- Garant předmětu:
- Zdeněk Hanzálek
- Zdeněk Hanzálek
- Zdeněk Hanzálek, Antonín Novák
- Department of Control Engineering
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.
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. Test I.
7. Flows and Cuts - Algorithms.
8. Flows and Cuts - Problem Formulation.
9. Multicommodity network flows.
10. Knapsack Problem and Pseudo-polynomial Algorithms.
11. Traveling Salesman Problem and Approximation Algorithms.
12. Monoprocessor Scheduling.
13. Scheduling on Parallel Processors.
- Syllabus of tutorials:
1. Introduction to the Experimental Environment and Optimization Library
2. SAT and nteger Linear Programming
3. Integer Linear Programming
4. Integer Linear Programming
5. Individual Project I - Assignment and Problem Classification
6. Traveling Salesman Problem
7. Individual Project II - Related Work and Solution
8. Applications of Network Flows and Cuts
9. Individual Project III - Consultation
10. Scheduling. Test II
11. Advanced Methods for Solving Combinatorial Problems
12. Individual Project IV - evaluation and written report
13. Ungraded Assessment
- Study Objective:
- Study materials:
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.
- Time-table for winter semester 2022/2023:
- Time-table is not available yet
- Time-table for summer semester 2022/2023:
Tue Wed ThuroomT2:H1-130
AlgDejvice - Veřejná
- The course is a part of the following study plans: