孙小晴1,,,
林平2,
罗强1,
徐浩天1
1.哈尔滨师范大学计算机科学与信息工程学院 哈尔滨 150025
2.哈尔滨医科大学 哈尔滨 150086
基金项目:国家自然科学基金(31971015),哈尔滨市科技局科技创新人才研究专项资助(2017RAQXJ050),哈尔滨师范大学硕士研究生学术创新基金(HSDSSCX2019-08)
详细信息
作者简介:季伟东:男,1978年生,教授,研究方向为人工智能和大数据
孙小晴:女,1994年生,硕士生,研究方向为群体智能和人工智能
林平:男,1962年生,研究方向为应用心理学和医学人工智能
罗强:男,1992年生,硕士生,研究方向为机器学习和神经网络
徐浩天:男,1996年生,硕士生,研究方向为群体智能和人工智能
通讯作者:孙小晴 sunxiaoqing2649@163.com
中图分类号:TP301.6计量
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被引次数:0
出版历程
收稿日期:2019-08-12
修回日期:2020-02-18
网络出版日期:2020-03-18
刊出日期:2020-08-18
Natural Computing Method Based on Nonlinear Dimension Reduction
Weidong JI1,Xiaoqing SUN1,,,
Ping LIN2,
Qiang LUO1,
Haotian XU1
1. College of Computer Science and Information Engineering, Harbin Normal University, Harbin 150025, China
2. Harbin Medical Sciences University, Harbin 150086, China
Funds:The National Natural Science Foundation of China (31971015), Harbin Science and Technology Bureau’s Special Subsidy for Scientific and Technological Innovation Talents Research (2017RAQXJ050), Harbin Normal University Master’s Academic Innovation Fund (HSDSSCX2019-08)
摘要
摘要:随着人工智能的发展,许多优化问题发展为高维的大规模优化问题。在自然计算方法中,针对高维问题虽然能避免算法陷入局部最优,但是在收敛速度和时间可行性上却不占优势。该文在传统自然计算方法的基础上,提出了非线性降维的自然计算方法(NDR),该策略不依赖具体的算法,具有普适性。该方法将初始化的N个个体看做一个N行D列的矩阵,然后对矩阵的列向量求最大线性无关组,从而减少矩阵的冗余度,达到降低维度的目的。在此过程中,由于剩余的任意列向量组均可由最大线性无关组表示,所以通过对最大线性无关组施加一个随机系数来维持种群的多样性和完整性。将该文所提策略分别应用到标准遗传算法(GA)和粒子群优化算法(PSO)中,并与标准粒子群算法、遗传算法以及目前主流的对维数进行优化的4个算法对比,实验证明,改进的算法对大部分标准测试函数都具有很强的全局收敛能力,其寻优能力超过了上述6个算法,同时改进后的算法在运行时间上远优于对比算法。
关键词:自然计算方法/
优化/
降维/
非线性
Abstract:Many optimization problems develop into high-dimensional large-scale optimization problems in the process of the development of artificial intelligence. Although the high-dimensional problem can avoid the algorithm falling into local optimum, it has no advantage in convergence speed and time feasibility. Therefore, the natural computing method for Nonlinear Dimension Reduction (NDR) is proposed. This strategy does not depend on specific algorithm and has universality. In this method, the initialized N individuals are regarded as a matrix of N rows and D columns, and then the maximum linear independent group is calculated for the column vector of the matrix, so as to reduce the redundancy of the matrix and reduce the dimension. In this process, since any remaining column vector group can be represented by the maximum linearly independent group, a random coefficient is applied to the maximum linearly independent group to maintain the diversity and integrity of the population. The standard genetic algorithm and particle swarm optimization using NDR strategy compare with Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and the four mainstream algorithms for dimension optimization. Experiments show that the improved algorithm has strong global convergence ability and better time complexity for most standard test functions.
Key words:Natural computing method/
Optimization/
Dimension reduction/
Nonlinearity
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