Combinatorial Optimization

Relations:

During a review of study plans, the course BE4M35KO can be substituted for the course B4M35KO.

It is not possible to register for the course B4M35KO if the student is concurrently registered for or has already completed the course BE4M35KO (mutually exclusive courses).

The requirement for course B4M35KO can be fulfilled by substitution with the course BE4M35KO.

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Control Engineering

Synopsis:

The goal is to show the problems and algorithms of combinatorial optimization (often called discrete optimization; there is a strong overlap with the term operations research).

Following the courses on linear algebra, graph theory, and basics of optimization, we show optimization techniques based on graphs, integer linear programming, heuristics, approximation algorithms and state space search methods.

We focus on application of optimization in stores, ground transportation, flight transportation, logistics, planning of human resources, scheduling in production lines, message routing, scheduling in parallel computers.

Requirements:

Optimisation, Discrete mathematics, Logics and graphs

Syllabus of lectures:

1. Introduction to Basic Terms of Combinatorial Optimization, Example Applications and a Test of Preliminary Knowledge

2. Integer Linear Programming - Algorithms

3. Problem Formulation by Integer Linear Programming

4. The Shortest Paths. Problem Formulation by Shortest Paths.

5. Problem Formulation by Shortest Paths.

6. Flows and Cuts - Algorithms and Problem Formulation. Test I.

7. Multicommodity network flows

8. Knapsack Problem and Pseudo-polynomial Algorithms

9. Traveling Salesman Problem and Approximation Algorithms

10. Monoprocessor Scheduling

11. Scheduling on Parallel Processors. Test II.

12. Project Scheduling with Time Windows.

13. Constraint Programming.

14. Reserved

Syllabus of tutorials:

1. Policy and Individual Project Market

2. Introduction to the Experimental Environment and Optimization Library

3. Integer Linear Programming

4. Individual Project I - Assignment and Problem Classification

5. Traveling Salesman Problem

6. Individual Project II - Related Work and Solution

7. Applications of Network Flows and Cuts

8. Individual Project III - Consultation

9. Test III

10. Scheduling

11. Advanced Methods for Solving Combinatorial Problems

12. Individual Project IV - evaluation and written report

13. Ungraded Assessment

14. Reserved

Study Objective:

Study materials:

B. H. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms.

Springer, sixth ed., 2018.

http://dx.doi.org/10.1007/978-3-662-56039-6

J. Blazevicz, Scheduling Computer and Manufacturing Processes. Springer,

second ed., 2001.

J. Demel, Grafy a jejich aplikace. Academia, second ed., 2015.

https://kix.fsv.cvut.cz/~demel/grafy/gr.pdf

Note:

Further information:

https://cw.fel.cvut.cz/wiki/courses/ko/start

No time-table has been prepared for this course

The course is a part of the following study plans:

• Medical electronics and bioinformatics (PS)
• Open Informatics - Human-Computer Interaction (compulsory course in the program)
• Open Informatics - Cyber Security (compulsory course in the program)
• Open Informatics - Computer Graphics (compulsory course in the program)
• Open Informatics - Computer Engineering (compulsory course in the program)
• Open Informatics - Computer Vision and Image Processing (compulsory course in the program)
• Open Informatics - Software Engineering (compulsory course in the program)
• Open Informatics - Artificial Intelligence (compulsory course in the program)
• Open Informatics - Bioinformatics (compulsory course in the program)
• Open Informatics - Data Science (compulsory course in the program)
• Medical electronics and bioinformatics (compulsory elective course)
• Medical electronics and bioinformatics (PS)
• Medical electronics and bioinformatics (compulsory elective course)