Seasonally ice-bound ground are subjected to cyclic freeze-thaw processes, which can significantly degrade their mechanical properties, including static strength (Ss). To accurately characterize and predict the Ss of seasonally frozen soils, this research employs advanced machine learning techniques. Specifically, the study utilizes the Least Square Support Vector Regression (LSSVR) method, which is known for its robust performance in nonlinear regression tasks. A critical aspect of the LSSVR model is the appropriate selection of its hyperparameters, namely the penalty agent (c) and the breadth of the kernel function (g). To determine these parameters with high precision, the research integrates the LSSVR model with two novel optimization techniques: the Flow Direction Algorithm (FDA) and the Artificial Rabbit Optimization (ARO). The resulting hybrid models, denoted as LS(ARO) and LS(FDA), are designed to outperform the previously published Artificial Neural Network (ANN) approach in predicting the Ss of seasonally frozen soils. The Implementation of the proposed hybrid approaches is assessed by a comprehensive database of 120 soil samples collected from relevant published studies. The input parameters used in the frameworks include water content, negative temperature, confining stress, freeze-thaw processes, thawing time, and compaction ratio. The results demonstrate the superiority of the hybrid models, with the LS(ARO) network achieving remarkable R2 amounts of 0.9924 and 0.9976 during the train and test steps, respectively. Moreover, the LS(ARO) model outperformed the LS(FDA) and the previously reported ANN model in terms of other performance metrics, such as Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The results of the present research expand the recognizing and predictive capabilities of Ss in seasonally frozen soils, which is crucial for infrastructure design and construction in cold regions. The integration of the LSSVR technique with the novel FDA and ARO optimization algorithms represent a significant advancement in the field of hybrid regression analysis for geotechnical engineering applications.