## 1 Introduction
BSI offers battery-swapping as an energy replenishment option for EVs, which can be completed within 3-10 min using specialized equipment or by trained technicians, significantly reducing energy replenishment times compared to charging. A schematic of this technology is shown in Figure 2. Tesla attempted to deploy battery swapping infrastructures (BSIs) in 2013. However, the project  
Figure 1: Impact of CI capacity under different node distributions. (**a**) CI capacity is not a bottleneck factor, (**b**) CI capacity is a bottleneck factor. ultimately failed due to financial constraints [13]. In fact, battery swapping solutions for EVs are now predominantly implemented in China. The Chinese EV manufacturer NIO has deployed over 3000 BSIs nationwide since 2018. Therefore, the collaborative use of CIs and BSIs represents an energy replenishment model with both technical feasibility and broad application prospects. Due to the NP-hard nature of EVRP and the complexity introduced by integrating HERI, vehicle energy replenishment decisions become highly intricate and challenging. Further incorporating the capacity constraints of CI amplifies the heterogeneity among energy replenishment infrastructures, significantly complicating the solution process. In light of the aforementioned challenges, this study introduces a novel variant of EVRP with heterogeneous energy replenishment infrastructures under capacity constraints (EVRP-HERI-CCs). The objective is to minimize the total delivery cost of the electric logistics vehicle fleet with integrated charging and battery swapping capabilities by leveraging HERI under limited charging resources. Here is a brief summary of this paper's main contributions:  
* Extension of EVRP to EVRP-HERI-CCs: Conventional EVRP studies have generally assumed charging-based energy replenishment, overlooking both HERI networks and CI capacity constraints in their problem formulations. By distinguishing the functional independence of CI and BSI and imposing capacity limitations on CI, we extend the classical EVRP into EVRP-HERI-CCs, highlighting the unique characteristics and advantages of heterogeneous energy replenishment networks. * MIP model and heuristic algorithm: We formulate the MIP model tailored to the problem and design a HACO algorithm integrated with a VNS mechanism. The algorithm incorporates a dynamic rescheduling mechanism that proactively resolves charging conflicts through global optimization during its two-phase solution construction process, thereby maximizing the utilization of available charging resources. Furthermore, it employs an energy management strategy to transition from full charging to partial charging, reducing energy replenishment costs. Extensive numerical experiments validate the algorithm's effectiveness. * In-depth analysis of capacity constraints of CI: Computational experiments confirm that the proposed algorithm adaptively optimizes routing plans under CI capacity constraints by leveraging HERI synergies, with comparative cost analyses and large-scale sensitivity studies providing actionable insights for CI capacity deployment. The remainder of this paper is structured as follows: Section 2 provides a comprehensive review of the relevant literature. Section 3 formulates the problem and develops the mathematical models. The proposed solution methodology is detailed in Section 4. Section 5 discusses the computational experiments and analyzes the results. The paper concludes with key findings and implications in Section 6. Figure 2: Schematic diagram of battery swapping technology.