Product design optimization

Summary
Numerical optimization is a well-established tool for designing new products, processes, and services in the best way possible. Knowledge of optimization theory and how it can be applied is useful for designing and producing better products, understanding and mapping design trade-offs, and improving profitability of product-developing companies. This course teaches doctoral-level students and professionals what they need to know about practical optimization for improving product development outcomes, including how to formulate problems, construct models, choose algorithms, solve problems, and interpret the results. Emphasis is on the practical aspects, and in this course participants will learn and experience the design optimization process by applying it to a term project of their choice.

Structure
The course is structured in two blocks of time, where we will hold a total of five full-day class sessions. These sessions will include lecture-style discussions, in-class problem-solving exercises, and computer-based exercises. The main assignment is a term project, where students will work on their own or in pairs to formulate, analyze, solve, and interpret the results for a design optimization problem of their choosing (preferably related to their research). The following time blocks are planned:

1. Week 16 (Tues 19 April - Thurs 21 April)
2. Week 18 (Tues 3 May - Wed 5 May)
3. Week 21 or 22 (TBD, 1-2 hours for final project presentations)

Learning outcomes
Upon successful completion of the course, students should be able to:

1. Formulate appropriate optimization problems
2. Analyze optimization formulations
3. Run designs of experiments to efficiently sample a design space
4. Construct surrogate models
5. Understand the basic principles of common optimization algorithms
6. Choose appropriate optimization algorithms for a problem
7. Solve problems using algorithms in MATLAB and Excel
8. Interpret results and provide design recommendations
9. Formulate and solve multi-objective optimization problems
10. Formulate and solve optimization problems that account for uncertainty
11. Formulate and solve multi-disciplinary optimization problems
12. Become familiar with advanced optimization methods and tools

Learning activities

• Class sessions and discussions, including in-class written and computer exercises (30-35 hours)
• 1 term project, topic of student's choice, individually or in pairs (expected effort 70-75 hours)
• 2-3 oral presentations of project progress

Class sessions (venue TBD, most likely in Gothenburg)

1. Tuesday, 22 April, 9:00-17:00 Learning outcomes 1,2,3,4,7 - Introduction to optimization, basic optimization in Excel, meta-modeling, introduce term projects
2. Wednesday, 23 April, 9:00-17:00 Learning outcomes 5,6,7,8 - Gradient-based optimization, gradient-free optimization, optimization in MATLAB
3. Thursday, 24 April, 9:00-17:00 Learning outcomes 7,8,9 - Multi-objective optimization, visualization in MATLAB, project proposal presentations
4. Tuesday, 27 May, 9:00-17:00 Learning outcomes 10,11 - Project progress oral presentations, robust and reliability-based optimization, systems and multi-disciplinary design optimization
5. Wednesday, 28 May, 9:00-17:00 Learning outcome 12 - Advanced topics in optimization, review session, written exam
6. TBD (sometime between 10-16 June) Learning outcome 8 - Final oral presentations and written reports due

Grading
Grading will be pass/fail, and students must successfully complete the following two tasks:

1. A written examination covering the lectured material (supported by complementary readings and exercises), administered at the end of day 5
2. Term projects, evaluated based on oral presentations and written reports

Expected pre-knowledge
Basic calculus (be comfortable with derivatives)
Familiarity with matrix algebra (linear algebra)
Some MATLAB or other coding language experience highly recommended

For those unfamiliar with MATLAB, you can find some good tutorials here:
http://www.mathworks.se/academia/student_center/tutorials/player/player/content/CoursePlayer.html

It is recommended that you go through these before the class starts. At the very least, you should be familiar with the interface, variables and expressions, and vector analysis and visualization (Units 2-4), but it would also be helpful to complete Units 5, 6, and 13 (you should skip Unit 12, as we will cover some of it during the course). Each unit is approximately 1 hour.

Enrollment:
To enroll, email Magnus Bengtsson (magnus.bengtsson@chalmers.se). Enrollment will be limited to 30 students.

Contact Magnus Bengtsson, magnus.bengtsson@chalmers.se

Magnus Bengtsson, Ph.D., Researcher Department of Product and Production Development Chalmers University of Technology Email: magnus.bengtsson@chalmers.se Tel: +46 (0)31-772 5019