关键词： 多目标优化   无人机   交通运输网络   算法  

摘要： 随着无人机技术的不断发展,目前已有相关企业开展无人机运输货物测试.在建筑材料运输方面,大型工业级无人机设备能够高效准确地运输建筑施工地所需的零配件.现基于多目标情况下无人机交通运输网络的算法,根据不同数量和不同网络位置的建筑材料仓库与建筑施工工地,求解无人机交通运输网络的路径规划问题.

关键词： 高光谱图像   端元提取   纯像元指数   数学形态学  

摘要： 自动形态学端元提取(automated morphological endmember extraction,AMEE)算法将结构元素内最纯像元与混合度最大的像元之间的光谱角距离定义为形态学离心率指数(morphological eccentricity index,MEI)来定量化地表示像元的纯净度。然而作为参考标准的混合度最大的像元在不同的结构元素内也是不同的,尤其是当结构元素内的纯净像元占大多数时,像元的均值光谱将更接近纯像元,此时像元的MEI越高,纯度反而越低。针对这一问题,本文提出一种像元纯度指数(pure pixel index,PPI)算法与AMEE算法相结合的端元提取算法PPI-AMEE。在结构元素内,利用PPI指数代替AMEE算法中的MEI指数来寻找最纯像元。变换结构元素时,只有最纯净的像元始终能够投影到随机生成的直线的两端,其PPI值会不断累计增大,而其他像元的PPI值则无法持续增大。累计记录每个像元的PPI值,直至满足迭代终止条件,最终形成一幅PPI图像,端元将在PPI值较大的像元中选取。PPI-AMEE算法只在相对较小的结构元素内运行PPI算法,然后再结合数学形态学中的膨胀操作对整幅图像进行处理,其同时兼顾了图像的光谱信息和空间信息。最后,采用模拟数据及美国内华达州Cuprite地区的机载可见光/红外成像光谱仪(airborne visible infrared imaging spectrometer,AVIRIS)高光谱数据对提出的PPI-AMEE算法进行试验验证。试验结果表明,PPI-AMEE算法的端元提取精度总体上优于AMEE算法和PPI算法。

关键词： 数学算法   计算机编程   优化  

摘要： 随着我国的计算机技术的发展,对于计算机编程的优化工作也显得尤为重要,数学算法在计算机编程过程中的应用可以让编程结构更加的完整,实现计算机编程的优化效果,数学算法应用在计算机的编程过程中,可以实现编程的优化,减少编程当中的无用部分的出现,使计算机编程结构更完善,同时计算运行速度得到提高。本文就数学算法在计算机编程方式的优化进行了简要的分析,说明了数学算法在编程方式当中的作用。

关键词： 分数乘法   数学思想方法   整体架构   教学实录   教学内容   教学目标   正确计算   整数  

摘要： 教学内容:苏教版数学六年级上册第28~29页例1、例2、"练一练"及练习五第1~5题。教学目标:第一,使学生体会分数与整数相乘的含义,理解并掌握分数乘整数的计算方法,并能正确计算。第二,使学生经历探究分数乘整数的意义,探索分数乘整数的计算方法,积累数学学习经验,培养观察、分析、推理和概括等能力。

关键词： Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP)   Contractor Selection (CS)   Non-Dominated Sorting Genetic Algorithm (NSGA-II)   Multi-Objective Particle Swarm Optimization algorithm (MOPSO)   Taguchi method  

摘要： Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision mak

关键词： EEG signal   Sleep stage   Feature selection   Ensemble learning algorithm   Stacking  

摘要： The aim of this study is to propose a high-accuracy and high-efficiency sleep staging algorithm using single-channel electroencephalograms (EEGs). The process consists four parts: signal preprocessing, feature extraction, feature selection, and classification algorithms. In the preconditioning of EEG, wavelet function and IIR filter are used for noise reduction. In feature selection, 15 feature algorithms in time domain, time-frequency domain, and nonlinearity are selected to obtain 30 feature parameters. Feature selection is very important for eliminating irrelevant and redundant features. Feature selection algorithms as Fisher score, Sequential Forward Selection (SFS), Sequential Floating Forward Selection (SFFS), and Fast Correlation-Based Filter Solution (FCBF) were used. The paper establishes a new ensemble learning algorithm based on stacking model. The basic layers are k-Nearest Neighbor (KNN), Random Forest (RF), Extremely Randomized Trees (ERT), Multi-layer Perceptron (MLP), and Extreme Gradient Boosting (XGBoost) and the second layer is a Logistic regression. Comparing classification of RF, Gradient Boosting Decision Tree (GBDT), and XGBoost, the accuracies and kappa coefficients are 96.67% and 0.96 using the proposed method. It is higher than other classification *** results show that the proposed method can accurately sleep staging using single-channel EEG and has a high ability to predict sleep staging.

关键词： 数学算法   数学命题   创新构造   算法探源  

摘要： 文章通过一个不等式证明中的算法启示,关注数学命题的算法内涵,研究由算法引起的不等式问题,创作出新的数学命题与数学模型,并引伸到超越函数,从数学命题视角关注人工智能时代的到来.