Subject description
Algorithm and numerical analysis (algorithm, time and space complexity).
Graph theory (description, operations on graphs, basic graph algorithms, the properties of graphs).
Introduction to operational research and optimization. Optimization task (formulation of solutions, cost function). Linear programming and integer programming (simplex method, examples from TC). Network analysis (maximum flow, minimum price, shortest path). Nonlinear optimization (gradient and Newton methods, optimization). Markov chains (classification of states, ergodicity). Time series and traffic models, queuing theory (primary analysis). Important applications in telecommunications. Optimal user interaction and the user-centric optimization. Measuring and modelling users, situation awarenes.
The subject is taught in programs
Objectives and competences
Basics optimization methods and algorithms. Understanding the basic principles of optimization and its procedures with application in telecommunications. Getting to know the various options to optimize and streamline processes and procedures in telecommunications. Getting to know selected classes of optimization problems and their basic solutions.
Getting to know measuring and modeling users. Getting to know user experiments.
Teaching and learning methods
Lectures provide theoretical backgrounds and basic reasoning supported by illustrative examples. Tutorials adds more examples and focus on improvement of analytical skills of students. Both methods are supported by the
Jupyter Python system and selected software optimization tools allowing hands-on learning and voluntary student’s work at home. It covers analyzable examples of optimization problems.
Expected study results
After successful completion of the course, students should be able to:
- To classify the type of the optimization problem such as linear program, nonlinear optimization etc;
- To development and design an optimization problem and its objective function based on a description of a real situation.
- To perform time and space complexity of an optimization algorithm
- To select the most appropriate method and tool based on the problem description.
- Know the role of operational research in the field of telecommunications
- Using the software and mathematical tools to solve the selected optimization task
- Design and implementation of user measurement and modeling
- Design and implementation of user experiments
Basic sources and literature
- W. L. Winston: Operations research Applications and Algorithms, Brooks/Cole, 2004.
- Mauricio G.C. Resende, Panos Pardalos: Handbook of Optimization in Telecommunications, Springer, 2006.
- M. W. Carter, C. C. Price: Operations Research, A Practical Introduction, CRC Press, 2000.
- D. C. Montgomery. Design and Analysis of Experiments. John Wiley & Sons, 2008.
- A. Košir: Operacijske raziskave v telekomunikacijah, Založbe FE in FRI, 2013.
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University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana