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Modern methods of computer modeling

Вибіркова дисципліна для ОП

First

2023/2024

6 Semester

2

PLO 9 Combine methods of mathematical computer modeling with informal expert analysis procedures to find optimal solutions. Modern methods of computer modeling. PLO 10. Build algorithms that are efficient in terms of calculation accuracy, stability, speed and cost of system resources for numerical study of mathematical models and solving practical problems. PLO 14. Use specialized software products and software systems of computer mathematics in practical work.

Distance form

Know: basic concepts and concepts of programming, algebra, mathematical analysis, discrete mathematics, theory of algorithms at the basic level (the volume of the second year of university), the essence of the concept of algorithm. Be able to: create programs in any language, read and analyze mathematical texts, implement simple algorithms. Have basic skills: working with a computer, searching for information on the Internet, using translation systems.it.

Module 1. Problems of cluster analysis, study of basic approaches to building cluster analysis algorithms. Lec. -12 g. Ind.work -14 g. General characteristics of clustering methods Basic approaches to algorithm development. K-means method, its field of application. Software implementation of the K-means method and its test. Fuzzy K-means method, its advantages over the K-means method. Software implementation. Other clustering methods such as Db Scan and grid type methods. Module 2 Natural algorithms of evolutionary type of search of extremum of functions. Lectures -16 g. Independent work -20. General characteristics of nature-like algorithms of evolutionary type. Study of the particle swarm method for finding the extremum of a function. Testing algorithms on functions of several variables. Study of the evolutionary algorithm of the genetic type. Software implementation of genetic algorithm. Testing of genetic algorithm on Rosenbock, Rastrigin, Eckley functions.

1. Panteleev, D.V. Metlitskaya, E.A. Aleshina Metodyi globalnoy optimizatsii. Metaevristicheskie strategii i algoritmyi A. V. 2013,. M. Vuzovskaya nauka. 244 s 2. Algoritmyi klasterizatsii v zadachah segmentatsii sputnikovyih izobrazheniy I. A. Pestunov, Yu. N. Sinyavskiy Vesnik KemGU 2012 # 4 (52) t. 2 s. 110-125 3. E .S. Semenkin, M.N. Zhukova, V.G. Zhukov, I.A. Panfilov, V.V. Tyinchenko Evolyutsionnyie metodyi modelirovaniya i optimizatsii slozhnyih sistem. Konspekt lektsiy. Krasnoyarsk 2007 515 s. 4. B.G. Mirkin Metodyi klaster-analiza dlya podderzhki prinyatiya resheniy: obzor Preprint WP7/2011/03 Seriya WP7 M. 2011 88 s.

Lectures, independent work, elaboration of recommended literature, implementation of projects.

Intermediate assessment: The maximal number of available points is 60. 1. Individual project 1 РН1.1, РН1.2, РН1.3, РН 2.1, РН2.2, РН2.3 - 20 points / 12 points 2. Individual project 2 РН1.1, РН1.2, РН1.3, РН 2.1, РН2.2, РН2.3 - 20 points / 12 points 3. Individual project 3 РН1.1, РН1.2, РН1.3, РН 2.1, РН2.2, РН2.3 - 20 points / 12 points Final assessment (in the form of exam): The maximal number of available points is 40. The results of study to be assessed are RN 1.1, RN 1.2, RN 1.3, RN 2.1, RN 2.2 and RN 2.3. - form and types of tasks: written with the defense of the answer, two theoretical questions of 10 points and two practical tasks (10 points).

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