The competition time is generally every year9月,提交的材料MD5生成之后,don't touch it again,不要打开.

Watch video advice：

1. 学习算法的过程,As long as you understand the advantages and disadvantages of the algorithm,适用范围,Knowing exactly what each algorithm can do,以及如何实现.
2. See a good paper,了解解题思路,See a problem, can think in that way

1 Baidu Skills

1. 加双引号”“,进行完全匹配
2. 标题Required keywords：add before queryintitle
3. 搜索文档：after query word 空格 再输入filetype:文件格式（doc/pdf/xls等等）
4. 去掉不想要的：Add a space after the query word followed by a minus sign and a keyword

        例如：线性规划 filetype:pdf -百度文库

2 How to Query Skills

先看HowNet's master thesis,按照”被引“排序,see background introduction,Take advantage of advanced search.

For the digital and analog national competition,No need to look up foreign literature

3 go there to find data

• Priority on HowNet、Search on Google Scholar and other platforms
• 国家统计局：最全面,Monthly Quarterly Annual,Every region, every sector, every industry

国家数据 (stats.gov.cn)https://data.stats.gov.cn/

• EPSDATA平台：Have a wealth of data processed data resources and a large number of analysis results,是收费的,But you can apply for7天的试用        EPSDATA官网 (epsnet.com.cn)https://www.epsnet.com.cn/index.html#/Index

 3.1 数据预处理

缺失值

• Data provided by the competition,found that some cells wereNULL或空的
• 缺失太多,For example, survey demographic information,发现”年龄“This item is missing40%.just delete the indicator
• 最简单的处理：take the mean instead of,Mode imputation
• Newton插值法
  • According to a fixed formula,Construct an approximate function,补上缺失值,Universal applicability
  • 缺点：Unstable oscillations at the edge of the range,The runge phenomenon,Do not use to tutor the title of the request.
  • Applicable questions：热力学温度、地形测量、Positioning, etc. only pursue the accuracy of the function value and do not care about the changed data
• 样条插值法
  • Interpolate with piecewise smooth curves,Smooth means that the curve is not only continuous,Must have the continuous curvature
  • Applicable questions：零件加工,Reservoir water flow,图像”基线漂移“,High precision requirements such as robot trajectory、No mutation of data

异常值

• Data that is significantly different from other numerical values ​​in the sample,For example, one of the elevated data for a group of people has3米2的
• 正态分布3σ原则
  • 求解步骤：1.计算均值u和标准差σ;2.Determine whether each data value is in（u-3σ,u+3σ）内,Absence is an outlier.
  • 适用题目：The general accord with normal distribution,such as population data、测量误差、Production and processing quality、考试成绩
  • topic not used：Meet other distribution as a whole,For example, people queuing at a bus stop,符合泊松分布

MATLAB异常值处理方法：

创建****.mlx live code file,This option is only available in higher versions

4 建模全过程

• A complete digital and analog paper
  • 包括摘要（最重要）,问题重述、模型假设和符号说明、模型建立与求解（内容最多）、模型的优缺点与改进方法、References and Appendices.
  • 摘要：论文研究的问题、用了什么方法、what result did,and the approximate steps for each part.
• 问题重述
  • 将题目简述一遍即可,并不重要.注意不要复制粘贴,避免查重.
• 模型假设和符号说明
  • Good assumptions can do more with less
  • 符号说明：Defined in the paper have important symbol list form.

model has to be built：

• 一组公式,Explanation for each variable in the formula,就是一个模型
• 先查阅资料,看着资料,Paraphrase a simple model in your own words,再根据题目中的约束条件去一步步修改模型,Substitute the variables in the question into the model.
• 模型求解
• Not every question on the subject needs to have a model
• 模型的优缺点与改进方法：这一部分不是必须的,可以简单分析下前文模型的优缺点,Disdain if there is no way to improve
• 结合查到的文献,In the analysis text, the model is often used in the kind of problem,又与本文所求解的问题有何区别

附录：The code used when solving in the text,Pay attention to changing the variable names in the found code,avoid being checked

5 论文排版注意事项

Headings and text at all levels are clearly structured,Don't have large blanks,No more than the general title level3级,The text in the text is in Song type,英文Times New Roman,表格采用Standard three-line meter.

6 标题怎么写

读完标题,You can know what model is built in this article.简明扼要、符合规范、便于检索,Try to use words that everyone knows.

