1st Edition

Optimization Algorithms and Applications

By Rajesh Kumar Arora Copyright 2015
    466 Pages 136 B/W Illustrations
    by Chapman & Hall

    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.

    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.


    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.

    Arora (senior engineer, Indian Space Research Organization) has written a textbook on linear and nonlinear optimization that might be used in an advanced undergraduate- or graduate-level introductory course in optimization for students in engineering and science. The book's 11 chapters discuss topics such as linear and integer programming, unconstrained and constrained nonlinear programming, multiobjective optimization, and geometric programming. This is a broad range of subjects, but many are introduced only briefly. For example, the author covers the important topic of interior point methods for linear programming in a single two-page section. Most exercises are simple computations, and there are few theoretical exercises. Arora includes sample MATLAB codes for solving many of the examples in the text. (...)

    --B. Borchers, New Mexico Institute of Mining and Technology