Course detail

Optimization and Mathematical Aspects of Process Control

FSI-9OMAAcad. year: 2020/2021

The objective of the course is to make PhD students familiar with basics of mathematical process theory in connection with formalized description and optimisation of processes. They will learn how to analyse and propose of the policy of the optimal decision and optimal control of important controllable processes including the project management processes. Students will be made familiar with methods, approaches and algorithms, based on the Bellman principle of optimality and Pontryagin principle of maximum, they will learn the method of formulation and solution of the optimal control problems. Solution of the problems occurring by the processes discrete as well as continuous, deterministic as well as stochastic, and by the fuzzy processes. Also discussed is an application of higher forms of the optimisation methods (e. g. quasiconvex programming) and the branch and bound method. Sensitivity analysis of the optimisation problems. Students will be made familiar with basics of gradient and heuristic methods including modern heuristics. In the lessons it shall be employed too, the methods and software systems, created in within the framework of grants, presented on the international forum abroad.

Language of instruction

Czech

Guarantor

doc. RNDr. Jindřich Klapka, CSc.

Department

Institute of Automation and Computer Science (ÚAI)

Learning outcomes of the course unit

Znalosti: Znát základní principy a algoritmy metod, použitelných k optimalisaci deterministických a stochastických i fuzzy procesů diskretních i spojitých. Znát základní principy a algoritmy metod, které jsou podstatou systémů na podporu rozhodování o projektech z hlediska jejich identifikace, výběru, průběhu a realisace. Dovednosti: Umět tyto metody používat k řešení praktických problémů z oblasti ekonomického rozhodování, ve zvyšování spolehlivosti technických zařízení, v automatisovaném řízení technologických procesů a v projektovém řízení s využitím soudobých prostředků informatiky. Získat znalosti, které doktorandovi umožní naučit se pracovat s moderními systémy na podporu rozhodování.

Prerequisites

The knowledge of the bases of Mathematical Analysis, Algebra, Set Theory, Statistics and Probability.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

Assesment methods and criteria linked to learning outcomes

Examination: Oral

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Rozvinout znalosti doktorandů v oblasti tvorby a aplikací matematických metod a přístupů k optimálnímu řízení procesů technologických a ekonomických, uplatnitelných v automatisaci strojírenství, v ekonomickém řízení strojírenské výroby, v projektovém řízení a v optimalisaci informačních systémů při využívání soudobých prostředků informatiky, s přihlédnutím k potřebám, plynoucím ze zaměření disertační práce doktoranda.

Specification of controlled education, way of implementation and compensation for absences

Kontrolu průběhu výuky a jejich výsledků provádí vyučující formou zkoušky. Dle potřeby budou kromě plánovaných přednášek poskytovány i individuální konsultace.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

