# Locating the Parameters of RBF Networks Using a Hybrid Particle Swarm Optimization Method
###### Abstract  
In the present work, an innovative two-phase method is presented for parameter tuning in radial basis function artificial neural networks. These kinds of machine learning models find application in many scientific fields in classification problems or in function regression. In the first phase, a technique based on particle swarm optimization is performed to locate a promising interval of values for the network parameters. Particle swarm optimization was used as it is a highly reliable method for global optimization problems, and in addition, it is one of the fastest and most-flexible techniques of its class. In the second phase, the network was trained within the optimal interval using a global optimization technique such as a genetic algorithm. Furthermore, in order to speed up the training of the network and due to the use of a two-stage method, parallel programming techniques were utilized. The new method was applied to a number of famous classification and regression datasets, and the results were more than promising. neural networks; particle swarm optimization; genetic algorithms +
Footnote †: journal:  
0000-0001-6000-0000-0000-0000-0000-0000-0000-00000-00000-0000-0  
equations [11; 12], digital communications [13; 14], physics [15; 16], chemistry [17; 18], economics [19; 20; 21], network security [22; 23], etc. RBF networks were thoroughly discussed in [24], and they have been parallelized in a variety of research papers [25; 26]. This model has been extended by various researchers in tasks such as creating new initialization techniques for the network parameters, [27; 28; 29], pruning techniques [30; 31; 32], the construction of RBF networks [33; 34; 35] etc. In this work, a hybrid technique is proposed for the optimal calculation of the parameters of an RBF network. This technique consists of two phases. During the first phase, information was collected from the training data of the neural network and an attempt was made to identify a small interval of values for the neural network parameters. To identify this interval, an optimization method was used, which gradually creates the optimal value interval, which was estimated to give the lowest value for the training error of the network. To locate the optimal interval, the Particle Swarm Optimization (PSO) technique was used [36]. The PSO method was chosen for the first phase because it is fast and flexible enough for optimization problems, does not require a large number of parameters to be input by the user, and has been successfully used in a variety of problems such as flow shop scheduling [37], developing charging strategies for electric vehicles [38], emotion recognition [39], robot trajectory planning [40], etc. The detection of the value interval was performed in order to then make the minimization of the network error faster and more efficient in the second phase of the optimization method. In the second phase, the parameters of the neural network were optimized within the optimal value interval of the first phase. The optimization can be performed by any global optimization method [41]. In this work, genetic algorithms [42; 43; 44] were chosen for the second phase. The main advantages of genetic algorithms are tolerance to errors, easy implementation in parallel, efficient exploration of the search space, etc. Recently, much work has been appeared to tune the parameters of machine learning models, such as the work of [PERSON] and [PERSON] [45] for the adaptation of the RBF parameters, the incorporation of an improved ABC algorithm to adapt the parameters of RBF networks [46], the usage of the Firefly algorithm for optimization [47], along with machine learning models for cervical cancer diagnosis [48], the adaptation of the CNN and XGBOOST models by an optimization algorithm for COVID-19 diagnosis [49], etc.