### Synopsis

The course discusses fundamentals of discrete optimization methods as applied to the problems in mechanical design and manufacturing. Topics include discrete optimization models, integer and mixed-integer programming algorithms, graph search algorithms, heuristic algorithms, an introduction to NP completeness (optional), and case studies.

Lectures present the key concepts and mathematical basis of each topic and its applications in mechanical design and manufacturing. A term project emphasizes the applications of the course materials to a realistic engineering problem.

### Prerequisites

Graduate standing with familiarity with MATLAB programming on Windows. Some knowledge in optimization, algorithms and discrete mathematics would be helpful, but not required.

### Textbooks

None. Course notes and a list of references are available on the Web.

### Lectures

Tuesdays and Thursdays at
2:30pm - 4:00pm
in **2305 GGB **
**(new room!)**

### Instructors

Professor Kazuhiro Saitou

Department of Mechanical Engineering

3211 EECS, kazu@umich.edu

Office hours: Mondays 1:30pm - 3:00pm

Shailesh Vedula

3590 GGB, vedula@umich.edu

Office hours: Mondays 10:30am -
12:30pm

### Grade breakdown

- problem sets:
**50%** - paper presentation:
**3%** - course project
**47%**

The Honor Code is in effect for both the problems sets and the course project. Unless otherwise announced, all problem sets are due at **2:40pm**** in the classroom
(submit a paper copy), **and all reports are due at **midnight
(email me PDF files)** on the dates indicated in Schedule page. Late submission is accepted according to the past due policy.

### Problem sets

Problem sets consist of written problems and computer assignments. The computer assignments include programming in MATLAB in CAEN Windows** **environment. Familiarity with or willingness to self-learn basic MATLAB programming is assumed, and therefore there will be **neither **tutorial **nor **troubleshooting offered on MATLAB.

All problem sets are to be done individually. This means:

- You may discuss the subject matter with your classmates (this is encouraged!) but not allowed to work out the details of the problems.
- You are not allowed to discuss the problem set with previous class members, nor anyone else who has significant knowledge of the details of the problems set,
- You should not compare your written solutions, whether in scrap paper form or your final work product, with other students (and vice versa).
- You are also not allowed to possess, look at, use, or in any way derive advantage from the existence of solutions prepared in previous years.

Violation of this policy is grounds for the Instructor(s) to initiate an action that would be filed with the Dean’s office and would come before the College of Engineering’s Honor Council. If you have any questions about this policy, please contact the Instructor.

### Paper reading and presentations

Each student team is required to give a presentation on a research paper related to discrete design optimization. The paper **must** be chosen from the journals listed under Course Project headling in References page. The presentations will be done during the first **10 minitues** of the lectures on the dates indicated in Schelule page and should use **5-6 Power Point slides**. Your presentation should include 1) the title page of the chosen paper, 2) a technical summary of the content, 3) discrete design variables in the problem, and 4) at least one point to critisize the paper. The paper you choose for the presenation can be different from the paper on which your project topic will be based.

### Course project

The primary focus of the course project is the definition, formulation, and implementation of an engineering design problem as an optimization problem. The secondary focus is the implementation and testing of an optimization algorithm(s). The engineering design problem for the course project should be the one related to your own research and/or of your technical interests, and **must** be drawn from a paper(s) in one (or more) scholary journals listed under the "Course projects" headling in the Reference page of the course Web site. You are expected to work on a simplified version of the engineering design problem discussed in the paper(s), and are not required to use the same method(s) to solve the problem. The paper from which you draw the engineering design problem does not have to be on optimization. Of course, the problem must involve decisions among discrete choices!

The couese project can be done individually or by a team of two or more depending on the enrollment. The project requires a proposal (2%), a progress report (15%), an oral presentation (10%), and a final paper (20%). Members of a team will receive same grades for the proposal, reports and final presentation. Detailed guidelines on each of these, as well as abstracts from past projects, are found in Project info page.

While is it acceptable to work on the same or similar project topic for another course taken in the past or concurrently with this course, the project reports must describe the work *distinctively *done for this course. In particular, the students must consult with the instructor *a priori* to work on the same or similar topic done in **ME555** and must submit a copy of the reports for the course * together with *ME558 reports.