遗传算法在求解反问题中的应用

Application of GA in Solving Inverse Problems

以数学物理方程为研究对象,采用改进的遗传算法与Tikhonov正则化方法,对方程的算子进行模拟与识别,分别用余弦函数与帽子函数对其进行拟合。在使用遗传算法搜索拟合系数的过程中,交叉概率逐渐取大,变异概率逐渐取小,提高了算法的收敛速度。采用该方法得到的曲线与原问题的曲线相比,结果更好。

Aiming at mathematical -physical problems, the improved GA and Tikhonov regularization methods were used to simulate and identify the operator of the function. The cosine function and hat function were separately used to fit it. In the progress of searching the modulus of fitting function by using GA, the probability of crossover is getting bigger, and the mutation is getting smaller, which enhances tbe speed of the algorithm convergence. Compared with the previous curve, the proposed method is preferable.