Combinatorial Algorithms

Relations:

During a review of study plans, the course B3M35KOA can be substituted for the course BE3M35KOA.

Course guarantor:

Zdeněk Hanzálek

Lecturer:

Zdeněk Hanzálek

Tutor:

Zdeněk Hanzálek

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. Complexity of combinatorial problems

3. Integer Linear Programming - Algorithms

4. Problem Formulation by Integer Linear Programming

5. The Shortest Paths. Problem Formulation by Shortest Paths.

6. Problem Formulation by Shortest Paths.

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

8. Multicommodity network flows

9. Knapsack Problem and Pseudo-polynomial Algorithms

10. Traveling Salesman Problem and Approximation Algorithms

11. Monoprocessor Scheduling

12. Scheduling on Parallel Processors. Test II.

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/rm35koa/start

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Cybernetics and Robotics (compulsory elective course)