# AAE 55000: Multidisciplinary Design Optimization

Description:

Basics of numerical optimization: problem formulation, conditions of optimality, search direction and step length. Calculus-based techniques for univariate and multivariate optimization. Constrained and unconstrained optimization methods. Global optimization methods. Multiobjective optimization: Pareto optimality and approaches. Recent Multidisciplinary Design Optimization techniques: approximations, response surface methodology, and collaborative optimization. Applications of various methods and techniques to representative engineering problems, culminating in a final project.

Format: 3 lecture hrs per week

Credit hours: 3

Status: Elective, Design, Structures

Offered: Fall

Pre-requisite:

Co-requisite: None

Course Instructor: Professor Crossley

Text: Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design, 3rd edition, VR&D, Colorado Springs, CO, 1999.

Assessment Method: Homework Projects 2/3; Final Project 1/3

## Course Objective:

Goal:

AAE 550 introduces the techniques of engineering optimization, leading into topics for Multidisciplinary Design Optimization (MDO). The application of these techniques to solve engineering design problems is also presented. First, students are exposed to basic knowledge about numerical optimization techniques, assuming that the student has little or no knowledge of these topics. Second, students investigate approaches for multiobjective and multidisciplinary optimization based upon knowledge the basic techniques.

Objectives include developing abilities to:

develop a proper engineering optimization problem statement

select which method(s) is/are appropriate for a given application

solve multidisciplinary engineering design optimization problems using a computer

interpret solutions generated by an optimization routine

write a technical paper, similar to those for professional society conferences

Necessary Background:

AAE 550 requires knowledge of linear algebra, multivariate calculus, and numerical methods. This course also requires that the student have computer-programming skills sufficient to use available functions and library routines (like those available in IMSL, Matlab, etc.).

Topics (number of Lectures):

1. Basic Concepts: Optimal Design Problem Formulation, Solution Existence and Uniqueness (3 lectures)

2. Functions of One Variable: Concepts and Newton's Method, Polynomial Fit and Golden Section Search (2 lectures)

3. Unconstrained Functions in N Variables: Zero-Order Methods, First-Order Methods, Scaling and Convergence, Conjugate Direction and Variable Metrics (DFP and BFGS), Newton's Method, Variable Scaling Issues (5 lectures)

4. Constrained Functions in N Variables - Sequential Unconstrained Minimization Techniques: Exterior Penalty Methods, Interior and Extended Interior Penalty Methods, Variable Penalty Function, Comparison of Penalty Methods, Constraint Scaling, Augmented Lagrange Method (ALM) for Equality Constraints, ALM for Inequality Constraints and Generalized ALM (3 lectures)

5. Linear Programming: Simplex Method (2 lectures)

6. Constrained Functions in N Variables - Direct Methods: Overview, Zero-Order Methods, Feasible Directions, Zoutendjik's Feasible Directions, Reduced Gradient, Sequential Quadratic Programming (6 lectures)

7. Global Optimization: Simulated Annealing, Nelder-Mead Simplex, Genetic Algorithm (8 lectures)

8. Multiobjective Optimization: Pareto Optimality, Global Function /Weighted Sum, "Gaming" Approach (e-constraint), Min-Max, Goal Attainment, Kreisselmeier-Steinhauser Function, (4 lectures)

9. Recent MDO Techniques: Approximations, Response Surface Methodology in MDO, Collaborative Optimization (7 lectures)

Discussion of final projects (1 lecture)

Relationship of course to program objectives:

Optimization is a critical technical component of systems design (1). This course requires students to formulate and solve open-ended design problems using computational tools (2a). The homework and final projects require effective written and graphical communication (2c). The final project requires the students to identify a problem of their choosing and to develop and solve this problem in the manner of a research project (3).

Prepared by: William A. Crossley

Date: February 17, 2001