Single Incremental Global Dimension Learning Firefly Algorithm And Its Application In Portfolio Problems

The swarm intelligence algorithm originates from the group behavior in nature,has the advantages of fewer parameters,simple modeling,and does not need to consider gradient problems.Moreover,it performs very well on large-scale problems.Classical swarm intelligence algorithms include genetic algorithms,particle swarm optimization algorithms,and so on.Firefly algorithm is a newly proposed swarm intelligence algorithm in recent years.It simulates the flash courtship behavior of fireflies,abstracts individual fireflies into the solution of the algorithm,and uses optimization strategies to model the process of attracting fireflies to each other.Firefly algorithm is simple in concept and highly feasible,but it also has defects such as being prone to premature convergence and not fully utilizing superior firefly individuals.Scholars have done a variety of studies,introducing inertial weights to adjust the search ability of the Firefly algorithm,greatly improving the ease of the algorithm falling into premature convergence.This article first introduces optimization problems and several classical algorithms in swarm intelligence algorithms,then introduces the firefly algorithm and its excellent improved algorithms,and proposes a firefly algorithm based on single increment strategy and global dimension learning strategy(IWFA_SD).This algorithm greatly reduces the inertial impact of the current position,improves the ability of the algorithm to jump out of the local optimal solution,and enhances the global search ability.For the globally optimal firefly,multiple optimization enhancements are performed on them in any one dimension,and compared with the current firefly population.Corresponding movements are made to effectively avoid the situation where fireflies fall into the optimal firefly neighborhood.To verify the effectiveness of the proposed algorithm,comparative experiments were conducted on 12 benchmark functions between the improved Firefly algorithm and other improved Firefly algorithms.The results show that the IWFA proposed in this paper.The SD algorithm has faster convergence speed,is easier to jump out of local optima,and has better overall performance.The portfolio problem is one of the most important issues in the classic financial field.The core issue is the need to choose the best portfolio among all asset portfolios,with the goal of achieving the highest possible returns and lowest possible risks.This is an NP-hard problem,which is difficult to solve using traditional optimization algorithms.This article will propose the IWFA_SD algorithm which is applied to the portfolio problem model.The experiment proves the effectiveness of the proposed algorithm,thus expanding the application range of the firefly algorithm.