Course detail
Optimization Methods
FSI-VO1 Acad. year: 2021/2022 Winter semester
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.
Language of instruction
Czech
Number of ECTS credits
7
Supervisor
Department
Learning outcomes of the course unit
<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.
Planned learning activities and teaching methods
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.
Aims
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.
Specification of controlled education, way of implementation and compensation for absences
Attendance at seminars is required. An absence can be compensated for via solving additional problems.
The study programmes with the given course
Programme B3S-P: Engineering, Bachelor's
branch B-AIŘ: Applied Computer Science and Control, compulsory
Type of course unit
Lecture
39 hours, optionally
Teacher / Lecturer
Syllabus
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
14 hours, compulsory
Teacher / Lecturer
Syllabus
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
12 hours, compulsory
Teacher / Lecturer
Syllabus
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.