Combinatorial Optimization

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.

Kód
AE4M77KO
Semestr
letní
Rozsah
3+2c
Obsazeno
0
Počet kreditů
6
Zakončení
zápočet a zkouška
Jazyk výuky
angličtina
Poznámka
Rozsah výuky v kombinované formě studia: 21p+6c
Obsah přednášek

1. Introduction of Basic Terms of Combinatorial Optimization, Example Applications and Test on Preliminary Knowledge
2. Integer Linear Programming - Algorithms
3. Problem Formulation by Integer Linear Programming
4. Heuristics, Test
5. Shortest Paths
6. Network Flows and Cuts
7. Multicommodity network flows
8. Dynamic Programming, Test
9. Knapsack Problem and Pseudo-polynomial Algorithms
10. Traveling Salesman Problem and Approximation Algorithms
11. Monoprocessor Scheduling
12. Scheduling on Parallel Processors
13. Project Scheduling with Time Windows
14. Constraint Programming

Náplň cvičení

1. Introduction to the Experimental Environment and Optimisation library
2. Integer Linear Programming
3. Applications of Integer Linear Programming
4. Assignment of Term Projects
5. Branch and Bound Technique
6. Shortest Paths
7. Applications of Network Flows and Cuts
8. Presentation of Term Projects
9. Monoprocessor Scheduling - Earliest Deadline First
10. Approximation Algorithms - List Scheduling
11. Reserved
12. Test
13. Giving over Term Projects
14. Credits