GM-CPSO: A New Viewpoint to Chaotic Particle Swarm Optimization via Gauss Map

Abstract

Chaos concept has been appealed in the recent optimization methods to achieve a convenient tradeoff between exploration and exploitation. Different chaotic maps have been considered to find out the appropriate one for the system dynamics. However, on particle swarm optimization (PSO), the usage of these maps has not been handled in an extensive manner, and the best fit one has not known yet. In this paper, ten chaotic maps are handled to reveal the best fit one for PSO, and to explore whether chaotic maps are necessary for PSO or not. Thirteen benchmark functions are used to perform a detailed evaluation at the first experiment. Chaotic PSO (CPSO) methods including different maps are tested on global function optimization. Concerning this, Gauss map based CPSO (GM-CPSO) has come to the forefront by achieving promising fitness values in all function evaluations and in comparison with the state-of-the-art methods. To test the efficiency of GM-CPSO on a different task, GM-CPSO is hybridized with neural network (NN) at the second experiment, and the epileptic seizure recognition is handled. Discrete wavelet transform (DWT) based features, GM-CPSO and NN are considered to design an efficient framework and to specify the type of electroencephalography signals. GM-CPSO-NN is compared with hybrid NNs including two state-of-the-art optimization methods so as to examine the efficiency of GM-CPSO. To accurately test the performances, twofold cross validation is realized on 11,500 instances, and four metrics [accuracy, area under ROC curve (AUC), sensitivity, specificity] are consulted for a detailed assessment beside of computational complexity analysis. In experiments, GM-CPSO including the necessary map, has provided remarkable fitness scores over the state-of-the-art optimization methods on optimization of various functions defined in different dimensions. Besides, the proposed framework including GM-CPSO-NN, has achieved remarkable performance by obtaining reliable accuracy (97.24%), AUC (95.67%), sensitivity (93.04%) and specificity (98.29%) scores, and by including less computational complexity than other algorithms. According to the results, GM-CPSO has arisen as the most convenient optimization method to be preferred in the formation of hybrid NNs. In addition to optimization and classification results, it's seen that the detail sub-bands of DWT comprise necessary information for seizure recognition. Consequently, it's revealed that GM-CPSO can be preferred on global function optimization for reliable convergence, and its usage can be extended to different disciplines like signal classification, pattern recognition or hybrid system design.