RARDIN, R .L. Optimization in Operations Research. Prentice Hall, 1997. 919 p. ISBN 0-13-281925-2.
DANTZIG, G. B. Linear Programming and Extensions. New Jersey: Princeton, 1998. 648 p. ISBN: 0-691-05913-6.
GRITZMANN, P., HORST, R., SACHS, E., TICHATSCHKE, R. (eds) Recent Advances in Optimization. Berlin: Springer, 1997. 379 p. ISBN 3-540-63022-8.
LEE, P., NEWELL, R. B., CAMERON, I. T. (eds.) Process Control and Management. London: Blackie, 1998. xvii, 509 p. ISBN 0-7514-0457-8.
WILLIAMS, T. M. (ed.) Managing and Modelling Complex Projects. London: Kluwer, 1997. 257 p. ISBN 0-7923-4844-3.
LOOTSMA, F. A. Fuzzy Logic for Planning and Decision Making. Dordrecht: Kluwer, 1997. x, 199 p. ISBN 0-7923-4681-5.
VINCKE, P. Multicriteria Decision-Aid. Chichester: Wiley, 1992. xx, 153 p. ISBN 0-471-93184-5.
DEMEULEMEESTER, E. L., HERROELEN, W. S. Project Scheduling: A Research Handbook. Boston: Kluwer, 2002. xxiii, 685 p. ISBN 1-4020-7051-9.
SMITH, D. K. Dynamic Programming: A Practical Introduction. New York: E. Horwood, 1991. 160 p. ISBN 0-13-221797-X.
Hersh M.: Mathematical Modelling for Sustainable Development. Springer 2006
Klapka J., Matoušek R., Ševčík V.: Improvement of time-periodical Production Schedule of the Group of Products in the Group of Workplaces through the Lot Sizes Alternation. Mendel 2011, Proceedings of the 17th International Conference on soft Computing, Brno University of Technology 2011, pp. 334 - 340. ISSN 1803-3814, ISBN 978-80-214-4302-0
Balkhi Z. T.: On the optimality of multi item integrated production inventory systems. In: Proceedings of the 3rd International Conference on Applied Mathematics, Simulation, Modelling, Circuits, Systems nd Signals. Wisconsin, WSEAS 2009, pp. 143 - 154. ISBN 978-960-474-147-2.
Bazaraa M.S., Sherali H.D., Shetty C.M.: Nonlinear Programming. Wiley 2013. (EN)
Klapka J., Piňos P., Ševčík V.: Multicriterial Projects Selection. In: Handbook of Optimization. Intelligent Systems Reference Library. Berlin - Heidelberg: Springer - Verlag Berlin - Heidelberg 2012, pp. 245 - 261. ISBN: 978-3-642-30503-0. (EN)
Klapka, J., Dvořák, J., Popela, P.: Metody operačního výzkumu. Brno: VUTIUM, 2001. iii, 165 s. ISBN 80-2014-1839-7. (CS)
Walter, J., Vejmola, S., Fiala, P.: Aplikace metod síťové analysy v řízení a plánování. Praha: SNTL, 1989, 282 s., ISBN 80-03-00101-3. (CS)
Klapka, J., Piňos, P.: Decision Support System for Multicriterial R and D and Information Systems Projects Selection. European Journal of Operational Research. July 2002, Vol. 140, No 2, pp. 434 - 446, doi: 10.1016/S 0377-2217(02)00081-4. (EN)
De Porter, E.L., Ellis, K.P.: Optimization of Project Networks with Goal Programming and Fuzzy Linear Programming. Computers And Ind. Engng., 1990, Vol. 19, No. 1 - 4, pp. 500 - 504, doi:10.1016/0360-8352(90)90168-1
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 (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, pp. 269 - 275. ISBN: 978-80-225-3868-8. (EN)
Winston, W.,L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmond 2004. (EN)
Brucker, P.: Scheduling Algorithms. Springer-Verlag, Berlin 2010. (EN)

Recommended reading

KLAPKA, J., DVOŘÁK, J., POPELA, P. Metody operačního výzkumu. Brno: VUTIUM, 2001. iii, 165 s. ISBN 80-214-1839-7.
WALTER, J., VEJMOLA, S., FIALA, P. Aplikace metod síťové analýzy v řízení a plánování. Praha: SNTL, 1989. 282 s. ISBN 80-03-00101-3.
KLAPKA, J., PIŇOS, P. Decision Support System for Multicriterial R&D and Information Systems Projects Selection. European Journal of Operational Research, July 2002, Vol 140, No 2, p. 434--446. doi:10.1016/S0377-2217(02)00081-4
DePORTER, E. L., ELLIS, K P. Optimization of Project Networks with Goal Programming and Fuzzy Linear Programming. Computer & Ind. Engng., 1990, Vol. 19, No. 1--4, p. 500--504. doi:10.1016/0360-8352(90)90168-L

Type of course unit

 

Lecture

20 hours, optionally

Teacher / Lecturer

doc. RNDr. Jindřich Klapka, CSc.

Syllabus

1. Mission of the optimisation methods in operations research, systems sciences and process engineering. Formulation of optimisation problems.
2. Linear programming, The Simplex method. Dual problems, sensitivity analysis of the optimisation problems solution
3. Kuhn-Tucker conditions. Convex and quasi-convex programming. Quadratic programming. Gradient methods.
4. Branch and Bound methods. Methods of step-by-step approximations.
5. Heuristic methods. Essence of modern heuristic methods, derived on the basis of the analogy with the functioning of the biologic systems and of the analogy with the physical processes.
6. Application of the optimisation methods to the solution of problems from the Process an Construction Engineering, Technical Cybernetics, Computer Science, Automation and Mechanical Engineering.
7. Basics of mathematical theory of processes. Optimal regulation. Bellman principle of optimality.
8. Optimal decision policy. Dynamic programming as a tool for a creation of methods for the solution of deterministic and stochastic decision optimisation problems in the discrete as well as continuous range and its numerical aspects.
9. Pontryagin principle of maximum
10. Fuzzy regulation
11. Optimisation of processes of Project Management in the creation of the portfolio of projects, in the time scheduling for deterministic, stochastic and fuzzy case, in the cost analysis of the projects, and in monitoring of the deviation between real and scheduled course of projects.