## 1 Introduction  
Global warming has emerged as a critical climate challenge, prompting nations worldwide to implement tailored energy-saving and emission-reduction policies [1, 2, 3]. According to a recent report by the European Environment Agency, the transportation sector is a major contributor, accounting for nearly a quarter of total EU-27 emissions in 2024, with over three quarters originating from road transport [4]. As vehicle numbers continue to rise, transportation is expected to remain a primary source of emissions [5]. Recognizing the pivotal role of electric vehicles (EVs) in reducing carbon emissions, an increasing number of governments have introduced favorable policies to incentivize logistics companies to transition from fossil fuel fleets to EVs [6]. Electric logistics vehicles are a category of electric commercial vehicles, which represent an emerging green transportation solution, offering significant environmental and economic benefits due to their electric propulsion, reduced noise, and lower air pollution. As of the end of 2024, EVs have surpassed 40% market penetration in China's automotive sector,while electric logistics vehicles account for 15% of the logistics vehicle market, with both segments demonstrating sustained year-on-year growth. These advantages and the rapid expansion of EVs have attracted increasing research attention to EVRP in recent years. EVRP traces its origins to [PERSON] and [PERSON] [PERSON] and [PERSON] (2016), who first introduced the green vehicle routing problem, emphasizing that fleets with limited range must visit energy replenishment infrastructures mid-route. Current main EVRP variants include EVRP with time windows (EVRP-TWs) [PERSON] _et al._ (2017), EVRP with heterogeneous fleets (EVRP-HFs) [PERSON] _et al._ (2017), and EVRP with multiple depots (EVRP-MDs) [PERSON] _et al._ (2017). Notably, few studies incorporate the capacity constraints of charging infrastructures (CIs), often assuming infinite capacity where vehicles can immediately start energy replenishment upon arrival. But real-world scenarios differ significantly, as the limited availability of CIs restricts the further adoption and widespread use of electric vehicles. This scarcity is reflected in both the number of CIs and the capacity of their internal charging units. During peak periods or holidays, electric vehicles frequently encounter long queues at CIs. For example, during the 2025 Spring Festival, severe charging congestion occurred on highways near major cities such as Beijing, Shanghai, and Hangzhou, with wait times reaching 1-2 h. For electric logistics vehicles, time-consuming charging queues are particularly detrimental. This hampers the operational efficiency of fleet, presenting a critical challenge that demands urgent resolution. It is worth noting that the assumption of infinite CI capacity holds partial validity in urban areas with dense charging networks, as illustrated by the node distribution in Figure 1a. In such regions, CIs are distributed among customer points and located relatively close to the depot, providing diverse replenishment options and reducing the likelihood of capacity bottlenecks at individual CIs. Nonetheless, as previously discussed, the capacity limitations of CIs remain a substantial constraint when the energy replenishment demand is high, particularly in scenarios where resource scarcity persists. In suburban or rural areas with sparse energy replenishment infrastructures and customer points far from a depot, these capacity limitations play a decisive role [PERSON] _et al._ (2017). The smaller the capacity, the higher the probability of charging resource contention among vehicles, as illustrated in Figure 1b. In addition to insufficient consideration of CI capacity constraints, most existing EVRP studies assume charging as the sole energy replenishment method, with limited exploration of heterogeneous energy replenishment infrastructures (HERIs), which integrate both CIs and battery swapping infrastructures (BSIs) [PERSON] _et al._ (2017).