Dimensional Weighted Firefly Algorithm And Its Application In A Class Of Variational Problems

Firefly algorithm is a bionic optimization algorithm based on biological swarm intelligence which has the advantages of simple concept,few parameters to adjust and easy to realize.It has aroused widespread concern of scholars at home and abroad.In order to improve the effect of standard firefly algorithm on high dimensional optimization problem,Verma et al.proposed an improved algorithm based on opposition and dimension,and improved the population initialization and algorithm iteration.Based on the dimensionality weighting method,this paper presents a new improvement to Verma et al.'s algorithm,and proposes an improved firefly algorithm based on dimension weighting,which takes into account the current best flame information and some firefly information.The experimental results show that the improved algorithm has better ability of searching.In addition,considering the potential effect of the initial point information on the optimal solution of the algorithm,this paper analyzes the dependency of the optimal solution of the firefly algorithm on the initial point by using the similarity coefficient and the correlation test of the data.Secondly,this paper transforms the two-point boundary value problem of the differential equation into the functional extremum problem by using the variational principle,and then constructs the approximate function by using the Ritz method or the two-point Hermite interpolation method.The functional extremum problem is transformed into a multiple optimization problem that can be solved by the improved firefly algorithm.Finally,an improved firefly algorithm with penalty function is proposed to solve the general constraint optimization problem by combining the dimensional weighted firefly algorithm with the penalty function method.Through the comparison of experimental results,the algorithm embodies better convergence and optimization ability.