Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization problems.Bald eagle search optimization(BES)as a new stochastic opt...Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization problems.Bald eagle search optimization(BES)as a new stochastic optimization algorithm with fast convergence speed has the ability of prominent optimization and the defect of collapsing in the local best.To avoid BES collapse at local optima,inspired by the fact that the volume of the sphere is the largest when the surface area is certain,an improved bald eagle search optimization algorithm(INMBES)integrating the random shrinkage mechanism of the sphere is proposed.Firstly,the INMBES embeds spherical coordinates to design a more accurate parameter update method to modify the coverage and dispersion of the population.Secondly,the population splits into elite and non-elite groups and the Bernoulli chaos is applied to elite group to tap around potential solutions of the INMBES.The non-elite group is redistributed again and the Nelder-Mead simplex strategy is applied to each group to accelerate the evolution of the worst individual and the convergence process of the INMBES.The results of Friedman and Wilcoxon rank sum tests of CEC2017 in 10,30,50,and 100 dimensions numerical optimization confirm that the INMBES has superior performance in convergence accuracy and avoiding falling into local optimization compared with other potential improved algorithms but inferior to the champion algorithm and ranking third.The three engineering constraint optimization problems and 26 real world problems and the problem of extracting the best feature subset by encapsulated feature selection method verify that the INMBES’s performance ranks first and has achieved satisfactory accuracy in solving practical problems.展开更多
煤炭作为我国的基础性能源,煤炭价格分析在能源研究中一直至关重要。本文采用相空间重构技术,对国际环球动力煤(NEWC Global Coal)、我国的环渤海动力煤BSPI(5500k)和CII冶金煤(15500K)3种煤炭价格的时间序列,通过提取描述系统混沌吸引...煤炭作为我国的基础性能源,煤炭价格分析在能源研究中一直至关重要。本文采用相空间重构技术,对国际环球动力煤(NEWC Global Coal)、我国的环渤海动力煤BSPI(5500k)和CII冶金煤(15500K)3种煤炭价格的时间序列,通过提取描述系统混沌吸引子等特征量参数,分析煤炭价格时间序列中的行为混沌特征,并计算得出各自的时间预测范围。研究结果表明:(1)国内外煤炭市场价格是一个复杂的非线性系统,G-P算法计算得出的嵌入维数与关联维数表明其具有明显的分形特征;(2)3种煤炭价格时间序列的嵌入维数为5、6和9,表明对国内外煤炭市场价格的短期预测可以基于相应维数的非线性模型来实现;(3)国内外煤炭的市场价格行为具有混沌特征,依据最大李雅普诺夫指数,计算得出国际和国内煤炭价格的有效预测期分别为5和12个月。研究结论可为相关部门和企业进行煤炭价格预测及相关政策制定提供理论指导和决策借鉴。展开更多
The localized features on chaotic attractor in phase space and predictability are investigated in the present study.It will be suggested that the localized features in phase space have to be considered in determining ...The localized features on chaotic attractor in phase space and predictability are investigated in the present study.It will be suggested that the localized features in phase space have to be considered in determining the predictability.The notions of the local instability including the finite-time and local- time instabilities which determine the growth rate of error are introduced,and the calculation methods are discussed in detail.The results from the calculation of the 3-component Lorenz model show that such instability,correspondingly the growth rate of error,varies dramatically as the trajectories evolve on the chaotic attractor.The region in which the growth rate of error is small is localized considerably,and is separable from the region in which the growth rate is large.The local predictability is of important interest.It is also suggested that such localized features may be the main cause for a great deal of case-to-case variability of the predictive skill in the operational forecasts.展开更多
基金supported by the National Natural Science Foundation of China No.61976176.
文摘Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization problems.Bald eagle search optimization(BES)as a new stochastic optimization algorithm with fast convergence speed has the ability of prominent optimization and the defect of collapsing in the local best.To avoid BES collapse at local optima,inspired by the fact that the volume of the sphere is the largest when the surface area is certain,an improved bald eagle search optimization algorithm(INMBES)integrating the random shrinkage mechanism of the sphere is proposed.Firstly,the INMBES embeds spherical coordinates to design a more accurate parameter update method to modify the coverage and dispersion of the population.Secondly,the population splits into elite and non-elite groups and the Bernoulli chaos is applied to elite group to tap around potential solutions of the INMBES.The non-elite group is redistributed again and the Nelder-Mead simplex strategy is applied to each group to accelerate the evolution of the worst individual and the convergence process of the INMBES.The results of Friedman and Wilcoxon rank sum tests of CEC2017 in 10,30,50,and 100 dimensions numerical optimization confirm that the INMBES has superior performance in convergence accuracy and avoiding falling into local optimization compared with other potential improved algorithms but inferior to the champion algorithm and ranking third.The three engineering constraint optimization problems and 26 real world problems and the problem of extracting the best feature subset by encapsulated feature selection method verify that the INMBES’s performance ranks first and has achieved satisfactory accuracy in solving practical problems.
文摘煤炭作为我国的基础性能源,煤炭价格分析在能源研究中一直至关重要。本文采用相空间重构技术,对国际环球动力煤(NEWC Global Coal)、我国的环渤海动力煤BSPI(5500k)和CII冶金煤(15500K)3种煤炭价格的时间序列,通过提取描述系统混沌吸引子等特征量参数,分析煤炭价格时间序列中的行为混沌特征,并计算得出各自的时间预测范围。研究结果表明:(1)国内外煤炭市场价格是一个复杂的非线性系统,G-P算法计算得出的嵌入维数与关联维数表明其具有明显的分形特征;(2)3种煤炭价格时间序列的嵌入维数为5、6和9,表明对国内外煤炭市场价格的短期预测可以基于相应维数的非线性模型来实现;(3)国内外煤炭的市场价格行为具有混沌特征,依据最大李雅普诺夫指数,计算得出国际和国内煤炭价格的有效预测期分别为5和12个月。研究结论可为相关部门和企业进行煤炭价格预测及相关政策制定提供理论指导和决策借鉴。
文摘The localized features on chaotic attractor in phase space and predictability are investigated in the present study.It will be suggested that the localized features in phase space have to be considered in determining the predictability.The notions of the local instability including the finite-time and local- time instabilities which determine the growth rate of error are introduced,and the calculation methods are discussed in detail.The results from the calculation of the 3-component Lorenz model show that such instability,correspondingly the growth rate of error,varies dramatically as the trajectories evolve on the chaotic attractor.The region in which the growth rate of error is small is localized considerably,and is separable from the region in which the growth rate is large.The local predictability is of important interest.It is also suggested that such localized features may be the main cause for a great deal of case-to-case variability of the predictive skill in the operational forecasts.
