| Particle swarm optimization(PSO)is arguably one of the most powerful swarm intelligence optimization algorithms in current use.The PSO algorithm has been widely applied to feature selection,pattern recognition,parameter estimation,production scheduling and other fields and has achieved good results with its simple structure and practical.Although PSO exhibits somehow convincing performance,things come into different when optimization problem becomes more complex which makes potential defects emerge.It has been found that PSO algorithm suffers from certain shortcomings of diversity losses when dealing with high-dimensional optimization problems,which affects global search performance.In addition,it shows a premature and convergent trend when dealing with multimodal functions,which results in insufficient local search.On the basis of in-depth research on the PSO’s search mechanism,this paper takes learning exemplars as the starting point.Two improved PSO variants are devised and applied them to the parameter estimation of Lotka-Volterra competition model.The research contents of this paper are as follows:(1)Elite-ordinary hybrid synergistic learning PSO method is proposedAiming for preserving population diversity and improving the global search ability,this paper proposes a PSO version with elite-ordinary particle hybrid synergistic search mechanism(EOPSO).In EOPSO,particles are divided into elite members and ordinary ones according to their performance.Each elite individual learns from itself to preserve population diversity and achieve a high level of global search performance.Ordinary individuals fly towards potential promising regions where optimum solutions are more likely to occur,to obtain better local search performance.In addition,a jump-out strategy based on elite-ordinary particle information interaction is devised to overcome stagnation situation.Experimental comparisons demonstrate that in EOPSO,particles have the ability to reasonably adjust population diversity,effectively avoid local optima,and exactly converge to global optimum.(2)Hybrid differential evolution learning PSO variant is devisedIn order to overcome the defects of canonical PSO’ learning mechanism and improve the learning exemplars’ quality,this paper devises a PSO variant based on a hybrid differential evolution mechanism(DEPSO).In DEPSO,the mutation,crossover and selection operations of differential evolution algorithm are organically embedded into PSO’s framework to generate diversified and high-quality learning exemplars.Specifically,DEPSO uses mutation and crossover operations to generate diversified learning exemplars,which effectively maintain the global search capability during the search process.In addition,DEPSO uses selection mechanism to construct high-quality exemplar,which effectively improves the local search performance.Experimental comparisons confirm that DEPSO can maintain a high level of population diversity in the early stage;perform reasonable convergence to the global optimal region in the middle stage;and complete a careful search of the global optimal region in the later stage.(3)Parameter estimation of fractal evolutionary game competition model is solvedLotka-Volterra competition model has a wide range of applications in economics and ecology,and the problem of parameter estimation is an important basis for modeling and optimization.Nevertheless,most of the existing parameter estimation work are based on the data fitting of chaotic time series,and the studies on parameter estimation based on the Julia set,the initial stable set of the system,are scarce.In this paper,we measure the regional error of the Julia set by constructing a suitable fitness function.The parameter estimation of Julia set is expressed as an optimization problem,and the two devised PSO variants are employed to firstly solve the problem,which is the first attempt to estimate the parameters of the L-V model based on fractal theory.The fractal Julia set is an important initial condition for quantifying the dynamical characteristics of the model.Therefore,the study of parameter estimation based on Julia set has an important complementary significance to the theory of competitive games. |
