# Purdue Engineering Professional Education

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AAE55000 - Multidisciplinary Design Optimization

Fall 2015

Days/Time: MWF / TBA
Credit Hours: 3

Learning Objective:
To acquire basic knowledge about engineering design optimization techniques and newer techniques for multidisciplinary optimization; develop proper engineering design optimization problem statements; select which optimization method(s) is/are appropriate for a given application; solve multidisciplinary engineering design optimization problems using a computer and available software libraries/toolboxes (primarily Matlab and Excel); interpret solutions generated by an optimization routine.

Description:
This fast-paced, graduate-level course introduces the techniques of engineering design 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 concepts about and implementations of numerical optimization techniques, assuming that the students have little or no knowledge of these topics. Second, students investigate approaches for multiobjective and multidisciplinary optimization based upon knowledge of the basic techniques.

Topics Covered:
Basic Concepts: Optimal Design Problem Formulation, Solution Existence and Uniqueness; Functions of One Variable: Concepts and Newton's Method, Polynomial Fit and Golden Section Search; 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; 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; Linear Programming: Simplex Method; Constrained Functions in N Variables - Direct Methods: Overview, Zero-Order Methods, Feasible Directions, Zoutendjik's Feasible Directions, Reduced Gradient, Sequential Quadratic Programming; Global Optimization: Simulated Annealing, Nelder-Mead Simplex, Genetic Algorithm; Multiobjective Optimization: Pareto Optimality, Global Function /Weighted Sum, Epsilon-Constraint or Gaming Approach , Min-Max, Goal Attainment; Recent MDO Techniques: Approximations and Response Surface Methodology in MDO, problem decomposition strategies; Final project discussion.

Prerequisites:
Computer programming skills sufficient to use available functions in Matlab. Knowledge of linear algebra, multivariate calculus, and numerical methods. Some knowledge of basic statics and strength of materials may help with example and homework problems.

Applied/Theory: 65/35

http://aae.www.ecn.purdue.edu/~crossley/aae550

Web Content:
Blackboard will contain: A link to my current course website, syllabus, grades, lecture notes, homework assignments, solutions, quizzes, chat room, and message board.

Homework:
Course grade is wholly homework and project-based. There are several (about 7) Blackboard-based "assessments", a few (about 3) longer "homework" assignments and 1 "final" project. All assignments to be submitted via the Blackboard course page (available to registered students only).

Projects:
Required. Final project requires individual students to identify problem of their choosing and to develop and solve this problem. Project is documented by a short final report. Project can, but is not required to, be related to the student's job. Recent course enrollment has been too large to allow for presentations.

Exams:
No exams. Note that general student opinion is that this course requires more time than courses that use traditional examinations.

Textbooks:
None required. Recommended -- G. N. Vanderplaats, "Multidiscipline Design Optimization," VR&D, Inc., Monterey CA, 2007 0-944956-04-1, available from VR&D, visit http://www.vrand.com. Recommended -- Arora, J. S., "Introduction to Optimum Design", Third Edition, Elsevier Academic Press, San Diego, CA, 2012. (ISBN: 9780-12-381375-6). Either text will provide good background to support material covered in the course; the instructor encourages students to obtain one of these texts.

Computer Requirements:
ProEd minimum requirements; all projects and assessments include computer work. Student required to write driver scripts in Matlab. Some assignments use Excel and Solver add-in. Each lecture will used handouts in Adobe Acrobat format; Acrobat or other *.pdf file reader is needed. Fall 2012 studio computer / tablet monitor was fine; plan to use this again.

ProEd Minimum Requirements: view

Tuition & Fees: view

Other Requirements:
Students must have access to Matlab (Student edition okay) with Optimization Toolbox and Excel with Solver add-in. Students have free access via Purdue's Software Remote - https://goremote.ics.purdue.edu. The student version of Matlab is reasonably priced if wanted to purchase. See The Mathworks, Inc. site: (http://www.mathworks.com/academia/student_version/index.html).

 William A. CrossleyPhone765-496-2872Emailcrossley@purdue.eduOfficePurdue UniversityNeil Armstrong Hall of Engineering701 W Stadium Ave ARMS 3209West Lafayette, IN 47907-2045 Fax765-494-0307Instructor HomePage