1、Preface
前言部分就中英文对照吧。至于为什么标题是中文的，题有长度限制，英文太长了。。。
Let's have the preface in both Chinese and English. As for why the title is in Chinese, there is a length limit on the question, as English is too long...
本文是对2020年亚太数学建模竞赛B题：美国总统候选人对美国和中国的经济影响分析的解题思路，希望能够对正在学习数学建模或者研究该类问题的读者提供帮助。
This article is a solution to question B of the 2020 Asia Pacific Mathematical Modeling Competition: Analysis of the Economic Impact of US Presidential Candidates on the United States and China. It is hoped that it can provide assistance to readers who are studying mathematical modeling or researching such problems.
由于亚太杯数学建模是纯英文竞赛，因此采用本篇使用英文进行叙述，中文版本可以访问：2020年亚太数学建模竞赛B题-中文版（美国总统候选人对美国和中国的经济影响分析）
Due to the fact that the Asia Pacific Cup Mathematical Modeling Competition is a pure English competition, this article is presented in English. The Chinese version can be accessed from Question B of the 2020 Asia Pacific Mathematical Modeling Competition - Chinese version 2020年亚太数学建模竞赛B题-中文版（美国总统候选人对美国和中国的经济影响分析）。
另，受本人英语水平所限，英文部分大多为机翻后优化，还请见谅。
Also, due to my limited English proficiency, most of the English parts are optimized after machine translation. Please forgive me.
2、 Problem Background
3、 Specific Issues
Question 1:
Question 2:
Question 3:
4、Train Of Thought
Question 1:
Establishing a mathematical model for quantitative analysis requires considering the following factors:
1. Tax Policy: The tax policies of different candidates, including tax reduction and tax increase policies, have different impacts on the US economy.
2. Trade Policy: The trade policies of different candidates, including trade restrictions and open trade, have different impacts on the US economy.
3. Infrastructure investment: Different candidates have different levels of attention and investment scale towards infrastructure investment, which can have an impact on the development of the US economy.
4. Medical insurance policies: The medical insurance policies of different candidates, including medical insurance reform and cancellation, will have an impact on the development of the US economy.
When establishing mathematical models, regression analysis can be conducted on the results of the 2008 and 2016 US elections to predict the potential impact of a specific candidate's election. After establishing the mathematical model, through the simulation of historical data and the prediction of actual data, we can quantitatively analyze the possible impact of the election of different candidates on the U.S. economy.
Question 2:
The following factors need to be considered:
1. Trade Policy: The trade policies of different candidates, including trade restrictions and open trade, have different impacts on the Chinese economy.
2. Investment policy: Different candidates have different levels and scales of attention to external investment, which will have an impact on the development of China's economy.
3. Environmental policies: Different candidates have different levels of attention and policy attitudes towards environmental protection, which will have an impact on the development of China's economy.
4. Foreign Policy: Different candidates have different attitudes towards foreign policy, which can have an impact on the development of China's economy.
Similarly, through regression analysis of historical data and prediction of actual data, mathematical models can be established to quantitatively analyze the possible impact of the election of different candidates on China's economy.
Question 3:
No matter which side wins, corresponding countermeasures and policies need to be formulated to cope with the potential impact. If the Democratic candidate is elected, it is recommended to strengthen economic cooperation with the United States and actively respond to trade policy adjustments. If the Republican candidate is elected, it is recommended to optimize economic and trade relations with the United States and take corresponding measures to alleviate trade pressure. In either case, China needs to continue to improve its technological level and innovation capabilities, strengthen infrastructure construction and environmental protection work, optimize market structure, and expand domestic demand to maintain stable economic growth.
5、 Mathematical modeling methods
There are many mathematical modeling methods applicable to this problem, and the following methods can be used:
1. Regression analysis: Regression analysis can obtain the potential impact of candidate election on the US or Chinese economy from historical data. By conducting regression analysis on historical data, a predictive model can be established to predict the potential impact of different candidates being elected.
2. Grey correlation analysis: Grey correlation analysis can compare the degree of impact of different factors on economic development, identify the factors with the greatest impact, and provide reference for formulating economic policies.
3. Goal planning: Goal planning can help formulate and achieve economic development goals, optimize economic indicators, improve efficiency and quality, and achieve sustainable economic development by establishing mathematical models.
4. Fuzzy comprehensive evaluation: Fuzzy comprehensive evaluation can comprehensively consider various factors and uncertainties, and obtain uncertainty analysis and prediction of the impact on economic development, providing reference for formulating economic policies.
5. System Dynamics Model: System dynamics models can help understand various dynamic relationships within and outside the economic system, predict future trends and changes, and provide reference for formulating reasonable economic policies.
