Research On Firefly Algorithm And Its Application In Constrained Optimization

Firefly Algorithm(FA)is a new group swarm intelligence algorithm,which has many advantages,including simple structure,few parameters,easy to implement.FA also has the advantages of automatic subgrouping and unique attraction mechanism,so that it can efficiently deal with optimization problems.Since firefly algorithm was proposed,it has aroused a large number of scholars attention and research boom.At present,the firefly algorithm has been applied in many fields and has achieved success.However,similar to other swarm intelligence algorithms,FA has some potential drawbacks.For instance,it may prematurely stop at locally optimal and its convergence speed is very slow when dealing with complex multimodal problems with many local peaks and valleys.In this paper,two improved algorithms are proposed by analyzing the causes of these shortages.The main contributions and innovation points are summarized as follows:For the fixed step of FA cannot meet the changing needs of the evolutionary process of the algorithm,an adaptive step FA based on population diversity called DASFA is proposed to improve the performance of FA.The DASFA designed an adaptive step which is decreasing as the search process and regulated by population diversity,it could help the algorithm maintains high diversity to getting out of the local optimal and balances the abilities of exploration and exploitation.In addition,in order to deal with different optimization problems,the dimension adjustment factor is introduced into the random step to adapt to the different needs of the optimization problem.Experiments are conducted on ten classic benchmark functions,the results show that DASFA achieves better performance than FA and some its variants.Considering the lack of an assessment mechanism for fireflies after each iteration,an adaptive FA based on the selection and mutation is proposed in this paper,which selection and mutation are based on the simulated annealing algorithm are implemented.The improved algorithm adds the comparison for the state of the fireflies after their movement,which would make fireflies move in the direction of evolution of the algorithm and accelerate the convergence speed of the algorithm.At the same time,in order to avoid the phenomenon of isolated individual,the position update formula in FA is improved to strengthen the communication and interrelation between fireflies.In addition,the random step and the rule of the firefly moving sequence are changed to improve the performance of the algorithm and reduce the computational complexity of the algorithm.Experiments are conducted on a set of well-known benchmark functions.Computational results suggest that the new approach achieves better solutions than FA and two other FA variants in accuracy,convergence rate and robustness.The proposed algorithms are applied to solve constrained optimization problems respectively,and results show that they have better performance and applicability.