A Pi-Sigma artificial neural network based on sine cosine optimization algorithm

Pi-Sigma artificial neural network, which is a special artificial neural network model, is an artificial neural network that can be thought as a combination of different types of neuron models. Since Pi-Sigma artificial neural networks contain both additive and multiplicative structures, it can also be expressed as an artificial neural network model in which both multiplicative neuron model and perceptron are used together. One of the most important success criteria of the Pi-Sigma artificial neural networks is the optimization algorithm used in the training of the network, as in many artificial neural networks. The optimization algorithms used in the training of the network are divided into two parts as derivative-based algorithms and artificial intelligence optimization method-based algorithms. The artificial intelligence optimization algorithms have been used frequently in recent years compared with derivative-based algorithms due to many advantages. As known, one of the success criteria of an artificial neural network model is its training algorithm. Although many optimization algorithms are used in the training of Pi-Sigma artificial neural networks in the literature, the sine cosine algorithm, which is simpler, understandable, and easy to use, has not yet been used compared with many artificial intelligence optimization algorithms. In this study, the sine cosine algorithm is used for the first time in the training of Pi-Sigma artificial neural networks. The motivation of the paper is the about the evaluation of sine cosine algorithm performance in the training of Pi-Sigma artificial neural networks. The reason for the preference of using sine cosine algorithm is that the algorithm has not some specific operators that many artificial optimizations have and it uses the advantages of sine cosine functions easily. The performance of the proposed method is compared with many methods that are frequently used in the forecasting literature, especially many artificial neural networks models that use different optimization algorithms in the training process. Some popular time series, which are frequently used in the forecasting literature, are used in the analysis process, and as a result of the analysis process, it is concluded that the proposed method has better performance than other methods.