Рассмотрена задача маршрутизации транспорта с ограничениями по временным окнам. Требовалось составить план доставки товара клиентам, построив маршруты движения идентичных транспортных средств так, чтобы общая длина пройденного пути была минимальной. Для решения задачи разработан гибридный алгоритм. Он состоит из методов построения исходных решений, муравьиного алгоритма и локального поиска. В муравьином алгоритме в процессе формирования маршрутов разрешается нарушение временных ограничений при условии добавления штрафа в целевую функцию. Предложенный метод показал высокую эффективность при решении задач кластерного типа и задач с долгосрочным горизонтом планирования.
The purpose of this paper is to improve the performance of a hybrid method based on ant colony optimization (ACO) that finds approximate solutions of the vehicle routing problem with time windows (VRPTW). In order to solve this problem it is required to design a plan for goods delivery to the customers generating the routes of identical vehicles so that the total travelled distance is minimal. For the VRPTW solving, the hybrid method is developed in which a usage of trial solutions makes it possible to explore the most promising parts of the search space. The initial methods for solution construction, an ant colony optimization (ACO) algorithm and local search are proposed in the framework of the hybrid method. In the ACO algorithm, when generating the routes, it is allowed to violate the time window constraints. A method to restore the feasibility of solutions is implemented within the relaxation scheme under “returns in time” principle. Numerical results for solving all problems with 25, 50 and 100 customers from the Solomon test set are obtained. We provide the results on the time and deviation of the solution of these problems in comparison with the results of other authors. Some problems and their classes were solved much faster by the algorithm proposed in this paper. Relative deviations from optimal values of the objective function for the most complex tasks decrease with increasing decision time. The proposed approach can be considered to be an additional or an alternative algorithm for solving the cluster type and the long-term planning horizon problems of the VRPTW.
VEHICLE ROUTING PROBLEM WITH TIME WINDOWS USING HYBRID ENCODING GENETIC ALGORITHM
