## 1 Introduction  
In recent years, the global surge in e-commerce adoption has significantly influenced distribution and last-mile delivery logistics. Last-mile delivery logistics denote the final phase of a product's delivery process, bringing it to the end customer. This stage has become a focal point in logistics strategies due to its critical influence on customer satisfaction, delivery speed, cost efficiency, and overall convenience. Over the past decade, electric vehicles (EVs) have become prevalent in last-mile delivery services due to their capacity to reduce greenhouse gas emissions, support renewable energy, and establish sustainable transportation systems. The benefits of EVs include decreased transportation costs, enhanced energy efficiency, and significantly reduced pollutant emissions. With the increasing use of EVs, the routing problem of these vehicles has emerged. The problem is known as the Electric Vehicle Routing Problem (EVRP) in the literature. The primary difference between the EVRP and the classic VRP is that vehicles have a battery as an energy source, and the charge level decreases as the vehicle travels on the road. Consequently, the EVRP places substantial emphasis on accounting for charging capacities and the strategic placement of charging stations, as these factors are crucial for the efficient operation of an EV fleet. A common constraint across all EVRP variations is the necessity to visit a recharging station due to the limited driving range of electric vehicles. In traditional Vehicle Routing Problems (VRPs), gas and diesel vehicles typically have longer ranges, enabling them to travel hundreds of kilometers on a single refuel. Refueling needs arise less frequently in daily route planning. Additionally, refueling durations generally range between 5 and 10 min, which does not substantially impact the overall travel time of the route. The widespread distribution of gas and diesel stations, extending from urban centers to rural areas, further mitigates the necessity to incorporate refueling points within route planning models. Conversely, within the framework of the EVRP, the integration of charging stations into routes becomes imperative due to the limited battery capacity and comparatively prolonged charging times of electric vehicles. Electric vehicles must recharge at specific intervals to address range limitations, and the strategic placement of charging stations directly influences this process. Consequently, the EVRP presents a more complex modeling challenge than the classical VRP, as it necessitates considering charging times and station visit decisions as additional variables in route planning. The decision to include charging station visits emerges as a critical component in the context of the EVRP. In this paper we address the Capacitated Electric Vehicle Routing Problem (CEVRP). The CEVRP aims to address operational and environmental objectives by accounting for electric vehicles' limited driving range and load capacities. Including capacity constraints facilitates more realistic industrial planning. CEVRP-based strategies promote environmental sustainability and reduce operational costs by optimizing routes for energy efficiency and minimizing carbon emissions. A fleet management that produces fewer emissions and considers energy efficiency supports corporate environmental policies. As a result, the CEVRP has been increasingly adopted in today's last-mile delivery operations, leading the way for broader implementation of eco-friendly solutions in the logistics sector. Since the VRP is an NP-hard problem and the EVRP is a generalization of the VRP, the EVRP can equally be considered NP-hard in the strong sense [1]. Solution methodologies proposed in the literature for addressing the EVRP and its variants can be categorized into exact solution methods, heuristic methods, metaheuristic methods, and learning-based methods [2; 3; 4; 5; 6; 7].