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Machine learning algorithms for the problem of optimizing the distribution of parcels in time-dependent networks: the case study

Tarapata Zbigniew, Kulas Wojciech, Antkiewicz Ryszard

Archives of Transport

2022

Vol. 61, iss. 1

133--147

In the paper we present machine learning algorithms for the problem of optimizing the distribution of parcels in stochastic time-dependent networks, which have been built as a part of some Distribution Optimization System. The problem solved was a modified VRPTW (Vehicle Routing Problem with Time Windows) with many warehouses, a heterogeneous fleet, travel times depending on the time of departure (stochastic time-dependent network) and an extensive cost function as an optimization criterion. To solve the problem a modified simulated annealing (SATM) algorithm has been proposed. The paper presents the results of the algorithm learning process: the calibration of input parameters and the study of the impact of parameters on the quality of the solution (calculation time, transport cost function value) depending on the type of input data. The idea is to divide the input data into classes according to a proposed classification rule and to propose several strategies for selecting the optimal set of calibration parameters. These strategies consist in solving some multi-criteria optimization tasks in which four criterion functions are used: the length of the designated routes, the computation time, the number of epochs used in the algorithm, the number of designated routes. The subproblem was building a network model of travel times that is used in constructed SATM algorithm to determine the travel time between recipients, depending on the time of departure from the start location. An attempt has been made to verify the research hypothesis that the time between two points can be estimated with sufficient accuracy depending on their geographical location and the time of departure (without reference to the micro-scale, i.e. the detailed structure of the road network). The research was conducted on two types of data for Warsaw: from transport companies and one of the Internet traffic data providers. Learning the network model of travel times has produced very promising results, which will be described in the paper.

Analysis of networks with time-dependent transition probabilities and messages bypass between the queuing systems

Matalytski M., Naumenko V.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2012

Vol. 11, nr 4

93-104

The object of investigation is an open exponential network with a messages bypass of systems in transient behavior. The purpose of the research is to find stationary probabilities of states and the average characteristics of the network when the transition probabilities between the messages and bypass systems of the network, parameters of the incoming flow of messages and services are time-dependent. To find the state probabilities and the characteristics of a network is used the apparatus for the multivariate generating functions. The examples are calculated on a computer.