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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

NIE-KOP Combinatorial Optimization Extent of teaching: 3P+1C
Instructor: Fišer P., Schmidt J. Completion: Z,ZK
Department: 18103 Credits: 6 Semester: Z

Annotation:
The students will gain knowledge and understanding necessary deployment of combinatorial heuristics at a professional level. They will be able not only to select and implement but also to apply and evaluate heuristics for practical problems.

Lecture syllabus:
1. Discrete optimization, examples of practical tasks. Combinatorial problems. Algorithm complexity, problem complexity.
2. Models of computation. The classes P and NP. Polynomial hierarchy.
3. The notion of completeness. Complexity comparison techniques. The classes NP-complete, NP-hard and NPI.
4. Communication and circuit complexity.
5. The classes PO and NPO and their structure. Deterministic approximation algorithms. Classification of approximative problems. Pseudopolynomial algorithms. Randomization and randomized algorithms.
6. Practical deployment of heuristic and exact algorithms. Experimental evaluation.
7. State space and search space, exact methods.
8. Local methods: heuristics.
9. Simulated annealing.
10. Simulated evolution: taxonomy, genetic algorithms.
11. Advanced genetic algorithms: competent GA, fast messy GA, Stochastic optimization: models and applications. Bayesian optimization.
12. Tabu search.
13. Global methods, taxonomy of decomposition-based methods. Exact and heuristic global methods, the Davis-Putnam procedure seen as a global method.

Seminar syllabus:
1. Seminar: terminology, examples of complexity.
2. Seminar: examples of state space.
3. Homework consultation when required, self-study: dynamic programming revision.
4. Solved problems session: the classes P and NP, complexity proofs, problems beyond NP.
5. Solved problems session: completeness, reductions.
6. Homework consultation when required.
7. Homework consultation when required.
8. Homework consultation when required.
9. Midterm test.
10. Homework consultation when required.
11. Solved problems session: advanced heuristics, applications.
12. Homework consultation when required.
13. Homework consultation when required.
14. Backup test term, evaluation.

Literature:
1. Arora, S. : Computational Complexity: A Modern Approach. Cambridge University Press, 2017. ISBN 978-1316612156.
2. Hromkovič, J. : Algorithmics for Hard Problems: Introduction to Combinatorial Optimization, Randomization, Approximation, and Heuristics 2nd Edition. Springer, 2004. ISBN 978 3540441342.
3. Kučera, L. : Kombinatorické algoritmy. SNTL, 1993.
4. Ausiello, G. - Crescenzi, P. - Kann, V. - Gambosi, G. - Spaccamela, A. M. : Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer, 2003. ISBN 3540654313.

Requirements:
Basic notions: algorithm, computational complexity, asymptotic complexity. Formal languages. Basic graph theory. Random variable. Boolean logic. Branch and bound algorithm. Basic dynamic programming. Practical programming in any imperative language.

Informace o předmětu a výukové materiály naleznete na https://moodle-vyuka.cvut.cz/course/view.php?id=6354

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NIE-SI.21 Software Engineering 2021 PP 1
NIE-TI.21 Computer Science 2021 PP 1
NIE-NPVS.21 Design and Programming of Embedded Systems 2021 PP 1
NIE-PSS.21 Computer Systems and Networks 2021 PP 1
NIE-PB.21 Computer Security 2021 PP 1
NIE-DBE.2023 Digital Business Engineering PP 1


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška