Course detail

Optimization II

FSI-VO2Acad. year: 2011/2012

The course deals with the following topics: Optimum decision policy. Dynamic programming as a tool for creation of methods for a solution of the stochastic decision optimization problems in discrete as well as continuous range and its computation aspects. Pontryagin maximum principle. Fuzzy regulation. Applications in practical problems solution in economical decisions and in technological process control. Optimization in project management in the stages of multicriterial projects selection into portfolio in case of a restricted resource, of resource scheduling in deterministic, stochastic and fuzzy case, of cost analysis of projects and monitoring the deviations between real and scheduled projects course.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jindřich Klapka, CSc.

Department

Institute of Automation and Computer Science (ÚAI)

Learning outcomes of the course unit

<B>Knowledge: </B>Students will know basic principles and algorithms of methods applicable to the optimization of the stochastic and fuzzy processes, discrete and continuous, stationary as well as non-stationary. 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 realisation of projects. They will be also made familiar with gradient methods, quadratic programming and modern heuristic methods.
<B>Skills: </B> Students will be able to apply the above methods to the solution of the practical problems from economic decision, problems of increasing of the reliability of technological devices, problems of automation control of technological processes and problems of project management, by using of contemporary tools of the computer science. They will be able to work with modern decision-support systems.

Prerequisites

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

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

<B>Course-unit credit: </B>Active participation in the seminars and elaboration of semester project. <B>Examination: </B>Oral.

Course curriculum

Not applicable.

Work placements

Not applicable.

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.

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

Attendance at seminars is controlled. An absence can be compensated for via solving additional problems.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

SKYTTNER, L.: General Systems Theory. An Introduction. Macmillan Press, London, pp. 290, 1996. ISBN 0-333-61833-5.
BOMZE, L.M.; GROSSMANN, W.: Optimierung Theorie und Algorithmen. BI-Wiss.-Verl., Mannheim, pp. 610, 1993. ISBN 3-411-15091-2.
LITTLECHILD, S.; SHUTLER, M. (eds.): Operations Research in Management. Prentice Hall, New York, pp. 298, 1991. ISBN 0-13638-8183
Demeulemeester E. L., Herroelen W.S.: Project Scheduling. A Research Handbook. Kluwer Academic Publishers, Boston 2002
Hersch M.: Mathematical Modelling for Sustainable Development. 557 pp. Springer 2006

Recommended reading

KLAPKA, J.; DVOŘÁK, J.; POPELA, P.: Metody operačního výzkumu. VUTIUM, Brno, 2001. ISBN 80-214-1839-7

Classification of course in study plans

  • Programme M2I-P Master's

    branch M-AIŘ , 1. year of study, summer semester, elective (voluntary)
    branch M-AIŘ , 2. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Jindřich Klapka, CSc.

Syllabus

1. Direct and indirect gradient methods. Theorem of Kuhn and Tucker.
2. Quadratic Programming. Wolfe method. Branch and Bounds methods.
3. The substance and essence of the optimization methods derived on the basis of the analogy with biological systems (genetic algorithms, neural networks) and with physical processes (simulated annealing) and others.
4. Differential equations for continuous control derivated from Bellman and Pontryagin principle.
5. Solving dynamic programming problems by means of step-by-step approximations in space of functions and in space of policies.
6. Dynamic programming of stochastic processes.
7. Applications of stochastic dynamic programming (e.g. in inventory control, in optimization of reliability of technical devices, in optimization of mining planning).
8. Stochastic project scheduling. PERT method.
9. Cost analysis of projects including fuzzy linear programming application.
10. Heuristic project scheduling in case of constrained resources.
11. Monitoring of deviations between scheduled state and real state of project (Microsoft Project, Primavera, SSD Graph, ...)
12. Balancing of manufacturing production belt and assembly line.
13. Higher forms of multicriterial projects selection (with respect of synergistic effects and hierarchical relationships among the projects.)

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

RNDr. Jiří Dvořák, CSc.

Syllabus

1. Numerical application of quadratic optimization.
2. Examples applications of genetic algorithms and simulated annealing.
3. Examples of optimizing discrete deterministic processes.
4. Examples of continuous processes optimizing from the area of regulation and control.
5. Examples of process optimization by means of step-by-step approximations methods.
6. Dynamic programming of stochastic processes. Example of warehouse optimization.
7. Example of optimal mining planning. Example of optimizing reliability of series-connected system.
8. Practical examples of graphs and networks. Applications of the CPM method.
9. Numerical applications of the PERT method.
10. Example of the project scheduling by fuzzy linear programming. Examples of heuristic scheduling in case of constrained resources.
11. Application of the system for projects selection into the portfolio.
12. Exercises with service of system SSD graph and of MS Project.
13. Numerical examples of the balancing of manufacture production belt and assembly line.