Двухэшелонная модель транспортной системы и муравьиный алгоритм: анализ масштабируемости вычислительных решений
Ключевые слова:
двухэшелонная транспортная задача, муравьиный алгоритм, метаэвристики, масштабируемость, вычислительный эксперимент, логистические системыАннотация
В статье рассматривается двухэшелонная модель транспортной системы, предназначенная для описания и анализа распределительных логистических процессов с промежуточными хабами и конечными потребителями. Модель учитывает совместную оптимизацию маршрутов магистрального уровня и маршрутов распределения при наличии ограничений по вместимости транспортных средств и требований по удовлетворению спроса. Рассматриваемая задача относится к классу NP-трудных, что существенно ограничивает применение точных методов оптимизации при росте размерности транспортного графа. Для решения предложенной модели используется двухэшелонная модификация алгоритма муравьиной колонии (2E-ACO), в которой процессы формирования решений для первого и второго эшелонов формализованы раздельно, но согласованы через единую целевую функцию, включающую транспортные затраты и штрафы за необслуженный спрос. Основное внимание в работе уделено вычислительному эксперименту, направленному на анализ масштабируемости и устойчивости алгоритма при увеличении мощности множества потребителей, числа хабов и сложности транспортной инфраструктуры. Эксперименты проводятся в режиме масштабируемых ресурсов, что позволяет отделить влияние алгоритмических решений от эффектов ресурсных ограничений. Для оценки воспроизводимости используются многократные независимые запуски с фиксированными силами генератора случайных чисел. Полученные результаты демонстрируют предсказуемый рост вычислительных затрат при увеличении размерности модели и устойчивость качества решений. Сравнение с намеренно простой базовой жадной эвристикой, используемой в качестве нижней оценки качества решений, показывает, что алгоритм 2E-ACO обеспечивает сопоставимый уровень обслуживания спроса при более высоких вычислительных затратах, обусловленных итерационным характером поиска. Представленные результаты подтверждают применимость предложенной модели и алгоритма для исследования крупномасштабных двухэшелонных транспортных систем.
Литература
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16. Macrina G., Di Puglia Pugliese L., Guerriero F. A Variable Neighborhood Search for the Vehicle Routing Problem with Occasional Drivers and Time Windows. Proceedings of the 9th International Conference on Operations Research and Enterprise Systems (ICORES 2020). 2020. pp. 270–277. DOI: 10.5220/0009193302700277.
17. Gunawan A., Widjaja A.T., Vansteenwegen P., Yu V.F. Adaptive large neighborhood search for vehicle routing problem with cross-docking // Proceedings of IEEE Congress on Evolutionary Computation (CEC). 2020. pp. 1–8. DOI: 10.1109/CEC48606.2020.9185514.
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20. Hemmelmayr V.C., Doerner K.F., Hartl R.F., Savelsbergh M.W.P. Delivery strategies for blood products supplies // OR Spectrum. 2009. vol. 31. pp. 707–725.
21. Yu V.F., Nguyen M.P.K., Putra K., Gunawan A., Dharma I.G.B.B. The Two-Echelon Vehicle Routing Problem with Transshipment Nodes and Occasional Drivers: Formulation and Adaptive Large Neighborhood Search Heuristic // Journal of Advanced Transportation. 2022. vol. 2022. DOI: 10.1155/2022/5603956.
22. Dorigo M., Stutzle T. Ant Colony Optimization. Cambridge, MA: MIT Press, 2004. 305 p.
23. Ren T., Luo T., Jia B., Yang B., Wang L., Xing L. Improved ant colony optimization for the vehicle routing problem with split pickup and split delivery // Swarm and Evolutionary Computation. 2023. vol. 77. DOI: 10.1016/j.swevo.2023.101228.
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26. Mavrovouniotis M., Menelaou C., Timotheou S., Ellinas G., Panayiotou C., Polycarpou M. Benchmark test suite for the electric capacitated vehicle routing problem // Proceedings of IEEE Congress on Evolutionary Computation (CEC). 2020. pp. 1–8. DOI: 10.1109/CEC48606.2020.9185753.
27. Wang M., Wang L., Xu X., Qin Y., Qin L. Genetic Algorithm-Based Particle Swarm Optimization Approach to Reschedule High-Speed Railway Timetables: A Case Study in China // Journal of Advanced Transportation. 2019. vol. 2019. pp. 1–12. DOI: 10.1155/2019/6090742.
28. Xu S.-H., Liu J.-P., Zhang F.-H., Wang L., Sun L. A Combination of Genetic Algorithm and Particle Swarm Optimization for Vehicle Routing Problem with Time Windows // Sensors. 2015. vol. 15. pp. 21033–21053. DOI: 10.3390/S150921033.
29. Oszczypala M., Konwerski J., Ziolkowski J., Malachowski J. A genetic algorithm and particle swarm optimization for redundancy allocation problem in systems with limited number of non-cooperating repairmen // Expert Systems with Applications. 2024. vol. 256. DOI: 10.1016/J.ESWA.2024.124841.
30. Glover F., Laguna M. Tabu Search. Boston: Kluwer Academic Publishers, 1997. 382 p. DOI: 10.1007/978-1-4615-6089-0.
31. Kirkpatrick S., Gelatt C.D., Vecchi M.P. Optimization by simulated annealing // Science. 1983. vol. 220. no. 4598. pp. 671–680.
32. Thangiah S., Osman I.H., Sun T. A Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Heuristic for Vehicle Routing Problems with Time Windows // Practical Handbook of Genetic Algorithms: Complex Coding Systems. Volume III. Boca Raton: CRC Press, 1999. pp. 347–384.
