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Анализ математических постановок задачи маршрутизации с ограничением по грузоподъемности и методов их решения

https://doi.org/10.15514/ISPRAS-2018-30(3)-17

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Аннотация

Задача маршрутизации является одной из важнейших NP-трудных задач комбинаторной оптимизации. Она заключается в нахождении множества оптимальных замкнутых маршрутов с целью развозки товаров клиентам, используя ограниченное количество транспортных средств. В данной работе анализируется особый вид задачи маршрутизации - задача маршрутизации с ограничением по грузоподъемности, в которой у каждого транспортного средства есть лимит на максимальный вес (объем) груза. Целью данной работы является составление классификации различных типов задачи маршрутизации с ограничением по грузоподъемности. В первой части работы дана общая информация о проблеме, указаны рамки, в которых проводилось исследование - не рассматривались динамические и стохастические подвиды задачи маршрутизации. Во второй части представлена впервые предложенная авторами работы математическая постановка трех классических вариантов задачи маршрутизации с ограничением по грузоподъемности. В третьей части работы представлен список подклассов рассматриваемой задачи, включающий описание, математические модели для некоторых задач, а также наиболее перспективные метаэвристики, с помощью которых можно решать поставленную задачу. В четвертой части приведено упоминание об алгоритме LKH-3, способном решать некоторые подклассы задач с меньшим отклонением от оптимального значения по сравнению с другими алгоритмами. В заключении, приведена таблица, объединяющая все методы, описанные ранее, и схема с взаимосвязями задачи маршрутизации с ограничением по грузоподъемности и её подклассами. В будущем авторы работы планируют расширить классификацию, включив в неё подклассы стохастических и динамических вариантов данной проблемы.

Об авторах

Е. Н. Береснева
Департамент программной инженерии, Национальный исследовательский университет “Высшая школа экономики”
Россия


С. М. Авдошин
Департамент программной инженерии, Национальный исследовательский университет “Высшая школа экономики”
Россия


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Для цитирования:


Береснева Е.Н., Авдошин С.М. Анализ математических постановок задачи маршрутизации с ограничением по грузоподъемности и методов их решения. Труды Института системного программирования РАН. 2018;30(3):233-250. https://doi.org/10.15514/ISPRAS-2018-30(3)-17

For citation:


Beresneva E..., Avdoshin S... Analysis of Mathematical Formulations of Capacitated Vehicle Routing Problem and Methods for their Solution. Proceedings of the Institute for System Programming of the RAS (Proceedings of ISP RAS). 2018;30(3):233-250. https://doi.org/10.15514/ISPRAS-2018-30(3)-17

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