## 1 Introduction  
Electrified railways are a vital component of modern transportation systems, as they have been globally developed owing to their high efficiency, environmental friendliness, and energy-saving benefits. A well-maintained catenary system is crucial for efficient and safe railway operations [1]. In current catenary system maintenance practices, catenary maintenance vehicles serve as one of the key operational units, capable of performing transportation, maintenance, and inspection tasks [2]. To enhance economic efficiency and adhere to sustainable development principles, adopting effective strategies that reduce the energy consumption of catenary maintenance vehicles is essential [3]. One promising approach is the optimization of the operating curves of these vehicles, commonly known as eco-driving. This method optimizes the operating curve by accounting for factors such as vehicle performance and track conditions, with the goals of maximizing energy savings, allowing smoother operations, and increasing safety [4]. Given the inherently multi-objective nature of train operation optimization, which involves generating multiple potential speed profiles via extensive solution space exploration, multi-objective evolutionary algorithms based on Pareto optimization have achieved significant advancements. For instance, [PERSON] et al. demonstrated that multi-objective particle swarm optimization (MOPSO) generates Pareto-optimal solutions for running time and energy consumption more efficiently than GA [5]. In addition, [PERSON] et al. developed an online optimization algorithm using MOPSO for high-speed trains, leveraging real-world operational data [6]. Furthermore, [PERSON] et al. developed a hybrid evolutionary algorithm that combines differential evolution (DE) and simulated annealing (SA) to identify Pareto fronts, enabling energy-efficient driving strategies across various journey times [7]. Recent advancements include the results achieved by [PERSON] et al., who introduced a real-time optimization framework utilizing NSGA-II and MOPSO for adjusting the dynamic speed trajectory during train delays [8]. In addition, [PERSON] et al. developed a hybrid strategy that accounts for energy efficiency, running time, and comfort, utilizing an improved particle swarm optimization (HS-MOPSO) algorithm [9]. Furthermore, [PERSON] et al. proposed a time-energy optimization framework that incorporates dynamic train mass estimation using K-means clustering of passenger flow data and an improved adaptive NSGA-II algorithm [10]. Moreover, [PERSON] et al. improved an enhanced multi-objective ant colony (MOACOr) algorithm, which demonstrated superior convergence and diversity compared to NSGA-II [11]. [PERSON] et al. introduced a novel conscious search (CS) heuristic algorithm featuring global and local search phases, which outperformed traditional heuristic methods in determining optimal train speed profiles [12]. [PERSON] et al. validated the effectiveness of an improved NSGA-II algorithm via comparative analyses with GA and PSO for metro train energy-saving operations [13]. However, recent studies on Pareto front solution sets predominantly focus on two or three objectives and do not extensively explore higher-dimensional problems [11; 14; 15; 16]. Algorithms such as NSGA-II perform well for low-dimensional multi-objective problems (M \(\leq\) 3) [15; 17; 13], but they encounter significant challenges in high-dimensional optimization (M \(>\) 3). These challenges stem from exponentially increasing computational demands to perform crowding distance calculations and the diminished selection pressure from Pareto dominance relations. Although these algorithms can generate Pareto solutions, the exponential growth of non-dominated individuals complicates the differentiation [18].