Several Improvements To Particle Swarm Optimization And Their Theoretical Fundamentals

Particle Swarm Optimization(PSO)is a swarm intelligence optimization algorithm inspired by the simulation of bird flocks and fish schooling foraging behavior to implement the optimization of swarm intelligence.It has been one of research hotspots in the field of computer intelligence and has been widely concerned because of its conceptual simplicity and convenience to implement since proposed in 1995.Hitherto,PSO still exist a lot of problems impacting its performance,such as insufficient theoretical basis,overmuch computation overhead,premature convergence,and so on.This paper has further understood PSO based on the theoretical analysis from the perspective of the basic PSO algorithm,and put forward some improvement directions based on the theoretical analysis results of its.As result,three improved PSO algorithms have been proposed and proved to be valid to improve performance of algorithms through a series of simulation experiments and theoretical analysis.Moreover,for verifying the effectiveness of the proposed algorithm in engineering problems,this paper use the improved PSO algorithm of best performance to solve the problem of hyper parameter optimization of gaussian process regression.The main works in this paper include as follows:1.First of all,the current research status is summarized:From the perspective of the optimization theory to the intelligent optimization algorithm as well as PSO algorithm,three aspects have been discussed,including related concepts,research developmentand trend.Specially,the thinking origin,research background and design thought of PSO have been reviewed thoroughly.At the same time,Critical issues and deficiencies of PSO algorithm have been pointed out,providing guidance for the research direction of this paper.2.In order to understand the essence of PSO more clearly,using the stability theory of differential equations and difference equations,random motion differential model of PSO motion system is set up after analyzing original PSO model.The whole particle swarm as the research object,rigorous and detailed theoretical derivation and analysis study of particle swarm trajectory,convergence,and convergent speed are carried out by means of mathematical analysis.As a result,overall trend characteristics of particle trajectory are obtained,and a particle swarm stable region of convergence and a set of heuristic parameter selection when PSO system tends to "equilibrium" are also obtained.Three aspects are discussed,including the variation trend of particle swarm velocity,the relation between velocity and the trajectory of the particle swarm and the fluctuation magnitude of velocity deviation from equilibrium.According to the conclusions of theoretical analysis,some improvement directions of PSO algorithm are given to lay the theoretical foundation for proposing following methods.3.On the basis of the theoretical analysis and research results of PSO,two improved PSO with adaptive mutation operator(AMOP(?)and OPSO-AEM&NIW)and a new improved PSO without inertial parameter(NOPSO)have been proposed in this paper.In AMOPSO,a generalized opposition-based strategy is introduced to accelerate convergence rate,which leads to the increasing probability of falling into local optimum.In order to avoid trapping into local optimum,an adaptive mutation strategy(AMS)is proposed which can achieve the goal of improving the global convergence rate of algorithm via increasing the diversity of particle swarm.Meanwhile,a nonlinear adaptive inertia weight strategy is introduced to adjust the active degree of each particle at different stages.The combination of above three strategies makes AMOPSO effectively improve the performance of PSO algorithm.Compared with AMOPSO,OPSO-AEM&NIW further increases the speed of convergence by using a new adaptive mutation strategy according to motion characteristics at different stages of a particle under the premise of ensuring its accuracy which is an improvement based on AMS.To thoroughly eliminate the impact of uncertainty caused by setting of inertia parmeter to the performance of algorithm,this paper proposes a non-inertial velocity update equation(NIV)inspired by the difference thought to change the trajectory of the particle.According to the different capture methods of environmental information,NIV formula includes three types such as NIV-D?NIV-U and NIV-R.Experimental results show NOPSO algorithm introducing NIV formula significantly increases the convergent speed of algorithm.4.From the theoretical point,PSO dynamical system introduced adaptive mutation strategy and no-inertial velocity formula(NIV)have been analyzed and discussed.Firstly,the analysis of the convergence theory of adaptive mutation strategy is pointed out that PSO introduced adaptive mutation strategy is still local optimal algorithm,but it can improve the probability of global convergence of the algorithm to effectively avoid falling into local optimum and accelerate the convergence speed of the algorithm.Secondly,PSO dynamical system introduced NIV is expressed as a randomly second order difference equation.By solving the difference equation,some results are obtained including the characteristics of the particle trajectory,a stable convergence region and its heuristic setingof related parameters.Meanwhile,it is proved that NIV can effectively speed up the convergence rate of PSO algorithm.5.Aiming at solving the hyper-parameters of gaussian process regression(GRP)optimization problem based on Bayes principle,this paper has proposed a PSO improved algorithm-NIPSO combining NIV and adaptive elite mutation strategy,which makes optimized parameters of GRP improve fitting precision and generalization performance of GPR effectively.At the same time,it is proved that improvement strategies directed at PSO proposed in this paper is effective.