This course will cover representative combinatorial optimization problems and their solutions which are present in real world situations. Representative combinatorial optimization problems and their applications are extractions of the most vital part of these problems and each of them are difficult in their own way. Also, they can be extended to cover several other problems. Additionally, their solutions involve ideas and algorithms of combinatorial optimization, and mostly depend on data structure. Therefore, it will require an overall approach involving all of this knowledge. Also, the instructor will explain some technical issues and details for implementing these algorithms.
Through this course, students will be able to recognize the representative combinatorial optimization problems which are present in real world situations and have a vague idea of their solutions. Also, they will be able to explain roughly the data structure, techniques, and constraints when implementing them to solve the problems.
Shortest path problem, dynamic programming, minimum cost flow problem, branch-and-bound method, matching, enumeration algorithms, scheduling, assignment problem, modeling
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
In each class, the instructor will give concrete examples for corresponding applications to explain the method and for students to understand its importance.
|Course schedule||Required learning|
|Class 1||Combinatorial optimization and approximation methods||Evaluation of the grade will be explained|
|Class 2||Dynamic programming and its applications|
|Class 3||Enumeration problem and its solution|
|Class 4||Assignment problem and its applications|
|Class 5||Minimum flow and production planning|
|Class 6||Class forming problem|
|Class 7||Delivery planning|
|Class 8||Optimization in financial engineering|
|Class 10||Data mining|
|Class 11||Practical shortest path method|
|Class 12||Algorithms in genome science|
|Class 13||Sport scheduling|
|Class 14||Recent topics|
|Class 15||Recent topics|
Tetsuo Ichimori, "Mathematical Programming - Methods of Optimization'', Kyoritsu-Shuppan, ISBN-13: 978-4320014749.
Hiroshi Konno, "Financial Engineering (1) - Mean/Variance Model and its Extensions'', Nikkagirenn, ISBN-13: 978-4817150257.
Hiroshi Konno, "Introduction to Mathematical Decisions - Operations Research in the Campus'', Asakura-Shoten, ISBN-13: 978-4254126082.
Hidetoshi Ibaraki, "Discrete Optimization and Algorithms'', (Iwanami Kouza Ouyou Suugaku) Iwanami-Shoten, ISBN4-00-010805-0 C3341.
Will be decided based on reports and assignments.
It is preferred that the credits for "Mathematical Optimization'' is already obtained.