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.

Graphical Abstract

中文翻译：

---

GM-CPSO：通过高斯图进行混沌粒子群优化的新观点

摘要

混沌概念在最近的优化方法中受到人们的欢迎，以实现勘探与开发之间的便利权衡。已经考虑了不同的混沌图来找到适合系统动力学的混沌图。但是，在粒子群优化（PSO）上，这些贴图的使用尚未得到广泛处理，最合适的贴图还未知。在本文中，处理了十张混沌图，以揭示最适合PSO的一种，并探讨了混沌图对于PSO是否必要。在第一个实验中，十三项基准函数用于执行详细评估。在全局功能优化上测试了包括不同映射的混沌PSO（CPSO）方法。关于这个，基于高斯图的CPSO（GM-CPSO）通过在所有功能评估中达到有希望的适应度值以及与最新方法进行比较而走在前列。为了测试GM-CPSO在不同任务上的效率，在第二个实验中将GM-CPSO与神经网络（NN）进行了杂交，并处理了癫痫发作识别。考虑使用基于离散小波变换（DWT）的功能GM-CPSO和NN设计有效的框架并指定脑电图信号的类型。将GM-CPSO-NN与包括两种最新优化方法的混合NN进行比较，以检验GM-CPSO的效率。为了准确测试性能，我们在11,500个实例上进行了双重交叉验证，并采用了四个指标[准确性，ROC曲线下面积（AUC），灵敏度，除了计算复杂性分析外，还可以咨询[特异性]。在实验中，包括必要图的GM-CPSO在最先进的优化方法（在不同维度上定义的各种功能的优化）上提供了显着的适应性评分。此外，包括GM-CPSO-NN在内的拟议框架通过获得可靠的准确度（97.24％），AUC（95.67％），敏感性（93.04％）和特异性（98.29％）得分以及包括较少的计算复杂性而取得了卓越的性能。比其他算法。根据结果​​，GM-CPSO已成为最便捷的优化方法，成为混合神经网络的首选。除了优化和分类结果，可以看出，DWT的细节子带包含癫痫发作识别所需的信息。因此，揭示了GM-CPSO可以在全局功能优化中首选，以实现可靠的收敛，并且其用法可以扩展到不同的领域，例如信号分类，模式识别或混合系统设计。

图形概要