Research On Flower Pollination Algorithm For Parameters Inversion Of Space Fractional Order Anomalous Diffusion Equation

In recent years,air pollution has seriously endangered people's health and living environment.The fog and haze appear frequently in some cities and cause varying degrees of problems of traffic and transport problems,which will hinder the development of the global economy.Air pollution is not only a problem for a city or a country,but also the problem of whole world.Therefore,the study of air pollution problems has become more and more urgent.Based on the space fractional order anomalous diffusion equation,diffusion coefficients and pollution source identification problems have been investigated with flower pollination algorithm and niche flower pollination algorithm in this thesis.It is well known that it is easy for the traditional flower pollination algorithm to be influenced by the local extremum,while the niche strategy can tackle this case effectively.So,in this dissertation,an improved flower pollination algorithm-niche flower pollination algorithm is proposed by combining the niche strategy based on the sharing principle with the flower pollination algorithm.The niche flower pollination algorithm deals with the influence of local extremum by adding the share function to the traditional algorithm,with which the fitness value between different individual can be adjusted.In order to verify the superiority of the improved algorithm,20 benchmark functions are used to compare the optimal results that obtained by different algorithms,such as niche flower pollination algorithm,flower pollination algorithm,genetic algorithm,improved genetic algorithm and cuckoo search algorithm.The numerical results show that the niche flower pollination algorithm has a higher precision and better convergence compared with the other algorithms.On the basis of the previous research results,the flower pollination algorithm and the improved algorithm are applied to invert the diffusion coefficients and the source term of the space fractional order anomalous diffusion equation.The sensitivity analysis of the proposed algorithms to initial interval,the perspectives of population,the transition probability and the number of niche has also been studied.Furthermore,the anti-noise properties of the proposed algorithms are discussed.The numerical results indicate that the improved flower pollination algorithm performs a higher accuracy.