Система символьной математики maple® в методе проекций для задач дискретной оптимизации
##plugins.themes.bootstrap3.article.sidebar##
Опубликован:
янв 20, 2020
Ключевые слова:
линейная оптимизация, дискретная оптимиза-ция, система ограничений, комбинаторный метод, метод Жордана-Гаусса, декомпозиция, редукция, графическое решение, Maple®
##plugins.themes.bootstrap3.article.main##
Аннотация
В рамках данного исследования предложен способ упрощения комбинаторного решения задачи дискретной оптимизации. Он основан на том, что выполняется декомпозиция системы, которая отражает систему ограничений многомерной исходной задачи на дву-мерную координатную плоскость. Такой способ позволяет получить простую систему графических решений сложной задачи линейной дис-кретной оптимизации. Автоматизация расчетов в среде Maple® состав-ляет предпосылки для дальнейшего развития и совершенствования подобных алгоритмов и использование в магистерских образовательных программах.
##plugins.themes.bootstrap3.article.details##
Как цитировать
Чернова, Л. (2020). Система символьной математики maple® в методе проекций для задач дискретной оптимизации. Весник Одеского национального морского университета, (59(2), 214-235. https://doi.org/10.33082/2226-1915-2-2019-214-235
Раздел
Управление проектами и программами
Литература
1. Korbut А.А., Finkelstein Y.Y. (1969). Dyskretnoe programmyro-vanye [Discrete programming]. Moscow: Nauka [in Russian]
2. Finkelstein Y.Y. (1976). Priblizhennyie metodyi i prikladnyie zadachi diskretnogo programmirovaniya [Approximate methods and applied problems of discrete programming]. Moscow: Nauka [in Russian]
3. Wagner H. (1973). Osnovyi issledovaniya operatsiy [Principles of Operations Research]. Moscow: Mir, 1973.
4. Burkov V.N., Gorgidze I.А., Lovetskiy S.Е. (1974). Prikladnyie zadachi teorii grafov [Applied problems of the theory of graphs]. Tbilisi: Computation Centre of Republican Adacemy of Science of Georgian SSR.
5. Sigal I.K., Ivanova A.P. (2003). Vvedenie v prikladnoe diskretnoe programmirovanie: modeli i vyichislitelnyie algoritmyi [Intro-duction to applied discrete programming: models and calculation algorithms]. Moscow.
6. F. Nozicka, J. Guddat, H. Hollatz. (1972). The Linear Opti-mization Theory. Berlin.
7. Titov S.D., Chernova L.S. (2017). Vyshcha ta prykladna matematyka [Higher and applied mathematics]. Manual: In 2 parts, Part 1, Kharkiv, Fakt.
8. Lau D. (2007). Algebra and Discrete Mathematics 1. Basic Terms of Mathematics, Algebraic Structures 1,Linear Algebra and Analytic Geometry, Numeric Algebra. Second corrected and supplement ededition. Berlin: Springer.
9. Jean Pierre David (2017). Low latency and division free Gauss-Jordan solver in floating pointarithmetic. Journal of Parallel and Distributed Computing, 106, 185-193.
10. Lax Peter D. (2007). Linear algebra and application. New York, Wiley, 2-nd ed.
11. Yeremin I. I., Astafiev N. N. (1976). Vvedenie v teoriyu lineynogo i vyipuklogo programmirovaniya [Introduction to the theory of linear and convex programming]. Moscow: FIZMATLIT.
12. Tytov S.D., Chernova L.S. (2016). Teoriia vyznachnykiv: Navchalno- metodychnyi posibnyk [Theory of determinants: Trai-ning and methodological manual]. Mykolaiv: Torubara V.V.
13. Teschl Gerald, Teschl Susanne. (2008). Mathematics for Infor-mation Scientists. Volume 1: Discrete Mathematics and Linear Algebra. Berlin, Springer.
14. Buhir M.K. (1998). Matematyka dlia ekonomistiv. Liniina alhebra, liniini modeli [Mathematics for economists. Linear algebra, linear models]. Kyiv.
