<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">ntv</journal-id><journal-title-group><journal-title xml:lang="ru">Научно-технический вестник информационных технологий, механики и оптики</journal-title><trans-title-group xml:lang="en"><trans-title>Scientific and Technical Journal of Information Technologies, Mechanics and Optics</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2226-1494</issn><issn pub-type="epub">2500-0373</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2226-1494-2022-22-6-1187-1196</article-id><article-id custom-type="elpub" pub-id-type="custom">ntv-353</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>КОМПЬЮТЕРНЫЕ СИСТЕМЫ И ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>COMPUTER SCIENCE</subject></subj-group></article-categories><title-group><article-title>Совместное обучение агентов и векторных представлений графов в задаче управления конвейерными лентами</article-title><trans-title-group xml:lang="en"><trans-title>Joint learning of agents and graph embeddings in a conveyor belt control problem</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0856-4276</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Рыбкин</surname><given-names>К. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Rybkin</surname><given-names>K. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Рыбкин Константин Евгеньевич – инженер</p><p>Санкт-Петербург, 197101</p></bio><bio xml:lang="en"><p>Konstantin E. Rybkin – Engineer</p><p>Saint Petersburg, 197101</p></bio><email xlink:type="simple">matveich1903@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1133-8432</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фильченков</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Filchenkov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Фильченков Андрей Александрович – кандидат физико-математических наук, инженер</p><p>Санкт-Петербург, 197101</p><p>sc 55507568200</p></bio><bio xml:lang="en"><p>Andrey A. Filchenkov – PhD (Physics &amp; Mathematics), Engineer</p><p>Saint Petersburg, 197101</p><p>sc 55507568200</p></bio><email xlink:type="simple">afilchenkov@itmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3240-597X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Азаров</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Azarov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Азаров Артур Александрович – кандидат технических наук, научный сотрудник; заместитель директора</p><p>Санкт-Петербург, 197101;</p><p>Санкт-Петербург, 199178</p><p>sc 56938354700</p></bio><bio xml:lang="en"><p>Artur A. Azarov – PhD, Scientific Researcher; Deputy Director</p><p>Saint Petersburg, 197101;</p><p>Saint Petersburg, 199178</p><p>sc 56938354700</p></bio><email xlink:type="simple">artur-azarov@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7494-4309</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Забашта</surname><given-names>А. С.</given-names></name><name name-style="western" xml:lang="en"><surname>Zabashta</surname><given-names>A. S.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Забашта Алексей Сергеевич – кандидат технических наук, доцент</p><p>Санкт-Петербург, 197101</p><p>sc 56902663900</p></bio><bio xml:lang="en"><p>Alexey S. Zabashta – PhD, Associate Professor</p><p>Saint Petersburg, 197101</p><p>sc 56902663900</p></bio><email xlink:type="simple">azabashta@itmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2723-2077</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шалыто</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Shalyto</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Шалыто Анатолий Абрамович – доктор технических наук, профессор, главный научный сотрудник</p><p>Санкт-Петербург, 197101</p><p>sc 56131789500</p></bio><bio xml:lang="en"><p>Anatoly A. Shalyto – D. Sc., Professor, Chief Reseacher</p><p>Saint Petersburg, 197101</p><p>sc 56131789500</p></bio><email xlink:type="simple">shalyto@mail.ifmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Университет ИТМО</institution><country>Россия</country></aff><aff xml:lang="en"><institution>ITMO University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Университет ИТМО; Северо-Западный институт управления – филиал РАНХиГС</institution><country>Россия</country></aff><aff xml:lang="en"><institution>ITMO University; North-West Institute of Management – branch of the Russian Presidential Academy of National Economy and Public Administration</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>19</day><month>12</month><year>2024</year></pub-date><volume>22</volume><issue>6</issue><fpage>1187</fpage><lpage>1196</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Рыбкин К.