Engineering Optimization: A Modern Approach
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Features
- Focuses on non-linear optimization, response surface method, and genetic algorithm optimization studied by engineers
- Bridges the gap between "nonlinear programming" studied by mathematicians and engineering
- Provides a chapter on response sulrface methods with basis and examples
Summary
This book provides a thorough understanding of the concepts of optimization methods from a modern perspective at the conceptual stage of complex technical systems. It focuses on nonlinear optimization with an emphasis on methods such as response surface and genetic algorithms. The text moves the concept of optimization from an academic setting to an industry platform yet gives a balanced treatment of classical methods, making it suitable for an undergraduate course.
Table of Contents
Basic Concepts
Statement of the Optimization Problem
Basic Definitions
Taylor Series Expansion
Quadratic Forms
Optimality Criteria for Unconstrained Optimization
Optimality Criteria for Constrained Optimization
Convexity
Examples in Engineering
Problems
Direct One-Dimensional Search
General Numerical Optimization Algorithm
Numerical Methods to Calculate Step Size
Equal-Interval Search
Golden-Section Search
Polynomial Interpolation
Inexact Line Search
Problems
Gradient-Based Methods
Properties of the Gradient Vector
Steepest-Descent Method
Rates of Convergence
Conjugate-Gradient Method
Basic Conjugate-Gradient Algorithms for Quadratic Functions
Conjugate-Gradient Directions for Quadratic Functions
Problems
Newtonian Methods
Newton's Method
Marquardt's Method
Quasi-Newton Methods
Direct-Update Methods
Broyden-Fletcher-Goldfarb-Shanno Method
Davidson-Fletcher-Powell Method
Numerical Derivatives
Automatic Differentiation
Analytical Gradients for Computational Problems
Problems
Constrained Optimization Methods
Linear Programming
The Simplex Method
Two-Phase Simplex Method
Penalty and Barrier Methods
Important Definitions
Sequential Linear Programming
Quadratic Programming
Constrained Steepest-Descent Method
Trust Region Methods
Problems
Response Surface Method
Response Surfaces
The Least-Squares Method
Two-Level Factorial Designs
Addition of Centre Points
Central Composite Design (CCD)
Sequential Nature of RSM
Limitations of RSM
Other Experimental Designs
Taguchi Orthogonal Arrays
Problems
Genetic Algorithm
Optimization Problems
Binary GA
Real Coded G A
Hybrid Genetic Algorithm
Automated Hybrid Genetic Algorithm
Problems
Bibliography
Index
