81508

Автор(ы): 

Автор(ов): 

4

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Построение многоагентных маршрутов с использованием близких задач

ISBN/ISSN: 

1729-3901

Наименование источника: 

  • Таврический вестник информатики и математики

Обозначение и номер тома: 

№ 4 (65)

Город: 

  • Симферополь

Издательство: 

  • Крымский федеральный университет имени В.И. Вернадского

Год издания: 

2024

Страницы: 

7-33
Аннотация
The paper addresses the problem of reducing the complexity of NP-hard problems by leveraging related problems for which optimal or acceptable solutions are already known. It explores the use of a clustering methodology aligned with routing strategies within each cluster, taking into account time window constraints in multi-agent routing problems. A mathematical model is presented, which is divided into logical blocks such as the routing block, the time constraint block, and others. The stages of forming a solution to the original problem TSP_j based on a related problem ~TSP_j (Traveling Salesman Problem) are described. The notion of problem similarity refers to the similarity of their mathematical models and the network fragments involved in the solution.The method for determining the similarity of fragments (clusters C_j) consists of calculating a weighted metric distance between the vectors of metaheuristic parameters of the corresponding graphs. An experiment is presented to support the hypothesis that the vectors of metric characteristics for related problems lie close to each other. Additional experiments are also described, demonstrating the maximum allowable difference between graphs for them to still be considered similar. The cluster considers the Euclidean Traveling Salesman Problem (ETSP) - an NP-hard combinatorial optimization problem. The main goal is to extend the applicability of polynomial algorithms for special cases of ETSP, such as problems with vertices lying on a convex hull, to more general point configurations. For this purpose, the pairwise comparison method is used. The result is a new heuristic algorithm with a guaranteed absolute error, which consists of three stages. At the first stage, the set of points is divided into subsets forming nested convex polygons. At the second stage, subproblems for each polygon are solved as a special case of ETSP with linear complexity. At the third stage, the solutions of the subproblems are combined into a single route. The results concerning the selection of metaheuristics based on related problems are applied in a software tool for calculating delivery routes across the territory of the Crimean Peninsula, taking time windows into account. The application includes a module for computing and comparing graph metric characteristics. Additionally, an approach is proposed for building an extendable database containing various graph structures and the most suitable metaheuristics (as determined through extensive experimentation) for each specific structure. This allows for faster problem-solving by reusing previously obtained knowledge and significantly reduces computational effort for new but structurally similar tasks. The proposed methodology can be extended to other domains involving complex network-based optimization problems, such as urban logistics or emergency response planning.

Библиографическая ссылка: 

Козлова М.Г., Лемтюжникова Д.В., Лукьяненко В.А., Макаров О.О. Построение многоагентных маршрутов с использованием близких задач // Таврический вестник информатики и математики. 2024. № 4 (65). С. 7-33.