Combinatorial Optimization

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.

Requirements:

Syllabus of lectures:

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

2. Integer Linear Programming - Algorithms

3. Problem Formulation by Integer Linear Programming

4. Heuristics, Test

5. Shortest Paths

6. Network Flows and Cuts

7. Multicommodity network flows

8. Dynamic Programming, Test

9. Knapsack Problem and Pseudo-polynomial Algorithms

10. Traveling Salesman Problem and Approximation Algorithms

11. Monoprocessor Scheduling

12. Scheduling on Parallel Processors

13. Project Scheduling with Time Windows

14. Constraint Programming

Syllabus of tutorials:

1. Introduction to the Experimental Environment and Optimisation library

2. Integer Linear Programming

3. Applications of Integer Linear Programming

4. Assignment of Term Projects

5. Branch and Bound Technique

6. Shortest Paths

7. Applications of Network Flows and Cuts

8. Presentation of Term Projects

9. Monoprocessor Scheduling - Earliest Deadline First

10. Approximation Algorithms - List Scheduling

11. Reserved

12. Test

13. Giving over Term Projects

14. Credits

Study Objective:

Study materials:

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

Springer, third ed., 2006.

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

second ed., 2001.

J. Demel, Grafy a jejich aplikace. Academia, second ed., 2002.

Note:

Further information:

https://moodle.dce.fel.cvut.cz/course/view.php?id=21

No time-table has been prepared for this course

The course is a part of the following study plans: