对流扩散方程系数反演的改进遗传算法

Coefficient Inverse Problem of Convection-diffusion Equation Using the Improved Genetic Algorithm

在标准遗传算法的基础上,利用欧氏距离来判断个体之间的相似程度。通过竞争,相似程度高且适应度差的个体被淘汰,并辅以随机交叉算子和随机变异算子,构造出了一种改进的遗传算法。改进的遗传算法在迭代过程中既能有效保持群体的多样性,避免出现局部极值,提高遗传算法的内在并行性,又能通过竞争淘汰,使搜索能力得到加强,加快了搜索速度。实验表明,改进的遗传算法能有效的应用于对流扩散方程系数反问题的求解。

An improved Genetic Algorithm is constructed based on the normal Genetic Algorithm, which using the Euclidean Distance to evaluate the similarity between the individuals, the individual of higher similarity and lower fitness eliminated, accompanying with the rand crossover operator and rand mutation operator. The improved Genetic Algorithm Can not only keep the population colorful, avoid local convergence and increase the inner property, but also can strengthen the ability of searching and increase the speed of searching through the elimination in the iterative process. Numerical example shows that the improved Genetic Algorithm can solve the coefficient inverse problem of convection-diffusion equation effectively.