Subject description - BE4M35KO

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BE4M35KO Combinatorial Optimization
Roles:PS, PV, P Extent of teaching:3P+2C
Department:13135 Language of teaching:EN
Guarantors:  Completion:Z,ZK
Lecturers:Hanzálek Z. Credits:6
Tutors:Too many persons Semester:L

Web page:


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.

Course outlines:

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

Exercises outline:

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


B. H. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms.
Springer, sixth ed., 2018.
J. Blazevicz, Scheduling Computer and Manufacturing Processes. Springer,
second ed., 2001.
J. Demel, Grafy a jejich aplikace. Academia, second ed., 2015.


Optimisation, Discrete mathematics, Logics and graphs

Subject is included into these academic programs:

Program Branch Role Recommended semester
MEBIO4_2018 Signal Processing PV 2
MEBIO1_2018 Bioinformatics PS 2
MEOI7_2018 Artificial Intelligence P 2
MEOI9_2018 Data Science P 2
MEOI8_2018 Bioinformatics P 2
MEOI4_2018 Computer Engineering P 2
MEOI3_2018 Computer Graphics P 2
MEOI2_2018 Cyber Security P 2
MEOI1_2018 Human-Computer Interaction P 2
MEOI6_2018 Software Engineering P 2
MEOI5_2018 Computer Vision and Image Processing P 2
MEBIO3_2018 Image Processing PS 2
MEBIO2_2018 Medical Instrumentation PV 2

Page updated 18.6.2024 05:51:17, semester: Z/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)