Combinatorial Optimization
Code  Completion  Credits  Range  Language 

AD4M77KO  Z,ZK  6  21KP+6KC  Czech 
 Lecturer:
 Tutor:
 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.
 Requirements:
 Syllabus of lectures:

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 Pseudopolynomial 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
 Syllabus of tutorials:

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
 Study Objective:
 Study materials:

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.
 Note:
 Further information:
 https://moodle.dce.fel.cvut.cz/course/view.php?id=21
 No timetable has been prepared for this course
 The course is a part of the following study plans: