## 2 Multi-Objective Operation Model  
### Operation Strategy Analysis  
Figure 1 schematically illustrates the operational workflow of railway overhead contact line maintenance vehicles within designated track sections. Following established daily operational protocols, the maintenance vehicle is deployed from a predetermined origin point (D\({}_{1}\)) to execute scheduled tasks within a predefined temporal window. The vehicle sequentially accesses multiple target nodes (D\({}_{2}\), D\({}_{3}\), \(\cdots\), D\({}_{K}\), \(\cdots\), D\({}_{N-1}\)) along the designated route to perform essential line maintenance operations while simultaneously facilitating personnel and equipment transportation. Following the completion of these scheduled interventions, the vehicle returns to its initial departure point D\({}_{1}\) (denoted as D\({}_{N}\) in the cyclic operational sequence), thereby forming a closed-loop operational circuit that fulfills comprehensive maintenance requirements within the specified track section. Figure 2 compares the speed profiles of two operational strategies between adjacent target points: the four-stage operational strategy and the minimum runtime strategy. The four-stage strategy divides operations into traction, cruising, coasting, and braking phases. In practice, operators often prioritize efficiency by adopting the minimum runtime strategy, which involves maximum traction acceleration, sustained cruising, and immediate maximum braking. While this method minimizes travel time, it may compromise other operational parameters such as energy efficiency, comfort, and safety. When analyzing operational strategies, the discrete sequences of operational conditions across maintenance sections can be consolidated into a matrix of condition transition points. This matrix can be systematically mapped to specific speed profiles, facilitating the derivation and comparative analysis of the corresponding energy consumption, time efficiency, comfort, and safety metrics. Specifically, for the section \((S_{SP},S_{TP})\), the operational sequence can be described as follows. The maintenance vehicle begins its journey from the starting point \(S_{SP}\), accelerating during the traction phases until reaching the traction-to-criuse transition point \(S_{TC}\). It then maintains a constant cruising speed until arriving at the cruise-to-coasting transition point \(S_{TC}\), where traction is discontinued. Subsequently, the vehicle continues in the coasting  
Figure 1: Schematic diagram of scheduled round-trip maintenance operations for a railway catenary maintenance vehicle. Figure 2: Speed profiles of the four-stage operational and minimum running time strategies. phases at a constant speed \(V_{CR}\) until reaching the coasting-to-braking transition point \(S_{CB}\), where the braking strategy is activated to completely stop the vehicle at the designated target point \(S_{TP}\). To address comfort considerations, relying solely on maximum traction and braking forces is suboptimal. Instead, a range of traction and braking forces should be utilized to enable a comprehensive comparison and analysis of the control strategies. Accordingly, based on the characteristic curves of the maximum traction and braking forces, the vehicle is configured to execute start-acceleration and brake-stop phases using specific levels of traction and braking forces by adjusting the proportionality coefficients \(\eta_{T}\) and \(\eta_{B}\). For the traction phase, the traction-to-cruise transition point and the corresponding cruise speed \(V_{CR}\) are determined using forward calculations of process data from the starting point \(S_{SP}\). Establishing these parameters involves sequentially computing each step in the traction mode. Conversely, for the braking phase, the braking initiation point \(S_{CB}\) is derived using the reverse calculation of process data from the endpoint \(S_{TP}\).