15. Buhir M.K. (2003). Matematyka dlia ekonomistiv [Mathematics for economists]. Alma-matir Academia, 2003.
16. Titov S.D., Chernov S.K., Chernova L.S. (2018). Reduction in Discrete Optimization Problem, 2018 IEEE 13th International Scientific and Technical Conference on Computer Sciences and Information Technologies, CSIT 2018.
17. Chernov S., Titov S., Chernova L., (...), Chernova L., Kolesni- kova K. Algorithm for the simplification of solution to discrete optimization problems Eastern-European Journal of Enterprise Technologies.
18. Kovalev М.М. (1977). Diskretnaya optimizatsiya [Discrete optimization]. Minsk: Byelorussian State University.
2. Finkelstein Y.Y. (1976). Priblizhennyie metodyi i prikladnyie zadachi diskretnogo programmirovaniya [Approximate methods and applied problems of discrete programming]. Moscow: Nauka [in Russian]
3. Wagner H. (1973). Osnovyi issledovaniya operatsiy [Principles of Operations Research]. Moscow: Mir, 1973.
4. Burkov V.N., Gorgidze I.А., Lovetskiy S.Е. (1974). Prikladnyie zadachi teorii grafov [Applied problems of the theory of graphs]. Tbilisi: Computation Centre of Republican Adacemy of Science of Georgian SSR.
5. Sigal I.K., Ivanova A.P. (2003). Vvedenie v prikladnoe diskretnoe programmirovanie: modeli i vyichislitelnyie algoritmyi [Intro-duction to applied discrete programming: models and calculation algorithms]. Moscow.
6. F. Nozicka, J. Guddat, H. Hollatz. (1972). The Linear Opti-mization Theory. Berlin.
7. Titov S.D., Chernova L.S. (2017). Vyshcha ta prykladna matematyka [Higher and applied mathematics]. Manual: In 2 parts, Part 1, Kharkiv, Fakt.
8. Lau D. (2007). Algebra and Discrete Mathematics 1. Basic Terms of Mathematics, Algebraic Structures 1,Linear Algebra and Analytic Geometry, Numeric Algebra. Second corrected and supplement ededition. Berlin: Springer.
9. Jean Pierre David (2017). Low latency and division free Gauss-Jordan solver in floating pointarithmetic. Journal of Parallel and Distributed Computing, 106, 185-193.
10. Lax Peter D. (2007). Linear algebra and application. New York, Wiley, 2-nd ed.
11. Yeremin I. I., Astafiev N. N. (1976). Vvedenie v teoriyu lineynogo i vyipuklogo programmirovaniya [Introduction to the theory of linear and convex programming]. Moscow: FIZMATLIT.
12. Tytov S.D., Chernova L.S. (2016). Teoriia vyznachnykiv: Navchalno- metodychnyi posibnyk [Theory of determinants: Trai-ning and methodological manual]. Mykolaiv: Torubara V.V.
13. Teschl Gerald, Teschl Susanne. (2008). Mathematics for Infor-mation Scientists. Volume 1: Discrete Mathematics and Linear Algebra. Berlin, Springer.
14. Buhir M.K. (1998). Matematyka dlia ekonomistiv. Liniina alhebra, liniini modeli [Mathematics for economists. Linear algebra, linear models]. Kyiv.
15. Buhir M.K. (2003). Matematyka dlia ekonomistiv [Mathematics for economists]. Alma-matir Academia, 2003.
16. Titov S.D., Chernov S.K., Chernova L.S. (2018). Reduction in Discrete Optimization Problem, 2018 IEEE 13th International Scientific and Technical Conference on Computer Sciences and Information Technologies, CSIT 2018.
17. Chernov S., Titov S., Chernova L., (...), Chernova L., Kolesni- kova K. Algorithm for the simplification of solution to discrete optimization problems Eastern-European Journal of Enterprise Technologies.
18. Kovalev М.М. (1977). Diskretnaya optimizatsiya [Discrete optimization]. Minsk: Byelorussian State University.