Course detail

Optimization Methods II

FSI-VPP-KAcad. year: 2024/2025

The course deals with the following topics: Dynamic programming and optimal control of stochastic processes. Bellman optimality principle as a tool for optimization of multistage processes with a general nonlinear criterion function. Optimum decision policy. Computational aspects of dynamic programming in discrete time. Hidden Markov models and the Viterbi algorithm. Project management, CMP and PERT methods. Algorithms for shortest paths in graphs and the branch and bound method. Multicriteria control problems. Deterministic optimal control in continuous time, Hamilton-Jacobi-Bellman equation, Pontryagin maximum principle. LQR and Kalman filter. Process scheduling and planning. Problems with infinitely many stages. Applications of the methods in solving practical problems.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Jakub Kůdela, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Entry knowledge

Knowledge of the basics of programming, mathematical analysis, algebra, theory of sets, statistics and probability.

Rules for evaluation and completion of the course

Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written and oral.
Attendance at seminars is required. An absence can be compensated for via solving additional problems.

Aims

The aim of the course is to inform the students about creations and applications of mathematical methods for optimal control of technological and economic processes e.g. in the automation of mechanical systems, in the management of production in mechanical engineering, in project management and in optimization of information systems, using contemporary tools of computer science.

Knowledge: Students will know basic principles and algorithms of methods applicable to the optimization of the deterministic and stochastic, discrete and continuous. They will be made familiar with basic principles and algorithms of methods that are appropriate to creation of decision-support systems for project management, as the tool for the identification, selection and realization of projects. Skills: Students will be able to apply the above methods to the solution of the practical problems from economic decision, problems of increasing the reliability of technological devices, problems of automation control of technological processes and problems of project management, by using contemporary tools of computer science.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

LEE, P.; NEWELL, R.B.; CAMERON, I.T. (Eds.): Process Control and Management. Springer, Berlin, pp. 528, 1998. ISBN 0-7514-0457-8.
LOOTSMA, F. A.: Fuzzy Logic for Planning and Decision Making. Kluwer Academic Publishers, Dordrecht, pp. 195, 1997. ISBN 0-7923-4681-5
WILLIAMS, T. M. (Ed.): Managing and Modelling Complex Projects. Kluwer Academic Publishers, London, pp. 257, 1997. ISBN 0-7923-4844-3.

Recommended reading

KLAPKA, J.; DVOŘÁK, J.; POPELA, P.: Metody operačního výzkumu. VUTIUM, Brno, 2001. ISBN 80-214-1839-7.
Klapka J., Piňos P.: Decision Support System for Multicriterial R and D and Information Systems Projects Selection. European Journal of Operational Research 2002, Vol. 140, is. 2, pp. 434 - 446. (EN)
Klapka J., Piňos P., Ševčík V.: Multicriterial Projects Selection (Article). Intelligent Systems Reference Library, Vol. 38 (2013), pp. 245 - 261, ISSN 1868-4394. (EN)
Navrátil P., Pekař L., Klapka J.: Possible way of control of heat output in hotwater piping system of district heating (Article). International Journal of Circuits, Systems and Signal Processing, Vol. 9 (2015), pp. 353 - 361. C. North Atlantic University Union. (EN)
Ševčík V., Klapka J.: Mathematical Method for Multicriterial Project Selection. In: Proceedings of the International Scientific Conference Quantitative Methods in Economics (Multiple Criteria Decision Making XVII). Bratislava: EKONOM, 2014, s. 269 - 275. ISBN 978-80-225-3868-8. (EN)
WALTER, J.; VEJMOLA, S.; FIALA, P.: Aplikace metod síťové analýzy v řízení a plánování. SNTL, Praha, 1989. ISBN 80-03-00101-3
Winston W.L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont 2004. (EN)

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme N-AIŘ-K Master's 2 year of study, winter semester, compulsory

Type of course unit

 

Guided consultation in combined form of studies

22 hod., compulsory

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

1. Basics of mathematical processes theory. Bellman optimality principle and dynamic programming.
2. Minimax (robust) formulation. Reformulations and state augmentation.
3. Deterministic finite-state problems. Forward DP algorithm.
4. Hidden Markov models and the Viterbi algorithm.
5. Basics of network analysis, topological ordering, CPM.
6. Calculation by stochastic evaluation of activities (PERT method).
7. Algorithms for shortest paths in a graph, the branch and bound method.
8. Multicriteria and constrained optimal control problems.
9. Deterministic continuous time optimal control, Hamilton-Jacobi-Bellman equation, Pontryagin maximum principle.
10. LQR a Kalman filter.
11. Problems with an infinite number of stages.
12. Process scheduling.
13. Approximate dynamic programming and Model predictive control.

Guided consultation

43 hod., optionally

Teacher / Lecturer

doc. Ing. Jakub Kůdela, Ph.D.

Syllabus

1. Solving dynamic programming problems in Matlab.
2. Resource allocation problems.
3. Dynamic programming in stochastic processes, optimizing a repair schedule.
4. State augmentation, optimal inventory control.
5. Viterbi algorithm, decoding of convolutional codes.
6. Examples of project graphs and networks. Implementation of CPM.
7. Numerical applications of the PERT method.
8. Algorithms for shortest paths in a graph, implementation of the A* algorithm.
9. Implementation of the branch and bound method.
10. Multicriteria knapsack problem.
11. LQR, drone control.
12. Job scheduling.
13. Semestral projects.

Elearning

eLearning: currently opened course