.6 Basic Approach in the Methods of Feasible Directions

    7.7 Zoutendijk’s Method of Feasible Directions

    7.7.1 Direction-Finding Problem

    7.7.2 Determination of Step Length

    7.7.3 Termination Criteria

    7.8 Rosen’s Gradient Projection Method

    7.8.1 Determination of Step Length

    7.9 Generalized Reduced Gradient Method

    7.10 Sequential Quadratic Programming

    7.10.1 Derivation

    7.10.2 Solution Procedure

    7.11 Transformation Techniques

    7.12 Basic Approach of the Penalty Function Method

    7.13 Interior Penalty Function Method

    7.14 Convex Programming Problem

    7.15 Exterior Penalty Function Method

    7.16 Extrapolation Techniques in the Interior Penalty Function Method

    7.16.1 Extrapolation of the Design Vector X

    7.16.2 Extrapolation of the Function f

    7.17 Extended Interior Penalty Function Methods

    17.1 Linear Extended Penalty Function Method

    7.17.2 Quadratic Extended Penalty Function Method

    7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints

    7.18.1 Interior Penalty Function Method

    7.18.2 Exterior Penalty Function Method

    7.19 Penalty Function Method for Parametric Constraints

    7.19.1 Parametric Constraint

    7.19.2 Handling Parametric Constraints

    7.20 Augmented Lagrange Multiplier Method

    7.20.1 Equality-Constrained Problems

    7.20.2 Inequality-Constrained Problems

    7.20.3 Mixed Equality–Inequality-Constrained Problems

    7.21 Checking the Convergence of Constrained Optimization Problems

    7.21.1 Perturbing the Design Vector

    7.21.2 Testing the Kuhn–Tucker Conditions

    7.22 Test Problems

    7.22.1 Design of a Three-Bar Truss

    7.22.2 Design of a Twenty-Five-Bar Space Truss

    7.22.3 Welded Beam Design

    7.22.4 Speed Reducer (Gear Train) Design

    7.22.5 Heat Exchanger Design [7.42]

    Solutions Using Matlab

    References and Bibliography

    Review Questions

    Problems

    8. Geometric Programming

    8.1 Introduction

    8.2 Posynomial

    8.3 Unconstrained Minimization Problem

    8.4 Solution of an Unconstrained Geometric Programming Program Using Differential Calculus

    8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic–Geometric Inequality

    8.6 Primal–Dual Relationship and Sufficiency Conditions in the Unconstrained Case

    8.7 Constrained Minimization

    8.8 Solution of a Constrained Geometric Programming Problem

    8.9 Primal and Dual Programs in the Case of Less-Than Inequalities

    8.10 Geometric Programming with Mixed Inequality Constraints

    8.11 Complementary Geometric Programming

    8.12 Applications of Geometric Programming

    References and Bibliography

    9. Dynamic Programming

    9.1 Introduction

    9.2 Multistage Decision Processes

    9.2.1 Definition and Examples

    9.2.2 Representation of a Multistage Decision Process

    9.2.3 Conversion of a Nonserial System to a Serial System

    9.2.4 Types of Multistage Decision Problems

    9.3 Concept of Suboptimization and Principle of Optimality

    9.4 Computational Procedure in Dynamic Programming

    9.5 Example Illustrating the Calculus Method of Solution

    9.6 Example Illustrating the Tabular Method of Solution

    9.7 Conversion of a Final Value Problem into an Initial Value Problem

    9.8 Linear Programming as a Case of Dynamic Programming

    9.9 Continuous Dynamic Programming

    9.10 Additional Applications

    9.10.1 Design of Continuous Beams

    9.10.2 Optimal Layout (Geometry) of a Truss

    9.10.3 Optimal Design of a Gear Train

    9.10.4 Design of a Minimum-Cost Drainage System

    References and Bibliography

    Review Questions

    Problems

    10. Integer Programming

    10.1 Introduction

    10.2 Graphical Representation

    10.3 Gomory’s Cutting Plane Method

    10.4 Balas’ Algorithm for Zero–One Programming Problems

    10.5 Integer Polynomial Programming

    10.5.1 Representation of an Integer Variable by an Equivalent System of Binary Variables

    10.5.2 Conversion of a Zero–One Polynomial Programming Problem into a Zero–One LP Problem

    10.6 Branch-and-Bound Method

    10.7 Sequential Linear Discrete Programming

    10.8 Generalized Penalty Function Method

    Solutions Using Matlab

    References and Bibliography

    Review Questions

    Problems

    11. Stochastic Programming

    11.2 Basic Concepts of Probability Theory

    11.2.1 Definition of Probability

    11.2.2 Random Variables and Probability Density Functions

    11.2.3 Mean and Standard Deviation

    11.2.4 Function of a Random Variable

    11.2.5 Jointly Distributed Random Variables

    11.2.6 Covariance and Correlation