33. Waligora G. Simulated Annealing and Tabu Search for Discrete-Continuous Project Scheduling with Discounted Cash Flows. RAIRO – Operations Research. 2014. vol. 48. no. 1. pp. 1–24. DOI: 10.1051/ro/2013045.
34. Anderluh A., Nolz P.C., Hemmelmayr V.C., Crainic T.G. Multi-objective optimization of a two-echelon vehicle routing problem with vehicle synchronization and 'grey zone' customers arising in urban logistics. European Journal of Operational Research. 2021. vol. 289. no. 3. pp. 940–958. DOI: 10.1016/j.ejor.2019.07.049.
35. Shuaibu A., Mahmoud A., Sheltami T. A Review of Last-Mile Delivery Optimization: Strategies, Technologies, Drone Integration, and Future Trends // Drones. 2025. vol. 9. no. 3. DOI: 10.3390/drones9030158.
36. Crainic T.G., Ricciardi N., Storchi G. Advanced freight transportation systems for congested urban areas // Transportation Research Part C. 2004. vol. 12. no. 2. pp. 119–137. DOI: 10.1016/j.trc.2004.07.002.
37. Kumar V.P., Gupta A. Analyzing scalability of parallel algorithms and architectures // Journal of Parallel and Distributed Computing. 1994. vol. 22. no. 3. pp. 379–391.
38. Gouvea A.M.M.M., Paulos N., Uchoa E., Nascimento Maria C.V. Instance space analysis of the capacitated vehicle routing problem // arXiv preprint. 2025. arXiv:2507.10397.
39. Uchoa E., Pecin D., Pessoa A., Poggi M., Vidal T., Subramanian A. New benchmark instances for the capacitated vehicle routing problem // European Journal of Operational Research. 2017. vol. 257. no. 3. pp. 845–858.
40. Gutierrez A., Labadie N., Prins C. A Two-echelon Vehicle Routing Problem with time-dependent travel times in the city logistics context // EURO Journal on Transportation and Logistics. 2024. vol. 13. DOI: 10.1016/J.EJTL.2024.100133.
41. Dumez D., Tilk C., Irnich S., Lehuede F., Olkis K., Peton O. A matheuristic for a 2-echelon vehicle routing problem with capacitated satellites and reverse flows. European Journal of Operational Research. 2023. vol. 305(1). pp. 64–84.
42. Zhou H., Qin H., Cheng C., Rousseau L.-M. An exact algorithm for the two-echelon vehicle routing problem with drones. Transportation Research Part B: Methodological. 2023. vol. 168. pp. 124–150. DOI: 10.1016/j.trb.2023.01.002.
43. Petris M., Archetti C., Cattaruzza D., Ogier M., Semet F. A Branch-Price-and-Cut algorithm for the Multi-Commodity two-echelon Distribution Problem. EURO Journal on Transportation and Logistics. 2024. vol. 13. DOI: 10.1016/J.EJTL.2024.100139.
44. Moradi N., Mirzavand Boroujeni N., Aftabi N., Aslani A. Two-echelon Electric Vehicle Routing Problem in Parcel Delivery: A Literature Review. arXiv preprint. 2024. arXiv:2412.19395.
45. Braekers K., Ramaekers K., Van Nieuwenhuyse I. The vehicle routing problem: State of the art classification. Computers & Industrial Engineering. 2016. vol. 99. pp. 300–313.
46. Zhang L., Ding P., Thompson R. A stochastic formulation of the two-echelon vehicle routing and loading bay reservation problem. Transportation Research Part E: Logistics and Transportation Review. 2023. vol. 177. DOI: 10.1016/j.tre.2023.103252.
47. Guo S., Hu H., Xue H. Two-echelon multi-trip capacitated VRP for e-commerce logistics. Systems. 2024. vol. 12(6).
48. Vidal T., Crainic T.G., Gendreau M., Prins C. A Unified Solution Framework for Multi-Attribute Vehicle Routing Problems. European Journal of Operational Research. 2014. vol. 234(3). pp. 658–673. DOI: 10.1016/j.ejor.2013.09.045.
Опубликован
2026-04-06
Как цитировать
Рогулин, Р. С. (2026). Двухэшелонная модель транспортной системы и муравьиный алгоритм: анализ масштабируемости вычислительных решений. Информатика и автоматизация, 25(2), 478-516. https://doi.org/10.15622/ia.25.2.8
Раздел
Математическое моделирование и прикладная математика
Copyright (c) rodion rogulin
Это произведение доступно по лицензии Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.
Авторы, которые публикуются в данном журнале, соглашаются со следующими условиями: Авторы сохраняют за собой авторские права на работу и передают журналу право первой публикации вместе с работой, одновременно лицензируя ее на условиях Creative Commons Attribution License, которая позволяет другим распространять данную работу с обязательным указанием авторства данной работы и ссылкой на оригинальную публикацию в этом журнале. Авторы сохраняют право заключать отдельные, дополнительные контрактные соглашения на неэксклюзивное распространение версии работы, опубликованной этим журналом (например, разместить ее в университетском хранилище или опубликовать ее в книге), со ссылкой на оригинальную публикацию в этом журнале. Авторам разрешается размещать их работу в сети Интернет (например, в университетском хранилище или на их персональном веб-сайте) до и во время процесса рассмотрения ее данным журналом, так как это может привести к продуктивному обсуждению, а также к большему количеству ссылок на данную опубликованную работу (Смотри The Effect of Open Access).