1st Edition

Algorithms and Applications

ISBN 9781498721127
Published May 6, 2015 by Chapman and Hall/CRC
466 Pages 136 B/W Illustrations

USD $220.00

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Book Description

Choose the Correct Solution Method for Your Optimization Problem

Optimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs.

The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden–Fletcher–Goldfarb–Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible directions, genetic algorithms, particle swarm optimization (PSO), simulated annealing, ant colony optimization, and tabu search methods. The author shows how to solve non-convex multi-objective optimization problems using simple modifications of the basic PSO code. The book also introduces multidisciplinary design optimization (MDO) architectures—one of the first optimization books to do so—and develops software codes for the simplex method and affine-scaling interior point method for solving linear programming problems. In addition, it examines Gomory’s cutting plane method, the branch-and-bound method, and Balas’ algorithm for integer programming problems.

The author follows a step-by-step approach to developing the MATLAB® codes from the algorithms. He then applies the codes to solve both standard functions taken from the literature and real-world applications, including a complex trajectory design problem of a robot, a portfolio optimization problem, and a multi-objective shape optimization problem of a reentry body. This hands-on approach improves your understanding and confidence in handling different solution methods. The MATLAB codes are available on the book’s CRC Press web page.

Table of Contents

Historical Review
Optimization Problem
Modeling of the Optimization Problem
Solution with the Graphical Method
Gradient Vector, Directional Derivative, and Hessian Matrix
Linear and Quadratic Approximations
Organization of the Book

1-D Optimization Algorithms
Test Problem
Solution Techniques
Comparison of Solution Methods

Unconstrained Optimization
Unidirectional Search
Test Problem
Solution Techniques
Additional Test Functions
Application to Robotics

Linear Programming
Solution with the Graphical Method
Standard Form of an LPP
Basic Solution
Simplex Method
Interior-Point Method
Portfolio Optimization

Guided Random Search Methods
Genetic Algorithms
Simulated Annealing
Particle Swarm Optimization
Other Methods

Constrained Optimization
Optimality Conditions
Solution Techniques
Augmented Lagrange Multiplier Method
Sequential Quadratic Programming
Method of Feasible Directions
Application to Structural Design

Multiobjective Optimization
Weighted Sum Approach
ε-Constraints Method
Goal Programming
Utility Function Method

Geometric Programming
Unconstrained Problem
Dual Problem
Constrained Optimization

Multidisciplinary Design Optimization
MDO Architecture
MDO Framework
Response Surface Methodology

Integer Programming
Integer Linear Programming
Integer Nonlinear Programming

Dynamic Programming
Deterministic Dynamic Programming
Probabilistic Dynamic Programming


Appendix A: Introduction to MATLAB
Appendix B: MATLAB Code
Appendix C: Solutions to Chapter Problems


Chapter Highlights, Formula Charts, and Problems appear at the end of each chapter.

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Rajesh Kumar Arora is a senior engineer at the Indian Space Research Organization, where he has been working for more than two decades. He obtained his PhD in aerospace engineering from the Indian Institute of Science, Bangalore. His research interests include mission design, simulation of launch vehicle systems, and trajectory optimization.