最佳化B-spline神經網路近似非線性函數-使用基因演算法

Abstract

在本文中，吾人提出一種利用最佳化B-spline類神經網路來近似非線性函數的方法。傳統的B-spline函數是固定基礎函數，然而本文是利用基因演算法來對 B-spline類神經網路的基礎函數及控制點做最佳化的調整。而且基因演算法可以藉由突變的運算，跳脫一般學習法則（如梯度下降法）在學習過程中可能會落入區域極值，無法找到系統的最佳值的問題。染色體由實數的方式組成，包括了B-spline類神經網路中的Knot向量及控制點。藉著B-spline區間調整的特性，使系統作細微的調整。最後以模擬例子驗證本論文方法的功效。

In this paper, we propose an optimal B-spline neural network to approximate a nonlinear function. Traditionally, a B-spline function has fixed-form blending functions. Genetic algorithms are used to optimize the blending functions and the control points of B-spline neural networks. The mutation operator in genetic algorithms can avoid falling into local minimum during the learning process. Chromosomes include the knot vectors and the control points of a B-spline neural network. Since the local tuning property, the fine-tuning ability of a B-spline neural network can be obtained. Finally, the simulation results demonstrate the effectiveness of the proposed method.