基于***模型/算法的***问题研究

• ***The model is the core model in the text
• ***The problem is the central word of the competition question
• Don't use too many modifiers

7 How to write an abstract

Ask the reviewer to read the abstract after,know this article解决的问题、建立的模型和求解结果.控制在3/4~1页.字数800~1100.

 opening paragraph template：本文主要研究了***问题.根据***,利用***模型/方法,求解出****.

1. 第一句：State the research question
2. 第二句：Explain the model used in the full text/算法、采取的操作
3. Do not write detailed solution results in the opening paragraph.

middle section template：针对问题一,考虑/根据***,...,建立***模型/利用****方法,....求解出****.Be sure to write clearly.

• 优化类、Prediction and Physics topics,To explicitly write the value.
• Questions Asking for Advice or Evaluation,Clearly write down the conclusions and data basis,but no form,Excessive data can illustrate data see appendix.

总结段：If the abstract exceeds one page after writing,可以不写,Don't repeat what was written before,Write some features of this article、Boast of statements.

关键词：一般为4~6个,Models and Algorithms Used,Professional name that everyone knows,question key word,中间以空格分开

 8 参考文献

Citing literature or public informationmust be specifiedList references andMark the corresponding text in the text.

9 作图技巧

注意排版,无首行缩进,居中对齐.

Common drawing software：AxGlyph、MATLAB,万能神器EChartsApache EChartshttps://echarts.apache.org/zh/index.html

10 Use page breaks smartly

Abstract on its own page,Insert a page break after the abstract.Note the difference between page breaks and section breaks,Section breaks are generally not used,Mainly use page breaks.

11 MATLAB如何导入数据

第一中方法：利用CTRLkey to select the data to be imported.export as table

 第二种方法：

horse_data = xlsread('E:\文件位置\new_data.xlsx','sheet1');  % 导入表格数据
horse_1 = horse_data(1,:);   % Import the first row of data

12 线性规划

线性规划：All variables are square.

Applicable questions：

• 题目中提到   如何分配/安排        尽量多（少）        最多（少）        利润最大        最合理    等词.
• 生产安排：原材料、Device is limited,总利润最大
• 投资收益：资产配置、收益率、损失率、组合投资、总收益最大
• sales shipping：产地、销地、产量、销量、运费、The lowest total shipping cost
• 车辆安排：路线、起点终点、承载量、时间点、The most reasonable arrangement of trains

有限的条件下,最大的收益,s.t.表示约束条件,设置的参数x1  x2  decision variable,max为目标函数

 MATLAB实现：Linprog函数

1. model asmatlab标准型：目标函数最小值、约束条件<=或=          
2.  [x, fval] = linprog(c, A, b, Aeq, beq, lb, ub)

   c	of the objective function coefficients列向量
   a, b	不等式约束条件The variable coefficient matrix and the parameter term matrix of
   aeq, beq	等式约束条件The coefficient matrix and constant term matrix of
   lb, ub	决策变量The minimum and maximum values ​​of

    

x        Returns the value of the variable for the optimal solution

fval        返回目标函数的最优值

• 若不存在不等式约束,用 []  代替A和b        [x, fval] = linprog(c, [], [], Aeq, beq, lb, ub)
• 若不存在等式约束,用  []  代替Aeq, beq       [x, fval] = linprog(c, A, b,[], [], lb, ub)
• No equality constraints and minimum、When the maximum value is constrained,可以不写Aeq, beq, lb, ub      [x, fval] = linprog(c, A, b)
• If the question finds the maximum value：The objective function is to add a negative sign at both ends of the equal sign to find the minimum value,After solving, the target value is negative again.

c = [-40; -30]; % Note that it is written as a column vector
a = [1 1; -1 0; 0 -1; 240 120];
b = [6; -1; -1; 1200];
% because of the constraintsa中,已经写了x1   x2  的范围,So there is no need to writelb,ub了
[x, y] = linprog(c, a, b);
y = -y;

 13 非线性规划

有限的条件下,求最大的收益

非线性规划：At least one variable is not a power,Involves the trigonometric functions

suitable for competition：such as angle adjustment,Flight management to avoid collisions,The best viewing angle in the cinema.

14 多目标规划问题

既要****,又要*****

• 例如,目标1是“不超过”,That is, as much as possible≤;目标2是   充分利用,That is, as much as possible = ,目标3is not less than,也就是≥
• 需要衡量每个目标的完成情况,And the importance of subjective to distinguish the three objectives,使得整体的完成情况尽量好.
• 绝对约束：Constraints built into the model,必须满足,Otherwise it is infeasible
• 目标约束：Model of inequality in the right end the pursuit of the value of the deviation is allowed
• 优先因子：The importance of setting goals

 求解方法：搜索MATLAB的fgoalattain函数,Or sequential algorithm,或用Lingo求解

15 最短路径问题

最短路径：从图Depart from some point in,In order to have another vertexThe sum of the weights of the passing edges is the smallest的一条路径.

