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梯度下降法与混沌优化法均具有各自的缺点。该文将二者结合起来,利用混沌运动的遍历性,将混沌因子引入到变步长中,对梯度下降法进行改进。首先利用混沌变量来初始化步长大小,并随着搜索过程向最优点靠近,逐渐调整混沌变量,从而使步长的变化也不断变小,以使最优点附近步长波动平稳,避免了梯度下降法拉锯现象的产生。通过3个典型算例,用该算法和梯度下降法以及其他2种算法进行了优化计算对比。结果表明,采用该算法的迭代次数减少了45%以上。
Gradient descent method and chaos optimization method all have their own shortcomings. In this paper, the two are combined to make use of the ergodicity of chaotic motion. The chaos factor is introduced into the variable step and the gradient descent method is improved. Firstly, chaos variables are used to initialize the step size. As the search process approaches the optimal point, the chaos variables are gradually adjusted so that the step size changes continuously, so that the step size near the optimal point is stable and the gradient is reduced Faw sawing phenomenon. Through three typical examples, the algorithm is compared with the gradient descent method and the other two algorithms. The results show that the number of iterations using this algorithm is reduced by more than 45%.