Optimization Methods (FSI-VO1)

Academic year 2021/2022
Supervisor: prof. RNDr. Ing. Miloš Šeda, Ph.D.  
Supervising institute: ÚAI all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The aim of the course is to extend students' basic knowledge of the applied mathematics towards interdisciplinary and system direction, and make students familiar with basic approaches and methods for the solution of mathematized problems of economics in mechanical engineering and technology with aids of computer science.
Learning outcomes and competences:
<b>Knowledge: </b>Students will know basic approaches to operational research and systems analysis as a tool for creation of methods for the solution of problems of automation and computer science, and technological and economical problems in mechanical engineering.
<b>Skills: </b>Students will be able to formulate simple problems of operational research from the practice of mechanical engineering and economics. They will be able to create mathematical models for the above problems, select methods of their solution and implement them using computer technology.
Prerequisites:
Knowledge of the basics of mathematical analysis, algebra, theory of sets, statistics and probability.
Course contents:
The course deals with the following topics: The role of optimization methods in operations research, cybernetics and systems sciences. Systems modelling. Systems analysis tasks. Optimization problems. Formulation and properties of optimization problems. Simplex method. Artificial basis applications. Non-linear and convex problems. Quasi-convex programming. Dynamic programming of discrete deterministic processes. Critical Path Method. Examples of applications of operations research methods in technical and economic practice.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
Course-unit credit: Active participation in the seminars, elaboration of a given project. Examination: Written and oral.
Controlled participation in lessons:
Attendance at seminars is required. An absence can be compensated for via solving additional problems.
Type of course unit:
    Lecture  13 × 3 hrs. optionally                  
    Exercise  7 × 2 hrs. compulsory                  
    Computer-assisted exercise  6 × 2 hrs. compulsory                  
Course curriculum:
    Lecture 1. Operations research, its methodology and relations to systems theory and cybernetics. Modelling of the system.
2. Problems of the systems analysis. Optimization problems.
3. Formulations and properties of the linear programming problems.
4. Basic theorem of linear programming.
5. Simplex method and its deduction and derivation.
6. Artificial basis method (two-phase simplex method).
7. Dual problem and sensitivity analysis.
8. Convex non-linear problems. Kuhn-Tucker theorem. Wolfe's method for quadratic programming.
9. Quasi-convex nonlinear problems. Linear fractional programming.
10. Bellman Optimality Principle.
11. Dynamic programming of discrete deterministic processes and its applications.
12. Basics of network analysis. Critical Path Method.
13. Multi-criterial optimization and multi-criterial selection.
    Exercise 1. Formulation of linear optimization models.
2. Formulation of linear problems, graphical solution.
3. Simplex algorithm.
4. Solution of linear problems applying artificial basis.
5. Solution of simple non-linear problems by means of Kuhn-Tucker conditions.
6. Solution of quadratic and linear fractional problems.
7. Network analysis. CPM method.
    Computer-assisted exercise 1. Solution of linear optimization problems in MS Excel.
2. Solution of linear optimization problems by means of GAMS.
3. Solution of non-linear and integer problems in MS Excel.
4. Solution of non-linear and integer problems by means of GAMS.
5. Solution of dynamic programming problems in MS Excel.
6. Solution of multi-criteria problems in MS Excel.
Literature - fundamental:
1. SKYTTNER, L.: General Systems Theory. An Introduction. Macmillan Press, London, pp. 290, 1996. ISBN 0-333-61833-5.
2. BOMZE, L.M.; GROSSMANN, W.: Optimierung Theorie und Algorithmen. BI-Wiss.-Verl., Mannheim, pp. 610, 1993. ISBN 3-411-15091-2.
3. LITTLECHILD, S.; SHUTLER, M. (eds.): Operations Research in Management. Prentice Hall, New York, pp. 298, 1991. ISBN 0-13638-8183
4. KLAPKA, J., PIŇOS, P.: Decision support system for multicriterial R&D and information systems projects selection. European Journal of Operational Research. 2002, vol. 140, is. 2, s. 434-446. Dostupný z WWW: .
5. WINSTON, W.L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont, 2004.
6. BAZARAA, M, S.; SHERALI, H. D.; SHETTY, C. M.: Nonlinear Programming. Wiley, 2013.
Literature - recommended:
1. WINSTON, W.L.: Operations Research. Applications and Algorithms. Thomson - Brooks/Cole, Belmont, 2004.
2. KLAPKA, J.; DVOŘÁK, J.; POPELA, P.: Metody operačního výzkumu. VUTIUM, Brno, 2001.
3. JABLONSKÝ, J. Operační výzkum: kvantitativní modely pro ekonomické rozhodování. Professional Publishing, 2007.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
B3S-P full-time study B-AIŘ Applied Computer Science and Control -- Cr,Ex 7 Compulsory 1 3 W