    11.2.7 Functions of Several Random Variables

    11.2.8 Probability Distributions

    11.2.9 Central Limit Theorem

    11.3 Stochastic Linear Programming

    11.4 Stochastic Nonlinear Programming

    11.4.1 Objective Function

    11.4.2 Constraints

    11.5 Stochastic Geometric Programming

    References and Bibliography

    Review Questions

    Problems

    12. Optimal Control and Optimality Criteria Methods

    12.1 Introduction

    12.2 Calculus of Variations

    12.2.1 Introduction

    12.2.2 Problem of Calculus of Variations

    12.2.3 Lagrange Multipliers and Constraints

    12.3 Optimal Control Theory

    12.3.1 Necessary Conditions for Optimal Control

    12.3.2 Necessary Conditions for a General Problem

    12.4 Optimality Criteria Methods

    12.4.1 Optimality Criteria with a Single Displacement Constraint

    12.4.2 Optimality Criteria with Multiple Displacement Constraints

    12.4.3 Reciprocal Approximations

    References and Bibliography

    Review Questions

    Problems

    13. Modern Methods of Optimization

    13.1 Introduction

    13.2 Genetic Algorithms

    13.2.1 Introduction

    13.2.2 Representation of Design Variables

    13.2.3 Representation of Objective Function and Constraints

    13.2.4 Genetic Operators

    13.2.5 Algorithm

    13.2.6 Numerical Results

    13.3 Simulated Annealing

    13.3.2 Procedure

    13.3.3 Algorithm

    13.3.4 Features of the Method

    13.3.5 Numerical Results

    13.4 Particle Swarm Optimization

    13.4.1 Introduction

    13.4.2 Computational Implementation of PSO

    13.4.3 Improvement to the Particle Swarm Optimization Method

    13.4.4 Solution of the Constrained Optimization Problem

    13.5 Ant Colony Optimization

    13.5.1 Basic Concept

    13.5.2 Ant Searching Behavior

    13.5.3 Path Retracing and Pheromone Updating

    13.5.4 Pheromone Trail Evaporation

    13.5.5 Algorithm

    13.6 Optimization of Fuzzy Systems

    13.6.1 Fuzzy Set Theory

    13.6.2 Optimization of Fuzzy Systems

    13.6.3 Computational Procedure

    13.7 Neural-Network-Based Optimization

    References and Bibliography

    Review Questions

    Problems

    14. Metaheuristic Optimization Methods

    14.1 Definitions

    14.2 Metaphors associated with metaheuristic optimization methods

    14.3 Details of Representative Mataheuristic Algorithms

    14.3.1 Crow search algorithm

    14.3.2 Firefly Optimization Algorithm (FOA)

    14.3.3 Harmony Search Algorithm

    14.3.4 Teaching-Learning-Based Optimization (TLBO)

    14.3.5 Honey Bee Swarm Optimization Algorithm

    References

    Review Questions

    15. Practical Aspects of Optimization

    15.1 Introduction

    15.2 Reduction of Size of an Optimization Problem

    15.2.1 Reduced Basis Technique

    15.2.2 Design Variable Linking Technique

    15.3 Fast Reanalysis Techniques

    15.3.1 Incremental Response Approach

    15.3.2 Basis Vector Approach

    15.4 Derivatives of Static Displacements and Stresses

    15.5 Derivatives of Eigenvalues and Eigenvectors

    15.5.1 Derivatives of λi

    15.5.2 Derivatives of Yi

    15.6 Derivatives of Transient Response

    15.7 Sensitivity of Optimum Solution to Problem Parameters

    15.7.1 Sensitivity Equations Using Kuhn–Tucker Conditions

    References

    Review Questions

    Problems

    16. Multilevel and Multiobjective Optimization

    16.1 Introduction

    16.2 Multilevel Optimization

    16.2.1 Basic Idea

    16.2.1 Basic Idea

    16.3 Parallel Processing

    16.4 Multiobjective Optimization

    16.4.1 Utility Function Method

    16.4.2 Inverted Utility Function Method

    16.4.3 Global Criterion Method

    16.4.4 Bounded Objective Function Method

    16.4.5 Lexicographic Method

    16.4.6 Goal Programming Method

    16.4.7 Goal Attainment Method

    16.4.8 Game Theory Approach

    Solutions Using Matlab

    References and Bibliography

    Review Questions

    Problems

    17. Solution of Optimization Problems Using MATLAB

    17.1 Introduction

    17.2 Solution of General Nonlinear Programming Problems

    17.3 Solution of Linear Programming Problems

    17.4 Solution of Lp Problems Using Interior Point Method

    17.5 Solution of Quadratic Programming Problems

    17.6 Solution of One-Dimensional Minimization Problems

    17.7 Solution of Unconstrained Optimization Problems

    17.8 Matlab Solution of Constrained Optimization Problems

    17.9 Solution of Binary Programming Problems Using Matlab

    17.10 Solution of Multiobjective Problems Using Matlab

    References

    Problems

    Index
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