Е., Фильченков А.А., Азаров А.А., Забашта А.С., Шалыто А.А., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Рыбкин К.Е., Фильченков А.А., Азаров А.А., Забашта А.С., Шалыто А.А.</copyright-holder><copyright-holder xml:lang="en">Rybkin K.E., Filchenkov A.A., Azarov A.A., Zabashta A.S., Shalyto A.A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ntv.elpub.ru/jour/article/view/353">https://ntv.elpub.ru/jour/article/view/353</self-uri><abstract><sec><title>Предмет исследования</title><p>Предмет исследования. Рассмотрена задача маршрутизации системы конвейерных лент на основе мультиагентного подхода. В большинстве данных конвейерных систем багажных лент в аэропортах используются алгоритмы маршрутизации, основанные на ручном моделировании поведения конвейеров. Такой подход плохо масштабируем. Новые исследования в области машинного обучения предлагают решать задачу маршрутизации с помощью обучения с подкреплением.</p></sec><sec><title>Метод</title><p>Метод. Сформулирован подход к совместному обучению агентов и векторных представлений графа. В рамках подхода предложен алгоритм QSDNE, использующий агентов DQN и векторные представления SDNE. Основные результаты. Выполнен сравнительный анализ разработанного алгоритма c алгоритмами мультиагентной маршрутизации без совместного обучения. На основании результатов работы алгоритма QSDNE сделан вывод о его эффективности для оптимизации времени доставки и энергопотребления в конвейерных системах. Алгоритм позволил сократить среднее время доставки на 6 % по сравнению с лучшим аналогом.</p></sec><sec><title>Практическая значимость</title><p>Практическая значимость. Разработанный подход может быть использован для решения задач маршрутизации со сложными функциями оценки пути и динамически меняющимися топологиями графов, а предложенный алгоритм – для управления конвейерными лентами в аэропортах и в цеховых производствах.</p></sec></abstract><trans-abstract xml:lang="en"><p>We focus on the problem of routing a conveyor belts system based on a multi-agent approach. Most of these airport baggage belt conveyor systems use routing algorithms based on manual simulation of conveyor behavior. This approach does not scale well, and new research in machine learning proposes to solve the routing problem using reinforcement learning. To solve this problem, we propose an approach to joint learning of agents and vector representations of a graph. Within this approach, we develop a QSDNE algorithm, which uses DQN agents and SDNE embeddings. A comparative analysis was carried out with multi-agent routing algorithms without joint learning. The results of the QSDNE algorithm showed its effectiveness in optimizing the delivery time and energy consumption in conveyor systems as it helped to reduce mean delivery time by 6 %. The proposed approach can be used to solve routing problems with complex path estimation functions and dynamically changing graph topologies, and the proposed algorithm can be used to control conveyor belts at airports and in manufacturing workshops.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>мультиагентное обучение</kwd><kwd>обучение с подкреплением</kwd><kwd>адаптивная маршрутизация</kwd><kwd>конвейерные ленты</kwd><kwd>графовое представление</kwd></kwd-group><kwd-group xml:lang="en"><kwd>multi-agent learning</kwd><kwd>reinforcement learning</kwd><kwd>adaptive routing</kwd><kwd>conveyor belt</kwd><kwd>graph representation</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено за счет гранта Российского научного фонда (проект № 20-19-00700).</funding-statement><funding-statement xml:lang="en">The study was supported by a grant from the Russian Science Foundation (project № 20-19-00700).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">The World of Air Transport in 2019. ICAO Annual Report, 2019 [Электронный ресурс]. URL: https://www.icao.int/annualreport-2019/Pages/the-world-of-air-transport-in-2019.aspx (дата обращения: 01.10.2022).</mixed-citation><mixed-citation xml:lang="en">The World of Air Transport in 2019. ICAO Annual Report, 2019. Available at: https://www.icao.int/annual-report-2019/Pages/theworld-of-air-transport-in-2019.aspx (accessed: 01.10.2022).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">COVID-19 Air Travel Recovery, OAG, 2022 [Электронный ресурс]. URL: https://www.oag.com/coronavirus-airline-schedules-data. (дата обращения: 01.10.2022).