6、 Related codes
For the above mathematical modeling methods, the classic code that can be used is as follows:
1. Regression analysis: Data analysis tools such as R and Python can be used for regression analysis, and Python libraries such as sklearn and statsmoodels can be used for model training and testing. The following is a simple code example for Python:
```
import pandas as pd
import numpy as np
import statsmodels.api as sm
# 导入数据
data = pd.read_csv('data.csv')
# 设置自变量和因变量
X = data[['x1', 'x2', 'x3']]
y = data['y']
# 构建回归模型
model = sm.OLS(y, X)
# 拟合模型
results = model.fit()
# 查看回归结果
print(results.summary())
```2. Grey correlation analysis: Professional grey correlation analysis tools such as GAR and Matlab can be used, as well as third-party libraries in Excel or Python for calculations. The following is a simple code example for Python:
```
import numpy as np
# 导入数据
data = np.loadtxt('data.csv', delimiter=',')
# 计算各因素与经济指标的关联系数
def gray_relation(x, y):
x_mean = np.mean(x)
y_mean = np.mean(y)
n = len(x)
k = 0.5
tmp = np.zeros(n)
for i in range(n):
tmp[i] = min(x[i]/x_mean, y[i]/y_mean)
return (sum(tmp)/n)**k
gray_relations = []
for i in range(data.shape[1]-1):
gray_relations.append(gray_relation(data[:,i], data[:,-1]))
# 给出各因素的权重
weights = gray_relations / np.sum(gray_relations)
print(weights)
```3. Goal Planning: Professional planning software such as Lingo and GAMS can be used for goal planning modeling, as well as third-party libraries in Python for model construction and solution. The following is a simple code example for Python:
```
import numpy as np
import scipy.optimize as opt
# 定义目标函数和约束条件
def objective(x):
return np.sum(x)
def constraint1(x):
return x[0] + x[1] - 10
def constraint2(x):
return x[0] - 2*x[1] + 5
def constraint3(x):
return x
x0 = np.array([1,1])
# 设定变量的取值范围
bnds = ((0, None), (0, None))
# 设置约束条件和求解器
con1 = {'type': 'eq', 'fun': constraint1}
con2 = {'type': 'eq', 'fun': constraint2}
cons = [con1, con2, {'type': 'ineq', 'fun': constraint3}]
solution = opt.minimize(objective, x0, method='SLSQP', bounds=bnds, constraints=cons)
print(solution)
```4. Fuzzy comprehensive evaluation: Professional fuzzy comprehensive evaluation software such as FCE and Startinsoft can be used, as well as tools such as Matlab and Python for fuzzy comprehensive evaluation. The following is a simple code example for Python:
```
import numpy as np
import skfuzzy as fuzz
# 设定输入变量和输出变量的范围
x1 = np.arange(0, 10, 1)
x2 = np.arange(0, 10, 1)
y = np.arange(0, 10, 1)
# 设定模糊集合
x1_lo = fuzz.trimf(x1, [0, 0, 5])
x1_md = fuzz.trimf(x1, [0, 5, 10])
x1_hi = fuzz.trimf(x1, [5, 10, 10])
x2_lo = fuzz.trimf(x2, [0, 0, 5])
x2_md = fuzz.trimf(x2, [0, 5, 10])
x2_hi = fuzz.trimf(x2, [5, 10, 10])
y_lo = fuzz.trimf(y, [0, 0, 5])
y_md = fuzz.trimf(y, [0, 5, 10])
y_hi = fuzz.trimf(y, [5, 10, 10])
# 设定输入变量和输出7、 Summary
The process of this mathematical modeling is to propose problem-solving ideas and modeling methods for the discussion of US presidential candidates' policies in the fields of economy, trade, etc.
On the one hand, we can establish a regression analysis model based on historical data to predict the possible economic impact of different candidates after being elected. The model includes several important factors, such as tax policy, trade policy, infrastructure investment, medical insurance policy, etc. Possible relevant factors can be selected from historical data for regression analysis to predict the potential impact of a specific candidate's election. At the same time, we pointed out that targeted comparative analysis of influencing factors can also be carried out through methods such as grey correlation analysis, goal planning, and fuzzy comprehensive evaluation.
In question two, we can establish a regression analysis model based on historical data to predict the potential economic impact of different candidates after their election in China. Similar to problem one, we can also conduct systematic analysis and research on different influencing factors through methods such as grey correlation analysis, goal planning, and fuzzy comprehensive evaluation.
In terms of the third aspect of the problem, this modeling process suggests that in different situations, China needs to continue to improve its technological level and innovation capabilities, strengthen infrastructure construction and environmental protection work, optimize market structure, and expand domestic demand to maintain stable economic growth.
Overall, this mathematical modeling study focuses on the understanding of the problems faced and their solutions in the context of data.