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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Combinatorial Optimization

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Code Completion Credits Range Language
B4M35KO Z,ZK 6 3P+2C Czech

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.

Garant předmětu:
Zdeněk Hanzálek
Lecturer:
Zdeněk Hanzálek
Tutor:
Ondřej Benedikt, Josef Grus, Zdeněk Hanzálek, Vilém Heinz, Jakub Med, Anna Minaeva, István Módos, Antonín Novák, Marek Vlk
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
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
roomT2:D3-309
Hanzálek Z.
11:45–14:15
(lecture parallel1)
Dejvice
T2:D3-309
roomT2:H1-131
Med J.
14:30–16:00
(lecture parallel1
parallel nr.101)

Dejvice haly
AlgDejvice
roomT2:H1-130
Grus J.
16:15–17:45
(lecture parallel1
parallel nr.103)

Dejvice haly
AlgDejvice - Veřejná
roomT2:H1-130

18:00–19:30
(lecture parallel1
parallel nr.104)

Dejvice haly
AlgDejvice - Veřejná
roomT2:H1-130
Grus J.
14:30–16:00
(lecture parallel1
parallel nr.102)

Dejvice haly
AlgDejvice - Veřejná
Wed
Thu
roomT2:H1-130
Heinz V.
11:00–12:30
(lecture parallel1
parallel nr.109)

Dejvice haly
AlgDejvice - Veřejná
roomT2:H1-130
Heinz V.
12:45–14:15
(lecture parallel1
parallel nr.105)

Dejvice haly
AlgDejvice - Veřejná
roomT2:H1-130
Med J.
14:30–16:00
(lecture parallel1
parallel nr.106)

Dejvice haly
AlgDejvice - Veřejná
roomT2:H1-131

16:15–17:45
(lecture parallel1
parallel nr.107)

Dejvice haly
AlgDejvice
roomT2:H1-131

18:00–19:30
(lecture parallel1
parallel nr.108)

Dejvice haly
AlgDejvice
Fri
The course is a part of the following study plans:
Data valid to 2024-02-23
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