# Optimizing Electric Vehicle Routing Efficiency Using K-Means Clustering and Genetic Algorithms
## 1 Introduction  
The vehicle routing problem (VRP) presents a significant challenge in optimizing delivery routes from a central depot to dispersed customers while adhering to various constraints [1]. First introduced by [PERSON] and [PERSON] [2] as the truck dispatching problem, the VRP is a generalization of the well-known traveling salesman problem (TSP), which seeks the shortest route to visit all customers. The VRP encompasses a range of variants, including the capacitated VRP (CVRP) [3], the VRP with time windows (VRPTW) [4], and the multi-depot VRP (MDVRP), each designed to address specific real-world scenarios and constraints [5, 6, 7]. The rapid adoption of electric vehicles (EVs) has brought significant attention to the challenges associated with their efficient operation, particularly in the context of route planning. While EVs promise to reduce greenhouse gas emissions and contribute to a more sustainable transportation system, their practical deployment faces critical hurdles, especially concerning recharging logistics. Effective route planning for EVsmust account for the unique constraints of charging infrastructure, a challenge that has given rise to the electric vehicle routing problem (EVRP) [8; 9]. In the context of modern transportation, the sector faces critical challenges as conventional vehicles account for approximately 75% of its greenhouse gas emissions [10]. This alarming contribution has serious implications for climate change, resource depletion, and the sustainability of the planet [11; 12]. While EVs are known for being emissions-free during operation, their reliance on electricity, often generated from fossil fuels, raises concerns about their overall environmental benefits. Additionally, their rapid adoption could strain energy grids, introducing further complexities. Despite these challenges, EVs offer undeniable advantages. Governments worldwide are incentivization their adoption through policies and regulations, contributing to a rapidly expanding market [13]. The environmental benefits of EVs, however, are closely tied to their efficient route planning and utilization. This necessity gave rise to the EVRP, an extension of the VRP tailored to the unique requirements of EVs [14; 15]. The EVRP addresses charging constraints by integrating charging station locations and availability into route planning, ensuring that electric vehicles maintain sufficient battery charge to complete their routes. By optimizing stopovers at charging stations, the EVRP minimizes delays and enhances the efficiency of delivery schedules, thus making EVs more suitable for long-distance and time-sensitive transportation tasks. The primary goal of the EVRP is to optimize routes for EVs by considering charging constraints, energy consumption, and other critical factors such as travel distance, time, and charging station logistics [16; 17]. The growing complexity of electric vehicle routing problems (EVRPs) has spurred significant research on innovative optimization models and algorithms. [PERSON] et al. [18] introduced a multi-temperature electric vehicle routing problem with soft time windows, focusing on minimizing transportation, refrigeration, and charging costs through a hybrid ant colony optimization combined with a two-opt algorithm, demonstrating that co-distribution can reduce costs and improve efficiency. [PERSON] et al. [19] expanded the scope by considering state-of-charge-dependent charging and discharging rates, highlighting that ignoring these nonlinear functions could lead to suboptimal or infeasible solutions, and proposed a mixed-integer linear programming model for more accurate and effective routing decisions. Building on these advancements, [PERSON] et al. [20] explored multi-objective EVRPs by integrating hybrid ant colony optimization (HACO) with artificial bee colony algorithms (ABCA) to simultaneously optimize multiple conflicting objectives, concluding that partial and multiple recharge technologies can significantly enhance logistics decisions.