基于BP神经网络的无约束优化方法

An Unconstrained Optimization Method Based on BP Neural Network

针对具有黑箱特性的无约束优化问题,在BP神经网络函数拟合的基础上,提出基于双曲正切传递函数BP神经网络的无约束优化方法。文章以网络输出极小化数学模型为例,阐述了无约束优化方法的基本思路,推导了网络的输出对输入的一阶导数(梯度),给出了初始试验步长计算公式和优化方法的终止准则,在此基础上,阐述了优化方法的实现流程。最后,将优化方法应用到两个典型的无约束优化问题进行示例验证,优化结果表明该方法是解决黑箱优化问题的一种稳定可行算法。

On the basis of BP neural network function fitting, this paper proposes an optimization method based on back-propagation(BP) neural network that uses hyperbolic tangent function as transfer function to solve the unconstrained optimization problems with characteristic of black-box. The paper takes the mathematical model of network output minimization as an example to illuminate the basic idea of unconstrained optimization method and deduce the first-order derivative(gradient) of network output with respect to input, and then gives the formula for calculating the initial test step size and the termination criterion of the optimization method, on basis of which the realization process of the optimization method is described. Finally, the optimization method is applied to two typical unconstrained optimization problems for example verification, and the optimization result shows that the proposed method is a stable and feasible algorithm to solve the problem of black-box optimization.