基于Bernstein多项式构造前向神经网络的遗传算法

首先, 介绍一元Bernstein多项式的逼近定理和基本性质, 并引入二元甚至n元Bernstein多项式, 从而根据一元Bernstein多项式在相邻等距剖分点的差值为后置连接权构造一个三层前向神经网络； 其次, 通过编码机制、 模拟选择、 遗传复制、 交叉和变异等操作给出算法运行过程； 最后, 利用误差函数和适用度函数对前置连接权及阈值进行迭代更新设计遗传算法. 实验结果表明该算法有效.

Genetic Algorithm Based on Bernstein Polynomial for Constructing Forward Neural Network

Firstly, the approximation theorem and basic properties of one-dimensional Bernstein polynomial were introduced, and two-dimensional or even n-dimensional Bernstein polynomials were introduced, and then a three-layer forward neural network was constructed by using the difference values of Bernstein polynomials in the adjacent equidistant points as the back connection weights. Secondly, the operation process of the algorithm was given through coding mechanism, simulation selection, genetic duplication, crossover and mutation. Finally, the error function and fitness function were used to iterate and update the front connection weights and threshold to design a genetic algorithm for the network. The experimental result shows that the algorithm is effective.