MECH 691w  Optimization in Engineering

Department of Mechanical Engineering, Hong Kong University of Science and Technology

Course Description:

    This graduate course has two integral objectives. The first is to teach fundamental theories, concepts, and techniques in optimization. The second is to work through some real world geometric optimization problems that arise in computer-aided design and manufacturing. By achieving the former, the students will be equipped with the state-of-the-art optimization basic knowledge and techniques which they can apply to a general engineering optimization problem. By accomplishing the latter, the students will gain a first touch at how to solve some interesting optimization problems arising from design and manufacturing that are often of strong geometric flavor and usually cannot be solved by using traditional optimization techniques. This course is designed for cross-disciplinary study, in particular suitable for students of Engineering major and Computer science major.

Instructor:

    Dr. Kai Tang (Dept. of Mech. Engineering; E-mail: mektang@ust.hk; Tel: 852-2358-8656)

Textbooks:

• Chinyere Onwubiko, "Introduction to Engineering Design Optimization", ISBN 0-201-47673-8

• A. D. Belegundu and T. R. Chandrupatia, "Optimization Concepts and Applications in Engineering", ISBN 0-13-031279-7. (reference)

• "Painless Conjugate Gradient" (reference)

Assignments:

• Homework:    After each major chapter there will be some written homework.

• Projects:    Three or four group programming projects, each pertaining to a geometric optimization problem to be covered in the class. In  each project, the students are required to use C or C++ language to implement either an existing algorithm or a one they are required to design as well.

Grade Policy:      

• Homework                                             5%

• Projects                                                75%

• Final-exam                                            20%

Time and place:  

   Thursday, 6:30pm-9:20pm, room 4502.

Office Hours:      

   Thursday, 2:00pm – 4:00pm, room 2555; additional time available by appointments.

Syllabus and Schedule:  

    Part 1:    Introduction    (classnote)

    Part 2:    Linear Programming    (classnote)

                   Project 1

    Part 3:    Single-Variable Optimization Techniques    (classnote)

    Part 4:    Unconstrained Multivariable Optimization    (classnote)

                    Project 2

    Part 5:    Painless Conjugate Gradient Method    (classnote)

    Part 6:    Geometric Optimization in Manufacturing    (classnote)

    Part 7:    Group presentation and test run of project 2

                    Project 3

    Part 8:    Constrained Optimization    (classnote)

    Part 9:    Direct Search Methods    (classnote)

    Part 10:  Integer and Discrete Programming    (classnote)

    Part 11:  Dynamic Programming    (classnote)

                    Project 4

    Part 12:  Combinatorial Optimization    (classnote)