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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
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School of Environment and Society
- Department of Architecture and Building Engineering
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- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Industrial Engineering and Economics
- Instructor(s)
- Matsui Tomomi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Tue7-8() Fri7-8()
- Group
- -
- Course number
- IEE.A432
- Credits
- 2
- Academic year
- 2021
- Offered quarter
- 4Q
- Syllabus updated
- 2021/9/29
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Many of mathematical problems arising in the areas of economics and industrial engineering can be formulated as discrete optimization problems. In this lecture, we pick up integer programming problems, network programming problems, and combinatorial optimization problems. We explain the mathematical structures of the solution sets of the problems, and connection with combinatorics. We also review various algorithms for discrete optimization problems.
The objective is to let students learn skills which is necessary to solve discrete optimization problems.
Student learning outcomes
By the end of this course, students will be able to:
・Understand fundamental properties of discrete optimization problems.
・Understand fundamental properties of the branch and bound method.
・Understand fundamental properties of typical approximation algorithms.
・Understand fundamental properties of typical heuristics.
Keywords
discrete optimization problem, integer programming problem, combinatorial optimization problem, the branch and bound method, approximation algorithms, heuristics.
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
In each class we give a lecture and assign some exercise problems if needed.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | fundamental properties of discrete optimization problems. | understand the contents of each class |
| Class 2 | algorithm and complexity | |
| Class 3 | overview of linear programming and the duality theorem | |
| Class 4 | relaxation method | |
| Class 5 | Lagrange relaxation and subgradient method | |
| Class 6 | enumerative method | |
| Class 7 | linear relaxation problem | |
| Class 8 | branch and bounds method | |
| Class 9 | dual simplex method | |
| Class 10 | additive lower bounds | |
| Class 11 | approximation algorithm | |
| Class 12 | randomized algorithm | |
| Class 13 | heuristics | |
| Class 14 | introduction to complexity theory |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required
Reference books, course materials, etc.
Course materials will be provided as needed.
Assessment criteria and methods
Evaluation based on reports
Related courses
- IEE.B433 ： Advanced Topics in Mathematical Economics
Prerequisites (i.e., required knowledge, skills, courses, etc.)
No prerequisites are necessary, but enrollment in related courses is desirable.