图：Structure of Edges and Nodes,分为有向图和无向图

权重：道路的长度

MATLAB求解最短路径：Dijkstra算法,或MATLAB的graphshortestpath函数

第一步：生成邻接矩阵

W = [10,5,2,1,4,6,7,3,9,2];    % 每条边的权值

%     sparse生成稀疏矩阵,That is, except for a few elements noted,其余都是0
%    sparseThe value of the element in the same position of the first and second matrices is  从*到*的方向,对应Wweight in
DG = sparse([],[],W)    % DGThe adjacency matrix generated for

第二步,Generate graph objects,求解最短路径

%    distis the value of the shortest path,pathis the node order of the shortest path
%    predis the endpoint of the shortest path to each node before the previous node,一般用不到
%    1 代表起始节点,3 代表目标节点,即1到3的最短路径
[dist,path,pred] = graphshortestpath(DG,1,3);

%    biographGenerate graph objects,view显示该图
point_name = ["节点1","节点2","节点3","节点4"];
h = view(biograph(DG,point_name,'ShowWeights','on'))   % The last two parameters are the length of the display path

%     Mark the nodes and edges of the shortest path in red and increase the line width
%     getedgesbynodeid得到图hthe handle of the specified edge
%     The first parameter is the image,The second is the out point of the edge,The third is edge into the point
%     The handle ensures that the corresponding thing can be found
%     getQuery graph properties,h.Nodes(path),'ID'得到图hedge of shortest path in
%     set设置图形属性
edges = getedgesbyodeid(h,get(h.Nodes(path),'ID'));
set(edges,'LineColor',[1 0 0]);    % R G B
set(edges,'LineWidth',2);

注：Node labels and font size can also be modified,通过getedgesbyodeid函数获取相关信息,再进行set

16 最小生成树

Connect all vertices with minimum total path.

例：build connectivity7railway network of cities,The routes that can be constructed and the corresponding cost are shown in the figure,How to build to minimize total cost.

问题分析：

• 连通7个城市：generated graph,start from any vertex,All other vertices must be reachable along the edge,这种图叫做连通图.
• The course can be built and the corresponding cost：图的边,及其权值
• The total cost at least：The sum of the weights is the least
• difference from shortest path：The shortest path is for a vertex as the starting point,Minimum spanning tree is where all vertices are connected and the total path is the smallest. 

%    The first two matrix corresponding to the node,Avoid repetition when writing mostly undirected graphs,技巧第2matrices write nodes larger than the first matrix
s = [1 1 2 2 3 3 4 4 4 5];
t = [2 3 4 5 4 7 5 6 7 6];
wights = [50,60,65,40,52,45,50,30,42,70];
%     生成无向图,wights是对应的权值
G = graph(s,t,weights);
%    求出最小生成树,得到的TContains the weights of nodes and corresponding edges of the minimum spanning tree
T = minspantree(G);

% p = plot(G)Can show the pictures,The back is to set the font for aesthetics
p = plot(G,'EdgeLabel',G.Edges.Weight,'MarkerSize',8,'NodeFontSize',16,'EdgeFont',4)
%    Highlight nodes and edges in the drawn graph
highlight(p,T,'EdgeColor','red','LineWidth',3) 

Solving the Minimum Spanning Tree

1.利用MATLAB的minspantreefunction to solve minimum spanning tree,see above procedure

2.Kruskal算法：适合点多边少的图

3.Prim算法：Suitable for graphs with more edges and less edges

17 灰色预测GM(1,1)模型

GM(1,1)模型：1阶微分方程,1个变量

 特点：数据少,no obvious pattern,Suitable for using grey prediction

看不出规律,Using the cumulative method to create rules.

 new sequence generated,Generally looks like an exponential curve（直线）

• 可以用Expression of an exponential curve or even a straight line式来逼近This new order
• 构建一阶常微分方程来求解拟合曲线的函数表达式

优点：Available when there is little data and no obvious pattern,Using Differential Equations to Mining the Essential Laws of Data

缺点：Grey forecasts are only suitable for short-term forecasts、Exponential Growth Forecast