分数阶扩散方程参数反演的改进花朵授粉算法

An improved flower pollination algorithm for parameters inversion of fractional order diffusion equation

为解决传统花朵授粉算法容易受到局部极值影响的问题,将共享机制的小生境策略与花朵授粉算法相结合,提出了一种新的小生境花朵授粉算法,并将之应用于空间分数阶扩散方程的参数反演研究,以期为污染物寻源和空气污染防治提供一定的理论依据.为确保算法的寻优能力及寻优精度,首先,选取20个多模态函数,将算法改进前后的寻优性能进行对比,以验证改进算法的性能;然后,针对污染寻源问题,基于相应的空间分数阶反常扩散方程模型,运用隐式差分格式求解正问题,并采用花朵授粉算法和改进算法反演源项和扩散系数;最后,针对所提出的算法,从种群数、转换概率和搜索区间方面进行了灵敏度分析,并进一步讨论了算法的抗噪性.数值算例结果表明,对于空间分数阶反常扩散方程参数反演问题,改进后的花朵授粉算法反演效果更好,数值精度更高,可以达到理想水平.

To overcome the premature problem of the traditional flower pollination algorithm,a novel niche flower pollination algorithm is proposed by combining the niche strategy with flower pollination algorithm.It is designed for the parameter inversion of the space fractional order diffusion equation,so as to provide some theoretical basis for the pollutants source identification and air pollution prevention.Firstly,twenty multimodal functions were selected to verify the performance of the flower pollination algorithm and its improved algorithm.Then,we carried out direct simulation with implicit finite difference scheme.Based on the forward simulation results,the flower pollination algorithm and the improved algorithm were applied to invert the source term and the diffusion coefficients of the space fractional differential equation.The sensitivity analysis of the proposed algorithms regarding initial interval,perspectives of population and transition probability has also been completed.Furthermore,the anti-noise properties of the proposed algorithms were discussed.The numerical results demonstrate that the improved flower pollination algorithm has achieved a higher precision and accuracy.