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

Abstract

In the paper we present machine learning algorithms for the problem of optimizing the distribution of parcels in sto-chastic time-dependent networks, which have been built as a part of some Distribution Optimization System. The prob-lem solved was a modified VRPTW (Vehicle Routing Problem with Time Windows) with many warehouses, a heteroge-neous 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) de-pending on the type of input data. The idea is to divide the input data into classes according to a proposed classifica-tion 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.