基于BP神经网络的无约束优化方法  

An Unconstrained Optimization Method Based on BP Neural Network

作　　者：董志贵[1] 王福林[1] 宋庆凤 吴志辉[1] Dong Zhigui;Wang Fulin;Song Qingfeng;Wu Zhihui(College of Engineering,Northeast Agricultural University,Harbin 150030,China;Clinical College,HE University,Shenyang 110027,China)

机构地区：[1]东北农业大学工程学院,哈尔滨150030 [2]辽宁何氏医学院临床学院,沈阳110027

出　　处：《统计与决策》2019年第1期79-82,共4页Statistics & Decision

基　　金：国家自然科学基金面上项目(31071331);国家"十二五"科技支撑计划课题子课题(2014BAD06B04-2-9)

摘　　要：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.

关 键 词：BP神经网络 无约束优化 黑箱问题 试验步长 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]