摘要
柱形代数分解是广泛应用于求多项式系统实数解的一种计算方法。不同的变元序对其计算时间有显著影响。已有选序算法多基于启发式的经验算法,准确率不高。少数基于机器学习的方法使用的数据集较小,且基于复杂人工特征。文中在随机生成大量多项式系统与所有序计算时间标注的数据基础上,提出一类新的多项式显性表示特征和一种新的分级神经网络。首先根据最差序计算时间将数据集划分成4个不同计算难度的子集并分别建立预测最优序的分类模型,其次建立预测最长计算时间的回归模型,最后根据回归模型预测最长计算时间并据其自动选择相应难度分类模型预测最优变元序。实验结果表明,显性特征的性能优于复杂人工特征,且在困难问题上分级神经网络所预测最优序的性能约为经验选序算法的3倍。
Cylindrical algebraic decomposition(CAD)is a widely used approach for computing the real solutions of polynomial systems.The choice of variable ordering has a significant impact on its computation time.Most of existing ordering selection algorithms are based on heuristic empirical algorithms,whose accuracy are not high.A few approaches based on machine learning use small data sets and are based on complex human characteristics.In this paper,on the basis of randomly generating a large set of polynomial systems,which are tagged with timings obtained by applying different orderings for computing CAD,a new kind of explicit representation feature and a new hierarchical neural network are proposed.Firstly,according to the computation time of CAD with the worst ordering,the data set is divided into four subsets with different computation difficulties,and the classification models are established respectively.Secondly,a regression model for predicting the longest computation time is built.Finally,the longest computation time is predicted according to the regression model,based on which a classification model with right computation difficulty is automatically selected to predict the optimal variable ordering.Experimental results show that the performance of explicit features is better than that of complex handcrafted features,and the performance of the optimal ordering predicted by hierarchical neural network on difficult problems is about two times better than that of an empirical algorithm.
作者
朱章鹏
陈长波
ZHU Zhang-peng;CHEN Chang-bo(Chongqing University of Posts and Telecommunications,Chongqing 400065,China;Chongqing Institute of Green and Intelligent Technology,Chinese Academy of Sciences,Chongqing 400714,China)
出处
《计算机科学》
CSCD
北大核心
2020年第S02期106-110,138,共6页
Computer Science
基金
国家自然科学基金面上项目(11771421,1671377,61572024)
中国科学院“西部之光”
重庆市院士牵头科技创新引导专项(cstc2018jcyj-yszxX0002)。
关键词
分级神经网络
柱形代数分解
变元序
回归
特征选择
Hierarchical neural network
Cylindrical algebraic decomposition
Variable ordering
Regression
Feature selection
作者简介
朱章鹏,born in 1993,master,is a member of China Computer Federation.His main research interests include machine learning and so on.(z.zhangpeng@qq.com);通信作者:陈长波,born in 1981,Ph.D,associate professor,is a member of China Computer Federation.His main research interests include symbolic-numeric computation,automatic paralle-lization and optimization of computer programs and machine learning.(chenchangbo@cigit.ac.cn)。
