###### Abstract
This algorithm calibrates the relation of input and output variables by transforming the nonlinear problem in a low-dimensional space into high dimension and finding a hyperplane to fit the relation between the input and output. Commonly used kernel functions of SVR include linear kernel functions, polynomial kernel functions, radial basis kernel functions, and sigmoid kernel functions [16]. Gaussian radial basis kernel function is the most widely used kernel in SVR and it has been applied in related fields [17]. In SVR, insensitive loss coefficient \(\epsilon\), penalty parameter \(C\), and parameter of kernel function directly affect the accuracy of prediction, while obtaining the optimal parameter combination is usually time-consuming. Therefore, it demands a proper optimization algorithm to enhance the accuracy of prediction. Numerous optimization algorithms with different applications have been developed by researchers in the published studies [18; 19; 20]. The grid search (GS) algorithm tests all possible parameter values to optimize and compares the result of each parameter combination for the optimal solution [21]. Numerous attempts guarantee the effectiveness in optimizing the penalty parameter and kernel function parameter, leading to high time consumption as well. Thus, research has been conducted to reduce the time cost by automatically changing the search range and step [22]. The genetic algorithm (GA) method is another optimization algorithm imitating the revolution of creatures and is applicably administered to determine optimal SVR parameters [23]. However, the genetic variation and crossover in GA cannot be controlled, which may induce poor prediction capability at times. Swarm intelligence [24], a subset of artificial intelligence (AI), has gained more attention, as more high-complexity problems require the acquisition of optimal solutions that are not achievable within a reasonable time by previous methods. It can be divided into insect-based algorithms and animal-based algorithms, according to the previous research. Among these algorithms, the firefly algorithm (FFA) has exhibited promising accuracy in monthly rainfall forecasting [25]. The main parameters of FFA, including \(\alpha\), \(\beta_{0}\), and \(\gamma\), unavoidably affect the result of optimization, and the determination of optimal parameter combination is costly; thus, applying FFA in an SVR model may not be quite favorable. Besides FFA, the particle swarm optimization (PSO) algorithm is another popular and straightforward optimization methodology, inspired by the collective behavior of social animals [26]. The inertia factor of PSO is the major factor affecting the result of optimization, thus this algorithm has been applied in nonlinear problem prediction and demonstrates good performance [27]. To avoid the local optimal solution, different methods are proposed to change the inertia coefficient in the process of iteration [28]. Besides SVR parameters, the input data is another factor dominating the accuracy of prediction. Thus, it is necessary to calibrate the input data for modeling icing time prediction. To obtain better accuracy, response surface methodology (RSM) is used in this paper for the optimization of input variables. RSM is a collection of mathematical techniques based on the fit of equation to experimental or real statistics [29], which describes the relation between response and input data. In recent studies, RSM has been gradually utilized to optimize the input variables for modeling SVR [30]. The prediction accuracy of SVR is greatly promoted after RSM is utilized to calibrate the input variables, which shows superiority to other methodologies [31]. The commonly used SVR prediction models are summarized in Table 1.  
This paper develops a hybrid improved SVR model for the prediction of pavement icing time by combining the advantages of RSM and PSO when calibrating SVR.