In The Name of GOD

# Objectives

Finding the best design with the available resources is the goal of design optimization. Many of the design problems in aerospace systems (and also other areas) can be cast as optimization problems. These problems can then be solved using the optimization techniques. In this sense, optimization is only a mathematical tool. One can model the problems well only with a good understanding of the theory behind optimization. This course introduces you to the optimization theory and tells you how it can be applied to solve design problems.  In this course we will deal with continuous optimization methods with emphasis upon nonlinear programming. At the end of the course the student should master most of the issues in numerical optimization.

# Topics

1)     Basic Concepts

·          Introduction

·          Optimization Concepts

·          General Problem Statement

·          Classification of Optimization Problems

·          Optimization Techniques

2)     Linear Programming

·          Introduction

·          Standard Linear Programming Form

·          Possible Solutions

·          The Simplex Method

·          Revised Simplex Method

·          Duality in Linear Programming

·          Sensitivity Analysis

3)     One Variable Optimization

·          Introduction

·          Search Methods

·          Polynomial Approximations

·          Golden Section Method

·          Other Methods

·          Comparison of the Methods

4)     Unconstrained Optimization Techniques

·          Introduction

·          Zero-Order Methods

·          First-Order Methods

·          Second-Order Methods

·          Convergence Criteria

5)     Constrained Optimization Techniques

Direct Methods

·          Introduction

·          Random Search

·          Sequential Linear Programming

·          The Method of Feasible Directions

Indirect Methods

·          Introduction

·          The Exterior Penalty Function Method

·          The Interior Penalty Function Method

·          The Extended Interior Penalty Function Method

·          The Augmented Lagrange Multiplier Method

6)     Further Topics in Optimization

·          Structural Optimization

·          Mutiobjective Optimization

·          Genetic Algorithms

The final grade will be calculated as follows:

·        Homeworks (30%)

·        Design project (20%)

·        Mid-Term Exam (20%)

·        Final Exam (30%)

Outcomes

Students who successfully complete the course will demonstrate the following outcomes:

·        Become familiar with optimization methods

·        Mathematical modeling of optimization problems

·        Implementation of the algorithms discussed and solve realistic design problems

Related Web Sites

http://www.vrand.com  (Vanderplaats R&D)

http://gams.nist.gov  (search engine at this site to look for software on optimization)

http://www-fp.mcs.anl.gov/otc/Guide/guide.html (Network Enabled Optimization System Guide)

## Textbook

1.         G. N. Vanderplaats, Numerical Optimization Techniques for Engineering Design: With Applications, McGraw-Hill, 1984.

## Other References

2.         Haftka, R. T. and Gurdal, Z., Elements of Structural Optimization, third edition, Kluwer Academic Publishers, 1992.

3.          R. Fletcher, Practical Methods of Optimization, Second Edition, Wiley, 1987.

4.         SS Rao, Engineering Optimization: Theory and Practice, 3rd Ed, Wiley, 1996.