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Module 3. Modern problems of discrete optimization

Вибіркова дисципліна для ОП

First

2023/2024

8 Semester

2

Know modern approaches, optimization methods, computer technologies and tools for solving current scientific problems of discrete optimization. Know the theoretical methods of studying the complexity and speed of computational algorithms. Be able to develop and apply methods of discrete optimization for mathematical modeling and optimization of scientific and technical, economic, environmental and social processes and systems. Be able to analyze and solve practical problems of discrete optimization, choose the most effective methods for their research and solution. Substantiate their own view of the problem, communicate with colleagues on the development of mathematical models, methods, algorithms and programs, compile written reports. Demonstration of authority, innovation, high degree of independence, academic and professional integrity, consistent commitment to the development of new ideas or processes in the advanced contexts of professional and scientific activities.

Full-time form

1. Know: the material of standard university courses in mathematical analysis, linear algebra, operations research, decision theory, probability theory, graph theory, discrete optimization using modern computing resources; program in one of the current programming languages. 2. Be able to: creatively use in the educational process, research material of standard university courses in mathematical analysis, linear algebra, research of operations, probability theory, graph theory, discrete and vector optimization with the use of modern computing resources; solve typical tasks from these courses, program in one of the current programming languages.

Discipline "Problems of systems modeling and discrete optimization" belongs to the list of disciplines of the student's choice. The subject of study of module 2 "Modern problems of discrete optimization" of the discipline are current problems of discrete optimization, relating to the basic principles of development mathematical methods for studying the correctness and solving complex problems of discrete optimization, including vector. It provides acquaintance, deepening and improvement of knowledge, which is an element of fundamental mathematical training of students, and which can be used in the practical application of models and methods of discrete optimization in solving complex problems of optimal design, management of economic and technical facilities and systems. as well as in the implementation of research projects. Taught in the 8th semester, 50 hours. (2 ECTS credits), of which seminars - 20 hours, independent work - 30 hours. An exam is provided.

1. Sergienko IV Methods of optimization and system analysis for problems of transcomputational complexity. Kyiv: Akademperiodika, 2010. 296 p. 2. Corte B., Figen J. Combinatorial optimization. Theory and algorithms. M .: Izd-vo MCNMO, 2015. 720 s. 3. Sergienko IV, Shilo VP Problems of discrete optimization: problems, methods of solution, research. Kyiv: Nauk. opinion, 2003. 264 p. 4. Sergienko IV, Shilo VP, Roshchin VO Discrete optimization. Algorithms and their efficient use. Kyiv: Nauk. opinion, 2020. p. 5. Sergienko IV Mathematical models and methods for solving discrete optimization problems (2nd ed., Supplemented and revised). Kyiv: Nauk. opinion, 1988. 472 p. 6. Semenova NV, Kolechkina LM Vector problems of discrete optimization on combinatorial sets: research methods and solutions. Kyiv: Nauk. opinion, 2009. 266 p.

Seminar, independent work

Current evaluation

Ukrainian