Course detail

Computing Methods in Optimization Problems

FSI-VOUAcad. year: 2024/2025

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.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Guarantor

doc. Ing. Jakub Kůdela, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Entry knowledge

Basic of differential and integral calculus, linear algebra, probability and statistics, and programming.

Rules for evaluation and completion of the course

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 computer lessons.

Aims

The emphasis is on the aquisition of application-oriented of optimization models and methods, and on the use of computers and available software.
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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Boyd, S.P. a Vandenberghe, L. Convex Optimization, Cambridge University Press, 2004. (EN)
Williams, H.P. Model Building in Mathematical Programming, 4th edition. J.Wiley and Sons, 2012. (EN)

Recommended reading

Boyd, S.P. a Vandenberghe, L. Convex Optimization, Cambridge University Press, 2004. (EN)
Klapka,J. a kol.: Metody operačního výzkumu. FSI, 2001. (CS)
Williams, H.P. Model Building in Mathematical Programming, 4th edition. J.Wiley and Sons, 2012. (EN)

Classification of course in study plans

  • Programme B-STR-P Bachelor's

    specialization AIŘ , 3 year of study, summer semester, compulsory

  • Programme C-AKR-P Lifelong learning

    specialization CLS , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

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.

Computer-assisted exercise

39 hod., compulsory

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

The exercise follows the topics discussed in the lecture. The main focus is on software implementation.