基于混沌变量的变步长梯度下降优化算法

Decreasing gradient optimization algorithm with variable step length based on chaotic variables

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。

The decreasing gradient algorithm and chaos algorithm both have shortcomings for optimization problems. This paper presents a new algorithm which combines the 2 algorithms to produce a greatly improved decreasing gradient algorithm by introducing chaos variables into the variable step length to take advantage of the randomness of the chaotic movements. The step length was initialized using chaotic variables which were adjusted step by step as the search procedure reached the best point, so that the step length fluctuated smoothly and avoided oscillations which often arise in the decreasing gradient algorithm. The number of iterations was reduced by at least 45% compared with the other 2 algorithms mentioned above using 3 typical numerical examples.