## 1 Introduction  
Transmission lines encased in ice present multifaceted threats such as insulator flashover, conductor galloping, circuit tripping, power outages, and disruption of communication systems [1, 2]. These phenomena critically undermine productivity dsand livelihoods while accruing considerable economic losses [3], thereby posing a substantial obstacle to the secure and consistent operation of power systems [4]. Consequently, the investigation into icing prediction models is paramount for strategic line planning, efficient allocation of de-icing operations, and guaranteeing a safe and dependable electricity supply within the power grid [5]. In recent years, substantial research efforts have been undertaken by scholars, yielding significant advancements in the field of icing prediction on transmission lines. Present studies suggest that prediction models for icing on transmission lines can be broadly categorized into three distinct types, as delineated in Table 1 [6, 7]. In recent years, the profound integration of machine learning into fault diagnosis and power load forecasting has spurred its extension into the realm of transmission line icing prediction, where it has demonstrated notable success [8]. [PERSON] et al. advanced the field by proposing an online transmission line icing prediction model underpinned by data-driven methodologies. The findings reveal that this model surpasses traditional prediction models in both predictive accuracy and generalizability [9]. [PERSON] et al. introduced a novel machine-learning-based approach for predicting the health index of overhead transmission lines, specifically focusing on high-voltage overhead lines. The proposed method's elevated accuracy and applicability were corroborated through a comparative analysis of the model's predicted values against empirical data [10]. Nevertheless, most of the aforementioned studies neglected the optimization of hyperparameters in their machine-learning models, leading to unstable prediction accuracies and significant random fluctuations. Consequently, enhancing the model's predictive efficacy necessitates the integration of advanced artificial intelligence optimization techniques with machine-learning models for hyperparameter optimization, thereby constructing a sophisticated model foricing prediction [11]. [PERSON] et al. employed the classical Particle Swarm Algorithm (PSO) as an intelligent optimization tool to iteratively refine the primary parameters of the SVR. The extensive training of the model with a substantial dataset substantiated the proposed model's remarkable enhancements in both effectiveness and accuracy. Nevertheless, this model exhibits limited efficacy in extracting feature dimensions from chaotic time series, and its complexity escalates substantially with increased embedding dimensions [12]. [PERSON] et al. innovated with a hybrid icing prediction model, amalgamating wavelet transform (WT) and bat algorithm-enhanced extreme learning machine (BA-ELM). In this model, WT is utilized for denoising meteorological data, while the BA optimizes input weights and bias thresholds, culminating in a robust icing prediction framework. However, this offline model does not enhance the standard ELM, resulting in constrained generalizability [13]. The icing prediction for transmission lines is inherently uncertain and nonlinear, attributed to its vulnerability to climatic variables like temperature, humidity, and wind speed. Owing to their simplicity and adaptability, meta-heuristic algorithms, renowned for their efficacy in addressing nonlinear and multimodal challenges, have gained traction among scholars for parameter optimization in machine learning models. Nonetheless, meta-heuristic algorithms are commonly critiqued for their slow convergence rates and propensity to fall into local optimal solutions, necessitating further refinement. Enhancing and optimizing meta-heuristic algorithms is imperative to augment the predictive accuracy of conventional machine learning models.