</mixed-citation><mixed-citation xml:lang="en">COVID-19 Air Travel Recovery, OAG, 2022. Available at: https://www.oag.com/coronavirus-airline-schedules-data. (sccessed: 01.10.2022).</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">2019 SITA Baggage IT Insights report, SITA, 2019 [Электронный ресурс]. URL: https://www.sita.aero/resources/surveys-reports/baggage-it-insights-2019. (дата обращения: 06.09.2022)</mixed-citation><mixed-citation xml:lang="en">2019 SITA Baggage IT Insights report, SITA, 2019. Available at: https://www.sita.aero/resources/surveys-reports/baggage-itinsights- 2019. (accessed: 06.09.2022).</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Sørensen R.A., Nielsen M., Karstoft H. Routing in congested baggage handling systems using deep reinforcement learning // Integrated Computer-Aided Engineering. 2020. V. 27. N 2. P. 139–152. https://doi.org/10.3233/ICA-190613</mixed-citation><mixed-citation xml:lang="en">Sørensen R.A., Nielsen M., Karstoft H. Routing in congested baggage handling systems using deep reinforcement learning. Integrated Computer-Aided Engineering, 2020, vol. 27, no. 2, pp. 139–152. https://doi.org/10.3233/ICA-190613</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Kang Y., Wang X., Lan Z. Q-adaptive: A multi-agent reinforcement learning based routing on dragonfly network // Proc. of the 30th International Symposium on High-Performance Parallel and Distributed Computing (HPDC). 2021. P. 189–200. https://doi.org/10.1145/3431379.3460650</mixed-citation><mixed-citation xml:lang="en">Kang Y., Wang X., Lan Z. Q-adaptive: A multi-agent reinforcement learning based routing on dragonfly network. Proc. of the 30th International Symposium on High-Performance Parallel and Distributed Computing (HPDC), 2021, pp. 189–200. https://doi.org/10.1145/3431379.3460650</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Choi S., Yeung D.Y. Predictive Q-routing: A memory-based reinforcement learning approach to adaptive traffic control // Advances in Neural Information Processing Systems. 1995. V. 8. P. 945–951.</mixed-citation><mixed-citation xml:lang="en">Choi S., Yeung D.Y. Predictive Q-routing: A memory-based reinforcement learning approach to adaptive traffic control. Advances in Neural Information Processing Systems, 1995, vol. 8, pp. 945–951.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Mukhutdinov D., Filchenkov A., Shalyto A., Vyatkin V. Multi-agent deep learning for simultaneous optimization for time and energy in distributed routing system // Future Generation Computer Systems. 2019. V. 94. P. 587–600. https://doi.org/10.1016/j.future.2018.12.037</mixed-citation><mixed-citation xml:lang="en">Mukhutdinov D., Filchenkov A., Shalyto A., Vyatkin V. Multi-agent deep learning for simultaneous optimization for time and energy in distributed routing system. Future Generation Computer Systems, 2019, vol. 94, pp. 587–600. https://doi.org/10.1016/j.future.2018.12.037</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Мухудинов Д. Децентрализованный алгоритм управления конвейерной системой с использованием методов мультиагентного обучения с подкреплением: магистерская диссертация. СПб.: Университет ИТМО, 2019, 92 с. [Электронный ресурс]. URL: http://is.ifmo.ru/diploma-theses/2019/2_5458464771026191430.pdf (дата обращения: 01.10.2022).</mixed-citation><mixed-citation xml:lang="en">Mukhudinov D. Decentralized conveyor system control algorithm using multi-agent reinforcement learning methods. MSc Dissertation. St. Petersburg, ITMO University, 2019, 92 p. Available at: http://is.ifmo.ru/diploma-theses/2019/2_5458464771026191430.pdf (accessed: 01.10.2022). (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Dantzig G.B. Origins of the simplex method // A history of scientific computing. 1990. P. 141–151. https://doi.org/10.1145/87252.88081</mixed-citation><mixed-citation xml:lang="en">Dantzig G.B. Origins of the simplex method. A history of scientific computing, 1990, pp. 141–151. https://doi.org/10.1145/87252.88081</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Кузнецов А.В., Холод Н.И., Костевич Л.С. Руководство к решению задач по математическому программированию. Минск: Вышэйшая школа, 1978. 256 с.</mixed-citation><mixed-citation xml:lang="en">Kuznetcov A.V., Kholod N.I., Kostevich L.S. Guide to Solving Mathematical Programming Problems. Minsk, Vyshjejshaja shkola Publ., 1978, 256 p. (in Russian).</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Vutukury S., Garcia-Luna-Aceves J.J. MDVA: A distance-vector multipath routing protocol // Proc. of the 20th Annual Joint Conference on the IEEE Computer and Communications Societies (INFOCOM). 