Riemannian流形中DE算法算子最优特征量的量子渐进估计

数学物理学报 ›› 2020, Vol. 40 ›› Issue (1): 31-43.

Riemannian流形中DE算法算子最优特征量的量子渐进估计

王凯光¹(),高岳林^2,*

¹ 北方民族大学数学与信息科学学院银川 750021
² 北方民族大学宁夏智能信息与大数据处理重点实验室银川 750021

收稿日期:2019-04-01 出版日期:2020-01-26 发布日期:2020-04-08
通讯作者: 高岳林 E-mail:wkg13759842420@foxmail.com
作者简介:王凯光, E-mail:wkg13759842420@foxmail.com
基金资助:
国家自然科学基金(61561001);北方民族大学重大科研专项资助项目(ZDZX201901);北方民族大学研究生创新项目(YCX19120);宁夏高等教育一流学科建设资助项目(NXYLXK2017B09)

Quantum Asymptotic Estimation of the Optimal Eigenvalues of DE Operators in Riemannian Manifolds

Kaiguang Wang¹(),Yuelin Gao^2,*

¹ School of Mathematics and Information Science, North Minzu University, Yinchuan 750021
² Ningxia Key Laboratory of Intelligent Information and Big Data Processing, North Minzu University, Yinchuan 750021

Received:2019-04-01 Online:2020-01-26 Published:2020-04-08
Contact: Yuelin Gao E-mail:wkg13759842420@foxmail.com
Supported by:
国家自然科学基金(61561001);北方民族大学重大科研专项资助项目(ZDZX201901);北方民族大学研究生创新项目(YCX19120);宁夏高等教育一流学科建设资助项目(NXYLXK2017B09)

摘要/Abstract

摘要：

该文主要分析和探讨了差分进化算法（Differential Eveolutionary Algorithm，DE）在Riemannian流形中的几何关系，对P_-ε条件下Riemannian流形中的种群个体进行了收敛性分析，得到了迭代个体收敛精度与收敛速度的量子不确定渐进估计，如下式

$\Delta_{v}^{2}\cdot \Delta_{x_{\beta}^{\varepsilon}}^{2}\geq\Big(\frac{\sqrt{(\lambda_{\varepsilon})_{1}}+\cdots +\sqrt{(\lambda_{\varepsilon})_{n}}}{2}\Big)^{2},$

其中，Δ_v²为种群个体的速度分辨率，Δ_{x_β^ε}²为种群个体带有误差的位置分辨率，（λ_ε）_i，i=1，2，…，n.从本质上说明了Riemannian流形中迭代个体的局部特征量是不能从收敛精度和收敛速度同时达到算法高效.

关键词: DE算法, Riemannian流形, 收敛精度, 收敛速度, 量子不确定渐进估计

Abstract:

In this paper, the geometric relations of differential evolution algorithm in Riemannian manifolds are analyzed and discussed. The convergence of populations in Riemannian manifolds with P-ε is analyzed. A quantum uncertain asymptotic estimation of the convergence accuracy and convergence speed of the iterative individual is obtained as follows

$\Delta_{v}^{2}\cdot \Delta_{x_{\beta}^{\varepsilon}}^{2}\geq\Big(\frac{\sqrt{(\lambda_{\varepsilon})_{1}}+\cdots +\sqrt{(\lambda_{\varepsilon})_{n}}}{2}\Big)^{2},$

where, Δ_v² is speed resolution of individual populations, Δ_{x_β^ε}² is position resolution with error ε of individual populations, (λ_ε)_i, i=1, 2, …, n. The theorem expression essentially shows that the local eigenvalues of iterated individuals in Riemann manifolds can not achieve high convergent accuracy and convergent speed at the same time.

Key words: DE algorithm, Riemannian manifolds, Convergent accuracy, Convergent speed, Quantum uncertain asymptotic estimation

中图分类号:

O192

王凯光,高岳林. Riemannian流形中DE算法算子最优特征量的量子渐进估计[J]. 数学物理学报, 2020, 40(1): 31-43.

Kaiguang Wang,Yuelin Gao. Quantum Asymptotic Estimation of the Optimal Eigenvalues of DE Operators in Riemannian Manifolds[J]. Acta mathematica scientia,Series A, 2020, 40(1): 31-43.

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