The selection of global best(Gbest) exerts a high influence on the searching performance of multi-objective particle swarm optimization algorithm(MOPSO). The candidates of MOPSO in external archive are always estimate...The selection of global best(Gbest) exerts a high influence on the searching performance of multi-objective particle swarm optimization algorithm(MOPSO). The candidates of MOPSO in external archive are always estimated to select Gbest. However,in most estimation methods, the candidates are considered as the Gbest in a fixed way, which is difficult to adapt to varying evolutionary requirements for balance between convergence and diversity of MOPSO. To deal with this problem, an adaptive candidate estimation-assisted MOPSO(ACE-MOPSO) is proposed in this paper. First, the evolutionary state information,including both the global dominance information and global distribution information of non-dominated solutions, is introduced to describe the evolutionary states to extract the evolutionary requirements. Second, an adaptive candidate estimation method,based on two evaluation distances, is developed to select the excellent leader for balancing convergence and diversity during the dynamic evolutionary process. Third, a leader mutation strategy, using the elite local search(ELS), is devised to select Gbest to improve the searching ability of ACE-MOPSO. Fourth, the convergence analysis is given to prove the theoretical validity of ACE-MOPSO. Finally, this proposed algorithm is compared with popular algorithms on twenty-four benchmark functions. The results demonstrate that ACE-MOPSO has advanced performance in both convergence and diversity.展开更多
A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its referenc...A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its reference objectives were the best particle and the centroid of all particles except the best particle.The convergence theorems of linear time-varying discrete system proved that simplex-PSO is of consistent asymptotic convergence.In order to reduce the probability of trapping into a local optimal value,an extremum mutation was introduced into simplex-PSO and simplex-PSO-t(simplex-PSO with turbulence) was devised.Several experiments were carried out to verify the validity of simplex-PSO and simplex-PSO-t,and the experimental results confirmed the conclusions:(1) simplex-PSO-t can optimize high-dimension functions with 200-dimensionality;(2) compared PSO with chaos PSO(CPSO),the best optimum index increases by a factor of 1×102-1×104.展开更多
A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential equations.It is proven that the weighted empirical measure of this partic...A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential equations.It is proven that the weighted empirical measure of this particle system converges to the law of the McKean-Vlasov system as the number of particles grows.Based on the Wasserstein met-ric,quantitative propagation of chaos results are obtained for both linear and quadratic growth conditions.Finally,numerical experiments are conducted to validate our theoretical results.展开更多
To deal with the demerits of constriction particle swarm optimization(CPSO), such as relapsing into local optima, slow convergence velocity, a modified CPSO algorithm is proposed by improving the velocity update formu...To deal with the demerits of constriction particle swarm optimization(CPSO), such as relapsing into local optima, slow convergence velocity, a modified CPSO algorithm is proposed by improving the velocity update formula of CPSO. The random velocity operator from local optima to global optima is added into the velocity update formula of CPSO to accelerate the convergence speed of the particles to the global optima and reduce the likelihood of being trapped into local optima. Finally the convergence of the algorithm is verified by calculation examples.展开更多
A new adaptive mutation particle swarm optimizer,which is based on the variance of the population's fitness,is presented in this paper.During the running time,the mutation probability for the current best particle...A new adaptive mutation particle swarm optimizer,which is based on the variance of the population's fitness,is presented in this paper.During the running time,the mutation probability for the current best particle is determined by two factors:the variance of the population's fitness and the current optimal solution.The ability of particle swarm optimization(PSO)algorithm to break away from the local optimum is greatly improved by the mutation.The experimental results show that the new algorithm not only has great advantage of convergence property over genetic algorithm and PSO,but can also avoid the premature convergence problem effectively.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 61890930-5,61903010,62021003,and 62125301)the National Key Research and Development Project (Grant No. 2018YFC1900800-5)+1 种基金Beijing Natural Science Foundation (Grant No. KZ202110005009)Beijing Outstanding Young Scientist Program (Grant No. BJJWZYJH 01201910005020)。
文摘The selection of global best(Gbest) exerts a high influence on the searching performance of multi-objective particle swarm optimization algorithm(MOPSO). The candidates of MOPSO in external archive are always estimated to select Gbest. However,in most estimation methods, the candidates are considered as the Gbest in a fixed way, which is difficult to adapt to varying evolutionary requirements for balance between convergence and diversity of MOPSO. To deal with this problem, an adaptive candidate estimation-assisted MOPSO(ACE-MOPSO) is proposed in this paper. First, the evolutionary state information,including both the global dominance information and global distribution information of non-dominated solutions, is introduced to describe the evolutionary states to extract the evolutionary requirements. Second, an adaptive candidate estimation method,based on two evaluation distances, is developed to select the excellent leader for balancing convergence and diversity during the dynamic evolutionary process. Third, a leader mutation strategy, using the elite local search(ELS), is devised to select Gbest to improve the searching ability of ACE-MOPSO. Fourth, the convergence analysis is given to prove the theoretical validity of ACE-MOPSO. Finally, this proposed algorithm is compared with popular algorithms on twenty-four benchmark functions. The results demonstrate that ACE-MOPSO has advanced performance in both convergence and diversity.
基金Project(50275150) supported by the National Natural Science Foundation of ChinaProject(20070533131) supported by Research Fund for the Doctoral Program of Higher Education of China
文摘A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its reference objectives were the best particle and the centroid of all particles except the best particle.The convergence theorems of linear time-varying discrete system proved that simplex-PSO is of consistent asymptotic convergence.In order to reduce the probability of trapping into a local optimal value,an extremum mutation was introduced into simplex-PSO and simplex-PSO-t(simplex-PSO with turbulence) was devised.Several experiments were carried out to verify the validity of simplex-PSO and simplex-PSO-t,and the experimental results confirmed the conclusions:(1) simplex-PSO-t can optimize high-dimension functions with 200-dimensionality;(2) compared PSO with chaos PSO(CPSO),the best optimum index increases by a factor of 1×102-1×104.
基金supported by the National Natural Science Foundation of China(No.12222103)the National Key R&D Program of China(No.2018YFA0703900).
文摘A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential equations.It is proven that the weighted empirical measure of this particle system converges to the law of the McKean-Vlasov system as the number of particles grows.Based on the Wasserstein met-ric,quantitative propagation of chaos results are obtained for both linear and quadratic growth conditions.Finally,numerical experiments are conducted to validate our theoretical results.
基金supported by the National Natural Science Foundation of China(71171015)the National High Technology Research and Development Program(863 Program)(2012AA112403)
文摘To deal with the demerits of constriction particle swarm optimization(CPSO), such as relapsing into local optima, slow convergence velocity, a modified CPSO algorithm is proposed by improving the velocity update formula of CPSO. The random velocity operator from local optima to global optima is added into the velocity update formula of CPSO to accelerate the convergence speed of the particles to the global optima and reduce the likelihood of being trapped into local optima. Finally the convergence of the algorithm is verified by calculation examples.
基金supported by the Gansu Natural Science Foundation (No.ZS011-A25-016-G).
文摘A new adaptive mutation particle swarm optimizer,which is based on the variance of the population's fitness,is presented in this paper.During the running time,the mutation probability for the current best particle is determined by two factors:the variance of the population's fitness and the current optimal solution.The ability of particle swarm optimization(PSO)algorithm to break away from the local optimum is greatly improved by the mutation.The experimental results show that the new algorithm not only has great advantage of convergence property over genetic algorithm and PSO,but can also avoid the premature convergence problem effectively.