2001. V. 1. P. 557–564. https://doi.org/10.1109/INFCOM.2001.916780</mixed-citation><mixed-citation xml:lang="en">Vutukury S., Garcia-Luna-Aceves J.J. MDVA: A distance-vector multipath routing protocol. Proc. of the 20th Annual Joint Conference on the IEEE Computer and Communications Societies (INFOCOM), 2001, vol. 1, pp. 557–564. https://doi.org/10.1109/INFCOM.2001.916780</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Albrightson R., Garcia-Luna-Aceves J.J., Boyle J. EIGRP — A fast routing protocol based on distance vectors. 1994.</mixed-citation><mixed-citation xml:lang="en">Albrightson R., Garcia-Luna-Aceves J.J., Boyle J. EIGRP — A fast routing protocol based on distance vectors, 1994.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Verma A., Bhardwaj N. A review on routing information protocol (RIP) and open shortest path first (OSPF) routing protocol // International Journal of Future Generation Communication and Networking. 2016. V. 9. N 4. P. 161–170. https://doi.org/10.14257/ijfgcn.2016.9.4.13</mixed-citation><mixed-citation xml:lang="en">Verma A., Bhardwaj N. A review on routing information protocol (RIP) and open shortest path first (OSPF) routing protocol. International Journal of Future Generation Communication and Networking, 2016, vol. 9, no. 4, pp. 161–170. https://doi.org/10.14257/ijfgcn.2016.9.4.13</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Bang-Jensen J., Gutin G.Z. Digraphs: Theory, Algorithms and Applications. Springer Science &amp; Business Media, 2009. 795 p.</mixed-citation><mixed-citation xml:lang="en">Bang-Jensen J., Gutin G.Z. Digraphs: Theory, Algorithms and Applications. Springer Science &amp; Business Media, 2009, 795 p.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Clausen T., Jacquet P. Optimized link state routing protocol (OLSR). 2003. N RFC3626. https://doi.org/10.17487/RFC3626</mixed-citation><mixed-citation xml:lang="en">Clausen T., Jacquet P. Optimized link state routing protocol (OLSR). 2003, no. RFC3626. https://doi.org/10.17487/RFC3626</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Jacquet P., Muhlethaler P., Clausen T., Laouiti A., Qayyum A., Viennot L. Optimized link state routing protocol for ad hoc networks // Proceedings. IEEE International Multi Topic Conference, 2001. IEEE INMIC 2001. Technology for the 21st Century. 2001. P. 62–68. https://doi.org/10.1109/INMIC.2001.995315</mixed-citation><mixed-citation xml:lang="en">Jacquet P., Muhlethaler P., Clausen T., Laouiti A., Qayyum A., Viennot L. Optimized link state routing protocol for ad hoc networks. Proceedings. IEEE International Multi Topic Conference, 2001. IEEE INMIC 2001. Technology for the 21st Century, 2001, pp. 62–68. https://doi.org/10.1109/INMIC.2001.995315</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Noto M., Sato H. A method for the shortest path search by extended Dijkstra algorithm // Smc 2000 conference proceedings. 2000 IEEE International Conference on Systems, Man and Cybernetics. 2000. V. 3. P. 2316–2320. https://doi.org/10.1109/icsmc.2000.886462</mixed-citation><mixed-citation xml:lang="en">Noto M., Sato H. A method for the shortest path search by extended Dijkstra algorithm. Smc 2000 conference proceedings. 2000 IEEE International Conference on Systems, Man and Cybernetics, 2000, vol. 3, pp. 2316–2320. https://doi.org/10.1109/icsmc.2000.886462</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Mammeri Z. Reinforcement learning based routing in networks: Review and classification of approaches // IEEE Access. 2019. V. 7. P. 55916–55950. https://doi.org/10.1109/ACCESS.2019.2913776</mixed-citation><mixed-citation xml:lang="en">Mammeri Z. Reinforcement learning based routing in networks: Review and classification of approaches. IEEE Access, 2019, vol. 7, pp. 55916–55950. https://doi.org/10.1109/ACCESS.2019.2913776</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Yao Z., Wang Y., Qiu X. DQN-based energy-efficient routing algorithm in software-defined data centers // International Journal of Distributed Sensor Networks. 2020. V. 16. N 6. https://doi.org/10.1177/1550147720935775</mixed-citation><mixed-citation xml:lang="en">Yao Z., Wang Y., Qiu X. DQN-based energy-efficient routing algorithm in software-defined data centers. International Journal of Distributed Sensor Networks, 2020, vol. 16, no. 6. https://doi.org/10.1177/1550147720935775</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Belkin M., Niyogi P. Laplacian eigenmaps and spectral techniques for embedding and clustering // Advances in Neural Information Processing Systems. 