Graph structures are effectively capable of describing the complex relationship between the objects, i.e. nodes, through edges. Besides, Graph-based representation is an effective method for feature dimensionality reduction [4, 5]. GNNs, as powerful tools for representational learning on graph-structured data, have attracted increasing attention in recent years. GNNs are used for effective deep representational learning to perform graph analysis for tasks such as node classification, link prediction, and clustering in Euclidean and non-Euclidean domains [6]. Among the proposed methods for learning representations on graphs, GCNs proposed by Kipf et al. [7] proved to be a simple and effective GNN model. This model is able to learn hidden representations comprising both node features and local graph structure while scaling linearly relative to the number of edges in the given graph. Most classification algorithms, in GNNs, tend to minimize the average loss over all training examples which produces reasonable outcomes for class-balanced datasets.

This trend is particularly evident in the logistics sector, where companies are actively integrating EVs into their transportation fleets. At the heart of this transition is the electric vehicle routing problem (EVRP), an optimization problem central to the operations of these logistics companies, focusing on dealing with the complexities of deploying EVs instead of internal combustion engine vehicles. This article addresses a practical routing problem for EVs, named heterogeneous electric vehicle routing problem with time-window constraints (HEVRPTW). It considers both vehicle attributes, such as varying cargo and battery capacities [4] and customer preferences regarding delivery times [5]. These factors create a more realistic and applicable model for contemporary logistics challenges. HEVRPTW, recognized as an NP-hard optimization problem, seeks to determine a set of routes with minimal cost, total traveling time, or total traveling distance, for a fleet of Heterogeneous EVs to serve each geographically dispersed customer's demands within a specified time-window. Traditional methods, including exact and heuristics solvers, are conventionally employed to solve various vehicle routing problem (VRP) variants. Due to the NP-Hard nature of HEVRPTW, and VRPs in general, exact methods, such as branch-and-price [6] and branchand-price-and-cut [7], consume prohibitively long time for solving practical-size problems [8].