In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition...In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.展开更多
In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exac...In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.展开更多
传统的NSGA-Ⅱ(Non-dominated Sorting Genetic AlgorithmⅡ)算法使用拥挤度作为精英选择的第二指标,该方法在处理高维多目标优化问题时,常常由于选择压力不足,以及不同目标间优化冲突加剧等原因,很难维持种群收敛性和多样性的平衡。针...传统的NSGA-Ⅱ(Non-dominated Sorting Genetic AlgorithmⅡ)算法使用拥挤度作为精英选择的第二指标,该方法在处理高维多目标优化问题时,常常由于选择压力不足,以及不同目标间优化冲突加剧等原因,很难维持种群收敛性和多样性的平衡。针对上述问题,提出一种基于外部存档更新及截断机制的NSGA-Ⅱ改进算法NSGA-Ⅱ-UTEA(NSGA-Ⅱalgorithm based on Update and Truncation of External Archive)。该算法首先在精英选择中引入基于权重向量分解的外部存档机制,然后根据个体与所在权重向量及超平面距离之和更新外部存档,并基于个体间角度计算实现外部存档截断,进一步提升了算法在高维多目标优化问题中种群的收敛性和多样性。与NSGA-Ⅱ、NSGA-Ⅲ、MOEA/D(Multi-Objective Evolutionary Algorithm based on Decomposition)、NSGA-Ⅱ-ARSBX(NSGA-Ⅱwith Adaptive Rotation based Simulated Binary crossover)和RPD-NSGA-Ⅱ(Reference Point Dominance-based NSGA-Ⅱ)这5种先进的进化算法的对比实验结果表明,NSGA-Ⅱ-UTEA算法在10目标以上的高维DTLZ(Deb Thiele Laumanns Zitzler)和WFG(Walking Fish Group)系列测试函数上,各项性能指标整体优于其他算法,在解集的分布性和多样性方面具有显著优势。特别是在大部分高维WFG4~WFG7凹问题上都能取得最佳的性能指标值。与传统的NSGA-Ⅱ算法相比,NSGA-Ⅱ-UTEA算法在10目标以上的高维DTLZ系列测试函数上,反世代距离(IGD)性能平均提升了50.6%;在15目标以上的高维WFG系列测试函数上,超体积(HV)性能平均提升了60.7%。实验结果验证了NSGA-Ⅱ-UTEA算法改进的有效性。展开更多
最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)通过求解一个线性等式方程组来提高支持向量机(Support Vector Machine,SVM)的运算速度。但是,LSSVM没有考虑间隔分布对于LSSVM模型的影响,导致其精度较低。为了增强LS...最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)通过求解一个线性等式方程组来提高支持向量机(Support Vector Machine,SVM)的运算速度。但是,LSSVM没有考虑间隔分布对于LSSVM模型的影响,导致其精度较低。为了增强LSSVM模型的泛化性能,提高其分类能力,提出一种具有间隔分布优化的最小二乘支持向量机(LSSVM with margin distribution optimization,MLSSVM)。首先,重新定义间隔均值和间隔方差,深入挖掘数据的间隔分布信息,增强模型的泛化性能;其次,引入权重线性损失,进一步优化了间隔均值,提升模型的分类精度;然后,分析目标函数,剔除冗余项,进一步优化间隔方差;最后,保留LSSVM的求解机制,保障模型的计算效率。实验表明,新提出的分类模型具有良好的泛化性能和运行时间。展开更多
基金Supported by the National Nature Science Foundation of China(10671009,60534080,10871149)
文摘In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations.
基金supported by the National Natural Science Foundation of China (10901158)
文摘In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
文摘传统的NSGA-Ⅱ(Non-dominated Sorting Genetic AlgorithmⅡ)算法使用拥挤度作为精英选择的第二指标,该方法在处理高维多目标优化问题时,常常由于选择压力不足,以及不同目标间优化冲突加剧等原因,很难维持种群收敛性和多样性的平衡。针对上述问题,提出一种基于外部存档更新及截断机制的NSGA-Ⅱ改进算法NSGA-Ⅱ-UTEA(NSGA-Ⅱalgorithm based on Update and Truncation of External Archive)。该算法首先在精英选择中引入基于权重向量分解的外部存档机制,然后根据个体与所在权重向量及超平面距离之和更新外部存档,并基于个体间角度计算实现外部存档截断,进一步提升了算法在高维多目标优化问题中种群的收敛性和多样性。与NSGA-Ⅱ、NSGA-Ⅲ、MOEA/D(Multi-Objective Evolutionary Algorithm based on Decomposition)、NSGA-Ⅱ-ARSBX(NSGA-Ⅱwith Adaptive Rotation based Simulated Binary crossover)和RPD-NSGA-Ⅱ(Reference Point Dominance-based NSGA-Ⅱ)这5种先进的进化算法的对比实验结果表明,NSGA-Ⅱ-UTEA算法在10目标以上的高维DTLZ(Deb Thiele Laumanns Zitzler)和WFG(Walking Fish Group)系列测试函数上,各项性能指标整体优于其他算法,在解集的分布性和多样性方面具有显著优势。特别是在大部分高维WFG4~WFG7凹问题上都能取得最佳的性能指标值。与传统的NSGA-Ⅱ算法相比,NSGA-Ⅱ-UTEA算法在10目标以上的高维DTLZ系列测试函数上,反世代距离(IGD)性能平均提升了50.6%;在15目标以上的高维WFG系列测试函数上,超体积(HV)性能平均提升了60.7%。实验结果验证了NSGA-Ⅱ-UTEA算法改进的有效性。
文摘最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)通过求解一个线性等式方程组来提高支持向量机(Support Vector Machine,SVM)的运算速度。但是,LSSVM没有考虑间隔分布对于LSSVM模型的影响,导致其精度较低。为了增强LSSVM模型的泛化性能,提高其分类能力,提出一种具有间隔分布优化的最小二乘支持向量机(LSSVM with margin distribution optimization,MLSSVM)。首先,重新定义间隔均值和间隔方差,深入挖掘数据的间隔分布信息,增强模型的泛化性能;其次,引入权重线性损失,进一步优化了间隔均值,提升模型的分类精度;然后,分析目标函数,剔除冗余项,进一步优化间隔方差;最后,保留LSSVM的求解机制,保障模型的计算效率。实验表明,新提出的分类模型具有良好的泛化性能和运行时间。