2002.</mixed-citation><mixed-citation xml:lang="en">Belkin M., Niyogi P. Laplacian eigenmaps and spectral techniques for embedding and clustering. Advances in Neural Information Processing Systems, 2002.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Gao B., Pavel L. On the properties of the softmax function with application in game theory and reinforcement learning // arXiv. 2017. arXiv:1704.00805. https://doi.org/10.48550/arXiv.1704.00805</mixed-citation><mixed-citation xml:lang="en">Gao B., Pavel L. On the properties of the softmax function with application in game theory and reinforcement learning. arXiv, 2017, arXiv:1704.00805. https://doi.org/10.48550/arXiv.1704.00805</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Barros C.D., Mendonça M.R., Vieira A.B., Ziviani A. A survey on embedding dynamic graphs // ACM Computing Surveys. 2021. V. 55. N 1. P. 1–37. https://doi.org/10.1145/3483595</mixed-citation><mixed-citation xml:lang="en">Barros C.D., Mendonça M.R., Vieira A.B., Ziviani A. A survey on embedding dynamic graphs. ACM Computing Surveys, 2021, vol. 55, no. 1, pp. 1–37. https://doi.org/10.1145/3483595</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Ou M., Cui P., Pei J., Zhang Z., Zhu W. Asymmetric transitivity preserving graph embedding // Proc. of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016. P. 1105–1114. https://doi.org/10.1145/2939672.2939751</mixed-citation><mixed-citation xml:lang="en">Ou M., Cui P., Pei J., Zhang Z., Zhu W. Asymmetric transitivity preserving graph embedding. Proc. of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016, pp. 1105–1114. https://doi.org/10.1145/2939672.2939751</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Grover A., Leskovec J. Node2vec: Scalable feature learning for networks // Proc. of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016. P. 855–864. https://doi.org/10.1145/2939672.2939754</mixed-citation><mixed-citation xml:lang="en">Grover A., Leskovec J. Node2vec: Scalable feature learning for networks. Proc. of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016, pp. 855–864. https://doi.org/10.1145/2939672.2939754</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Wang D., Cui P., Zhu W. Structural deep network embedding // Proc. of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2016. P. 1225–1234. https://doi.org/10.1145/2939672.2939753</mixed-citation><mixed-citation xml:lang="en">Wang D., Cui P., Zhu W. Structural deep network embedding. Proc. of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016, pp. 1225–1234. https://doi.org/10.1145/2939672.2939753</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Goyal P., Chhetri S.R., Canedo A. dyngraph2vec: Capturing network dynamics using dynamic graph representation learning // Knowledge-Based Systems. 2020. V. 187. P. 104816. https://doi.org/10.1016/j.knosys.2019.06.024</mixed-citation><mixed-citation xml:lang="en">Goyal P., Chhetri S.R., Canedo A. dyngraph2vec: Capturing network dynamics using dynamic graph representation learning. Knowledge-Based Systems, 2020, vol. 187, pp. 104816. https://doi.org/10.1016/j.knosys.2019.06.024</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Ma Y., Guo Z., Ren Z., Tang J., Yin D. Streaming graph neural networks // Proc. of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval. 2020. P. 719–728. https://doi.org/10.1145/3397271.3401092</mixed-citation><mixed-citation xml:lang="en">Ma Y., Guo Z., Ren Z., Tang J., Yin D. Streaming graph neural networks. Proc. of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval, 2020, pp. 719–728. https://doi.org/10.1145/3397271.3401092</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Kool W., Van Hoof H., Welling M. Attention, learn to solve routing problems! // Proc. of the 7th International Conference on Learning Representations (ICLR). 2019.</mixed-citation><mixed-citation xml:lang="en">Kool W., Van Hoof H., Welling M. Attention, learn to solve routing problems! Proc. of the 7th International Conference on Learning Representations (ICLR), 2019.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Komer B., Bergstra J., Eliasmith C. Hyperopt-sklearn // Automated Machine Learning. 2019. P. 97–111. https://doi.org/10.1007/978-3-030-05318-5_5</mixed-citation><mixed-citation xml:lang="en">Komer B., Bergstra J., Eliasmith C. Hyperopt-sklearn. Automated Machine Learning, 2019, pp. 97–111. https://doi.org/10.1007/978-3-030-05318-5_5</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
