Multidisciplinary Design Optimization
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. Most recent syllabus
- 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 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 (usually 7) Blackboard-based assessments, a few (usually 3) longer homework assignments and one final project. All assignments are submitted via Blackboard.
Projects:The final project requires students to identify a design optimization problem of their choosing and then develop and solve the resulting formulation using an appropriate algorithm. A short final report documents the project effort. The project can but is not required to be related to the students job. In previous semesters, the instructor has signed non-disclosure agreements for job-related projects requiring this; students considering projects that will require this protection should start the process for obtaining a signed NDA a soon as they identify the project topic.
Exams:No exams. The homework assignments require fairly significant effort and replace mid-term exams. Similarly, the final project replaces a final exam.
Textbooks:No required text.
Multidiscipline Design Optimization, Vanderplaats, G. N., VR&D, 2007. (ISBN: 0-944956-04-1)
Introduction to Optimum Design, Arora, J. S., Fourth Edition, Elsevier Academic Press, San Diego, CA, 2016. (ISBN: 9780-12-800806-5)