Гибридный алгоритм для двухкритериальной задачи оптимизации трафика в сети

Гибридный алгоритм для двухкритериальной задачи оптимизации трафика в сети

Юськов А. Д., Кулаченко И. Н., Мельников А. А., Кочетов Ю. А.
Дискретный анализ и исследование операций, 32, 3, 117-144 (2025)
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УДК 519.8 
DOI: 10.33048/daio.2025.32.827

Аннотация:

Рассматривается задача оптимизации трафика в сети передачи данных. Для моделирования трафика используется имитационная модель. Пути передачи задаются неявно весами дуг. Если поток по дуге превышает её пропускную способность, то дуга считается перегруженной. Задача состоит в минимизации двух целевых функций: числа перегруженных дуг и расстояния от исходного вектора весов при соблюдении ограничений на суммарный поток в сети и появление новых перегруженных дуг. Предложена двухстадийная эволюционная схема, включающая алгоритм локального поиска по окрестностям большой мощности для получения стартового приближения границы Парето. Лучшее соседнее решение ищется при помощи оригинальной модели целочисленного линейного программирования. Проведено сравнение предложенного подхода с лучшими эволюционными алгоритмами на примерах с 628 каналами и 1324 запросами, и показано, что новая схема демонстрирует результаты, статистически лучшие на 15–49% по многим показателям качества (9 из 10). 

Табл. 3, ил. 6, библиогр. 42.

Литература:
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Исследование выполнено в рамках государственного задания Института математики им. С. Л. Соболева (проект № FWNF–2022–0019). Дополнительных грантов на проведение или руководство этим исследованием получено не было.

Юськов Александр Дмитриевич
  1. Новосибирский гос. университет, 
    ул. Пирогова, 2, 630090 Новосибирск, Россия

E-mail: a.yuskov@g.nsu.ru 

Кулаченко Игорь Николаевич
  1. Институт математики им. С. Л. Соболева, 
    пр. Акад. Коптюга, 4, 630090 Новосибирск, Россия

E-mail: ink@math.nsc.ru 

Мельников Андрей Андреевич
  1. Институт математики им. С. Л. Соболева, 
    пр. Акад. Коптюга, 4, 630090 Новосибирск, Россия

E-mail: melnikov@math.nsc.ru 

Кочетов Юрий Андреевич
  1. Институт математики им. С. Л. Соболева, 
    пр. Акад. Коптюга, 4, 630090 Новосибирск, Россия

E-mail: jkochet@math.nsc.ru 

Статья поступила 3 февраля 2025 г.
После доработки — 23 мая 2025 г.
Принята к публикации 22 июня 2025 г.

Abstract:

We consider an Internet traffic routing problem. The paths for requests are assigned implicitly by setting link weights. The loads of links are generated by a simulator. If the load of a link is greater than its capacity, then the link is called congested. Our goal is to minimize two objective functions: the number of congested links and the distance between the initial and current weight vectors. The problem also includes two constraints: the total link flow in the network has an upper bound and new congested links are unwanted. We propose a new two-stage evolutionary scheme. The scheme employs a local search algorithm with a large neighbourhood to find an initial approximation of the Pareto set. The algorithm utilizes an integer linear programming model to determine the best solution in the neighbourhood. We compare the proposed scheme with well-known evolutionary algorithms using instances with 628 links and 1324 requests. According to the experiments, the proposed scheme constructs solutions statistically better at 15–49% for many performance indicators (9 out of 10). 

Tab. 3, illustr. 6, bibliogr. 42.

References:
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  21. N. Wang, K. H. Ho, G. Pavlou, and M. Howarth, An overview of routing optimization for internet traffic engineering, IEEE Commun. Surv. Tutor. 10 (1), 36–56 (2008), DOI: 10.1109/COMST.2008.4483669.
     
  22. S. Kaneda, T. Uyematsu, N. Nagatsu, and K. Sato, Network design and cost optimization for label switched multilayer photonic IP networks, IEEE J. Sel. Areas Commun. 23 (8), 1612–1619 (2005), DOI: 10.1109/JSAC.2005. 851747.
     
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  25. K. Holmberg and D. Yuan, Optimization of internet protocol network design and routing, Networks 43 (1), 39–53 (2004), DOI: 10.1002/net.10102.
     
  26. M. Dehghani, V. Vahdat, M. Amiri, E. Rabiei, and S. Salehi, A multiobjective optimization model for a reliable generalized flow network design, Comput. Ind. Eng. 138, ID 106074 (2019), DOI: 10.1016/j.cie.2019.106074.
     
  27. H. Zhu, V. Gupta, S. S. Ahuja, Y. Tian, Y. Zhang, and X. Jin, Network planning with deep reinforcement learning, in Proc. ACM SIGCOMM 2021 Conf. (Delft, Netherlands, Aug. 23–28, 2021) (ACM, New York, 2021), pp. 258– 271, DOI: 10.1145/3452296.3472902.
     
  28. R. T. Wong, Telecommunications network design: Technology impacts and future directions, Networks 77 (2), 205–224 (2021), DOI: 10.1002/net.21997.
     
  29. A. D. Yuskov, I. N. Kulachenko, A. A. Melnikov, and Yu. A. Kochetov, Two-stage algorithm for bi-objective black-box traffic engineering, in Optimization and Applications, Rev. Sel. Pap. 14th Int. Conf. OPTIMA 2023 (Petrovac, Montenegro, Sept. 18–22, 2023) (Springer, Cham, 2023), pp. 110–125 (Lect. Notes Comput. Sci., Vol. 14395), DOI: 10.1007/978-3-031-47859-8_9.
     
  30. P. Hansen, N. Mladenović, R. Todosijević, and S. Hanafi, Variable neighborhood search: Basics and variants, EURO J. Comput. Optim. 5 (3), 423–454 (2016), DOI: 10.1007/s13675-016-0075-x.
     
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  32. C. Audet, J. Bigeon, D. Cartier, S. Le Digabel, and L. Salomon, Performance indicators in multiobjective optimization, Eur. J. Oper. Res. 292 (2), 397–422 (2021), DOI: 10.1016/j.ejor.2020.11.016.
     
  33. A. Konak, D. W. Coit, and A. E. Smith, Multi-objective optimization using genetic algorithms: A tutorial, Reliab. Eng. Syst. Saf. 91 (9), 992–1007 (2006), DOI: 10.1016/j.ress.2005.11.018.
     
  34. D. Hadka, MOEA framework: A free and open source Java framework for multiobjective optimization. Version 5.1 (2025), URL: moeaframework.org (accessed: 10.10.2025).
     
  35. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evolut. Comput. 6 (2), 182–197 (2002), DOI: 10.1109/4235.996017.
     
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