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AAE55000 - Multidisciplinary Design Optimization

Fall 2014

Days/Time: MWF / 9:30-10:20 am
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.
Fall 2014 Syllabus

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

Web Address:
http://www.itap.purdue.edu/learning/tools/blackboard/

Web Content:
Blackboard will contain: A link to my current course website, syllabus, grades, lecture notes, homework assignments, solutions, quizzes 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 a design optimization 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.

Exams:
No exams. Note: General student opinion is that thecourse requires more time for assessments and homework than courses using traditional exams.

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. Students are required to write scripts in Matlab to call toolbox functions. Some assignments use Excel and Solver add-in. Each lecture will use handouts in Adobe Acrobat format; Acrobat or other *.pdf file reader is needed.

ProEd Minimum Requirements: view

Tuition & Fees: view

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

William A. Crossley
Phone
765-496-2872
Email
crossley@purdue.edu
Office
Purdue University
Neil Armstrong Hall of Engineering
701 W Stadium Ave ARMS 3209
West Lafayette, IN 47907-2045
Fax
765-494-0307
Instructor HomePage