Computing Methods in Optimization Problems (FSI-VOU-K)

Academic year 2023/2024
Supervisor: Ing. Jakub Kůdela, Ph.D.  
Supervising institute: ÚAI all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The emphasis is on the aquisition of application-oriented of optimization models and methods, and on the use of computers and available software.
Learning outcomes and competences:
The student will aquire the ability to recognize a suitable optimization model for a given engineering problem. The student will be able to implement said model in an adequately chosen software and analyze the results.
Prerequisites:
Basic of differential and integral calculus, linear algebra, probability and statistics, and programming.
Course contents:
The course introduces to the basic concepts of optimization and the use of appropriate software. Subsequently, optimization problems in engineering are solved. The main content of the course is to recognize and use a suitable model and methods for specific engineering tasks.
Teaching methods and criteria:
The explanation of theory, basic principles and illustrative demonstrations on concrete examples will be given in lectures. Exercises will follow the lectures and will be of a computer character.
Assesment methods and criteria linked to learning outcomes:
The course will be completed by graded course-unit credit. Students develop a project on a specific topic. Final classification of the course is according to ECTS scale.
Controlled participation in lessons:
Controlled participation in computer lessons.
Type of course unit:
    Guided consultation in combined form of studies  1 × 22 hrs. compulsory                  
    Guided consultation  1 × 43 hrs. optionally                  
Course curriculum:
    Guided consultation in combined form of studies 1. Introduction to optimization (basic concepts).
2. Software tools for optimization: languages/enviroments: EXCEL, MATLAB, Julia. The use of solvers.
3. - 5. Optimization problems in engineering, types of optimization models (linear, quadratic, convex, etc.)
6. - 7. Integer programming problems – applications in logistics, scheduling, etc.
8. Linearization, modelling with SOS1 and SOS2 variables.
9. Black-box optimization and optimization within a simulation environment.
10. Dynamic optimization models.
11. - 13. Models with uncertain data – stochastic and robust formulations.
    Guided consultation The exercise follows the topics discussed in the lecture. The main focus is on software implementation.
Literature - fundamental:
1. Williams, H.P. Model Building in Mathematical Programming, 4th edition. J.Wiley and Sons, 2012.
2. Boyd, S.P. a Vandenberghe, L. Convex Optimization, Cambridge University Press, 2004.
Literature - recommended:
1. Klapka,J. a kol.: Metody operačního výzkumu. FSI, 2001.
2. Williams, H.P. Model Building in Mathematical Programming, 4th edition. J.Wiley and Sons, 2012.
3. Boyd, S.P. a Vandenberghe, L. Convex Optimization, Cambridge University Press, 2004.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B-STR-K combined study AIŘ Applied Computer Science and Control -- GCr 7 Compulsory 1 3 W