Subject description - AE4M35KO

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AE4M35KO Combinatorial Optimization Extent of teaching:3+2c
Guarantors:  Roles:P,V Language of
Teachers:  Completion:Z,ZK
Responsible Department:13135 Credits:6 Semester:L


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. Modeling Languages for Solving Combinatorial Problems
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 - hand in a code and a written report
13. Ungraded Assessment
14. Reserved


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.


Optimisation, Discrete mathematics, Logics and graphs


Subject is included into these academic programs:

Program Branch Role Recommended semester
MEKME1 Wireless Communication V 2
MEKME5 Systems of Communication V 2
MEKME4 Networks of Electronic Communication V 2
MEKME3 Electronics V 2
MEKME2 Multimedia Technology V 2
MEOI1 Artificial Intelligence P 2
MEOI5NEW Software Engineering P 2
MEOI5 Software Engineering P 2
MEOI4 Computer Graphics and Interaction P 2
MEOI3 Computer Vision and Image Processing P 2
MEOI2 Computer Engineering P 2
MEEEM1 Technological Systems V 2
MEEEM5 Economy and Management of Electrical Engineering V 2
MEEEM4 Economy and Management of Power Engineering V 2
MEEEM3 Electrical Power Engineering V 2
MEEEM2 Electrical Machines, Apparatus and Drives V 2
MEKYR4 Aerospace Systems V 2
MEKYR1 Robotics V 2
MEKYR3 Systems and Control V 2
MEKYR2 Sensors and Instrumentation V 2

Page updated 14.6.2019 17:52:56, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)