IEEE Trans Cybern. 2019 Jan;49(1):69-82. doi: 10.1109/TCYB.2017.2764744. Epub 2017 Oct 31.
One of the major obstacles in using radial basis function (RBF) neural networks is the convergence toward local minima instead of the global minima. For this reason, an adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm is designed to optimize both the structure and parameters of RBF neural networks in this paper. First, the AGMOPSO algorithm, based on a multiobjective gradient method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance. Second, the AGMOPSO-based self-organizing RBF neural network (AGMOPSO-SORBF) can optimize the parameters (centers, widths, and weights), as well as determine the network size. The goal of AGMOPSO-SORBF is to find a tradeoff between the accuracy and the complexity of RBF neural networks. Third, the convergence analysis of AGMOPSO-SORBF is detailed to ensure the prerequisite of any successful applications. Finally, the merits of our proposed approach are verified on multiple numerical examples. The results indicate that the proposed AGMOPSO-SORBF achieves much better generalization capability and compact network structure than some other existing methods.
径向基函数（RBF）神经网络的主要障碍之一是倾向于局部最小值而不是全局最小值。出于这个原因，本文设计了一种自适应梯度多目标粒子群优化（AGMOPSO）算法，用于优化 RBF 神经网络的结构和参数。首先，基于多目标梯度方法和自适应飞行参数机制开发了 AGMOPSO 算法，以提高计算性能。其次，基于 AGMOPSO 的自组织 RBF 神经网络（AGMOPSO-SORBF）可以优化参数（中心、宽度和权重），并确定网络规模。AGMOPSO-SORBF 的目标是在 RBF 神经网络的准确性和复杂性之间找到一个权衡。第三，详细分析了 AGMOPSO-SORBF 的收敛性，以确保任何成功应用的前提条件。最后，在多个数值示例上验证了所提出方法的优点。结果表明，与其他一些现有方法相比，所提出的 AGMOPSO-SORBF 具有更好的泛化能力和紧凑的网络结构。
