Time-Dependent Electric Vehicle Routing Problem with Time Windows and Path Flexibility

Abstract

With energy and environmental issues becoming increasingly prominent, electric vehicles (EVs) have become the important transportation means in the logistics distribution. In the real-world urban road network, there often exist multiple paths between any two locations (depot, customer, and charging station) since the time-dependent travel times. That is, the travel speed of an EV on each path may be different during different time periods, and thus, this paper explicitly considers path selection between two locations in the time-dependent electric vehicle routing problem with time windows, denoted as path flexibility. Therefore, the integrated decision-making should include not only the routing plan but also the path selection, and the interested problem of this paper is a time-dependent electric vehicle routing problem with time windows and path flexibility (TDEVRP-PF). In order to determine the optimal path between any two locations, an optimization model is established with the goal of minimizing the distance and the battery energy consumption associated with travel speed and cargo load. On the basis of the optimal path model, a 0-1 mixed-integer programming model is then formulated to minimize the total travel distance. Hereinafter, an improved version of the variable neighborhood search (VNS) algorithm is utilized to solve the proposed models, in which multithreading technique is adopted to improve the solution efficiency significantly. Ultimately, several numerical experiments are carried out to test the performance of VNS with a view to the conclusion that the improved VNS is effective in finding high-quality distribution schemes consisted of the distribution routes, traveling paths, and charging plans, which are of practical significance to select and arrange EVs for logistics enterprises.

Hyperpath Searching Algorithm considering Delay at Intersection and Its Application in CVIS for Vehicle Navigation

“…Conventionally, path selection in the road network in the time-dependent vehicle routing problem is denoted as flexibility [22][23][24]. However, not all alternative paths have flexibility, but the ones with the same constraint conditions can have it.…”

Optimization of Vehicle Paths considering Carbon Emissions in a Time-Varying Road Network

“…Similarly, Ge and Ran used the same treatment to divide the speed into three segments and introduced a waiting strategy for travel time calculation to solve time-varying traffic congestion conditions [24]. Wang considered that the driving speed of electric vehicles may vary in different periods and divided the speed into four segments [25].…”

“…Fan et al proposed that the relationship between vehicle speed (v) and time (t) during peak hours is V � ɑSin (yt) + δ (where ɑ, y, and δ are coefficients related to road conditions) [10,20]. Franceschetti et al argued that the vehicle travel process can be divided into normal and congested periods according to whether the traffic is congested or not, and the vehicle speed in different periods is different, but all are in uniform motion [23][24][25].…”

Effective Permutation Encoding for Evolutionary Optimization of the Electric Vehicle Routing Problem

“…The study conducted by [3] indicates the very high popularity of the MILP method based on the analysis of 175 literature items. The method is readily adapted by the authors of the publications to various types of problems, e.g., charging time and variable travel time [15], time windows and path flexibility [16], and nonlinear charging time [5,6,17].…”