Two Improved Firefly Algorithms

Firefly algorithm(FA)belongs to the swarm intelligence algorithms.Although it was put forward later,it has captured much attention of many scholars at home and abroad because of a small number of parameter settings and effortless operation.And now,firefly algorithm has been applied to solve many practical problems,such as cluster analysis,0-1 knapsack problem,vehicle routing problem,job shop scheduling problem and so on.Thus,firefly algorithm has a good development prospect.As a swarm intelligent algorithm,FA has the following drawbacks:doughty oscillation phenomenon in the search process,the high selection pressure of firefly,the slow convergence speed,and the poor search precision.To overcome the above shortcomings,this paper proposes two improved firefly algorithms:pFA algorithm and ERaFA algorithm.Compared with the original firefly algorithm and other current mainstream intelligent algorithms,pFA algorithm and ERaFA algorithm have a great improvement in performance.The main contents are given as follows:In Chapter 1,the background and significance of the research for firefly algorithm are given firstly.And then the related research on firefly algorithm is described.Finally,the main contents of this paper are given.In Chapter 2,the basic knowledge of the proposed algorithm is given.First,the original firefly algorithm is introduced.Secondly,we give the definition of Opposition-based Learning.In Chapter 3,an improved algorithm(pFA)is proposed.First of all,unlike the full attraction mode of the classical firefly algorithm,in the pFA,the firefly utilizes probability selection to identify the fireflies that attract it.In this way,the poor solutions in the population will be eliminated.This strategy can guarantee those good fireflies have more chance to be selected,accelerate the convergence speed and raise optimization accuracy of the algorithm.Then,a new improved step size factor is introduced to balance the global search capability and local search capability of the algorithm.Next,the proposed algorithm employs Opposition-based Learning strategy to ensures the diversity of the algorithm population.Finally,the performance of the pFA algorithm is verified through some experiments.In Chapter 4,ERaFA algorithm is proposed.Firstly,the population NP is ranked from small to large according to the objective function value.Secondly,a proportional value of r is given to select the top[r*NP]elite neighbors.Then,a firefly is randomly selected as a mobile object from the[r*NP]elite neighbors.Finally,the step size factor and Opposition-based Learning strategy in Chapter 3 are adopted to ensure the diversity of the algorithm population and to improve the convergence speed of the algorithm.The numerical results show that ERaFA algorithm is feasible and effective.