Engineering Optimization : Theory and Practice

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  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2009-07-20
  • Publisher: Wiley

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This is the only book on the market that discusses all the important methods of optimization. All the methods are presented in a simple language in the most comprehensive manner. Nonlinear, linear, geometric, dynamic and stochastic programming techniques are presented with a focus on engineering applications. Other more specialized methods such as optimal control, multiobjective optimization, genetic algorithms, simulated annealing, neural networks and fuzzy optimization methods are also included. In each case examples and cases are presented to show how the mtheod is actually used in the real world.

Author Biography

Singiresu S. Rao, PhD, is a Professor and Chairman of the Department of Mechanical Engineering at the University of Miami. Dr. Rao has published more than 175 technical papers in internationally respected journals and more than 150 papers in conference proceedings in the areas of engineering optimization, reliability-based design, fuzzy systems, uncertainty models, structural and mechanical design, and vibration engineering. He has authored several books, including The Finite Element Method in Engineering, Mechanical Vibrations, Vibration of Continuous Systems, Reliability-Based Design, and Applied Numerical Methods for Engineers and Scientists.

Table of Contents

Introduction to Optimization
Historical Developments
Engineering Applications of Optimization
Statement of an Optimization Problem
Classification of Optimization Problems
Optimization Techniques
Engineering Optimization Literature
Solution of Optimization Problems Using MATLAB
References and Bibliography
Review Questions
Classical Optimization Techniques
Single Variable Optimization
Multivariable Optimization with no Constraints
Multivariable Optimization with Equality Constraints
Multivariable Optimization with Inequality Constraints
Convex Programming Problem
References and Bibliography
Review Questions
Linear Programming I: Simplex Method
Applications of Linear Programming
Standard Form of a Linear Programming Problem
Geometry of Linear Programming Problems
Definitions and Theorems
Solution of a System of Linear Simultaneous Equations
Pivotal Reduction of a General System of Equations
Motivation of the Simplex Method
Simplex Algorithm
Two phases of the Simplex Method
MATLAB Solution of L.P. Problems
References and Bibliography
Review Questions
Linear Programming II: Additional Topics and Extensions
Revised Simplex Method
Duality in Linear Programming
Decomposition Principle
Sensitivity or Postoptimality Analysis
Transportation Problem
Karmarkar?s Interior Method
Quadratic Programming
MATLAB Solutions
References and Bibliography
Review Questions
Nonlinear Programmimg I: One-Dimensional Minimization Methods
Unimodal Function
Elimination Methods
Unrestricted Search
Exhaustive Search
Dichotomous Search
Interval Halving Method
Fibonacci Method
Golden Section Method
Comparison of Elimination Methods
Interpolation Methods
Quadratic Interpolation Method
Cubic Interpolation Method
Direct Root Methods
Practical Considerations
MATLAB Solution of One-Dimensional Minimization Problems
References and Bibliography
Review Questions
Nonlinear Programming II: Unconstrained Optimization Techniques
Direct Search Methods
Random Search Methods
Grid Search Method
Univariate Method
Pattern Directions
Powell's Method
Simplex Mehod
Indirect Search (Descent) Methods
Gradient of a Function
Steepest Descent (Cauchy) Method
Conjugate Gradient (Fletcher-Reeves) Method
Newton's Method
Marquardt Method
Quasi-Newton Methods
Rank 1 Updates
Rank 2 Updates
Davidon-Fletcher-Powell Method
Broydon-Fletcher-Goldfarb-Shanno Method
Test Functions
MATLAB Solution of Unconstrained Optimization Problems
References and Bibliography
Review Questions
Nonlinear Programming III: Constrained Optimization Techniques
Characteristics of a Constrained Problem
Direct Methods
Random Search Methods
Complex Method
Sequential Linear Programming
Basic Approach in the Methods of Feasible Directions
Zoutendijk's Method of Feasible Directions
Rosen's Gradient Projection Method
Generalized Reduced Gradient Method
Sequential Quadratic Programming
Indirect Methods
Transformation Techniques
Basic Approach of the Penalty Function Method
Interior Penalty Function Method
Convex Programming Problem
Exterior Penalty Function Method
Extrapolation Techniques in the Penalty Function Method
Extended Interior Penalty Function Methods
Penalty Function Method for Problems with Mixed Equality and Inequality Constraints
Penalty Function Method for Parametric Constraints
Augmented Lagrange Multiplier Method
Checking the Convergence of Constrained Optimization Problems
Test Problems
MATLAB Solution of Constrained Optimization Problems
References and Bibliography
Review Questions
Geometric Programming
Unconstrained Minimization Problem
Solution of an Unconstrained Geometric Programming Problem Using Differential Calculus
Solution of an Unconstrained Geometric Programming Problem Using Arithmetic-Geometric Inequality
Primal-Dual Relationship and Sufficiency Conditions in the Unconstrained Case
Constrained Minimization
Solution of a Constrained Geometric Programming Problem
Primal and Dual Programs in the Case of Less-Than Inequalities
Geometric Programming with Mixed Inequality Constraints
Complementary Geometric Programming
Applications of Geometric Programming
References and Bibliography
Review Questions
Dynamic Programming
Multistage Decision Processes
Concept of Suboptimization and Principle of Optimality
Computational Procedure in Dynamic Programming
Example Illustrating the Calculus Method of Solution
Example Illustrating the Tabular Method of Solution
Conversion of a Final Value Problem into an Initial Value Problem
Linear Programming as a Case of Dynamic Programming
Continuous Dynamic Programming
Additional Applications
References and Bibliography
Review Questions
Integer Programming
Integer Linear Programming
Graphical Representation
Gomory's Cutting Plane Method
Balas' Algorithm for Zero-One Programming Problems
Integer Nonlinear Programming
Integer Polynomial Programming
Branch-and-Bound Method
Sequential Linear Discrete Programming
Generalized Penalty Function Method
Solution of Binary Programming Problems Using MATLAB
References and Bibliography
Review Questions
Stochastic Programming
Basic Concepts of Probability Theory
Stochastic Linear Programming
Stochastic Nonlinear Programming
Stochastic Geometric Programming
References and Bibliography
Review Questions
Optimal Control and Optimality Criteria Methods
Calculus of Variations
Optimal Control Theory
Optimality Criteria Methods
References and Bibliography
Review Questions
Modern Methods of Optimization
etic Algorithms
Simulated Annealing
Particle Swarm Optimization
Ant Colony Optimization
Optimization of Fuzzy Systems
Neural-Network-Based Optimization
References and Bibliography
Review Questions
Practical Aspects of Optimization
Reduction of Size of an Optimization Problem
Fast Reanalysis Techniques
Derivatives of Static Displacements and Stresses
Derivatives of Eigenvalues and Eigenvectors
Derivatives of Transient Response
Sensitivity of Optimum Solution to Problem Parameters
Multilevel Optimization
Parallel Processing
Multiobjective Optimization
Solution of Multiobjective Problems Using MATLAB
References and Bibliography
Review Questions
Convex and Concave Functions
Some Computational Aspects of Optimization
Choice of Method
Comparison of Unconstrained Methods
Comparison of Constrained Methods
Availability of Computer Programs
Scaling of Design Variables and Constraints
References and Bibliography
Introduction to MATLAB
Features and Special Characters
Defining Matrices in MATLAB
Creating m-files
Optimization Toolbox
Answers to Selected Problems
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