├── 2022国赛C题论文155代码复现 ├── C题.pdf ├── Regression equations available to gaojia.xlsx ├── Regression equations available to qianba.xlsx ├── c12.xlsx ├── gaojia_chemical_means.xlsx ├── qianba_chemical_means.xlsx ├── transformed_gaojia_weathered_state.xlsx ├── transformed_qianba_weathered_state.xlsx ├── weathering_summary_gaojia.xlsx ├── weathering_summary_qianba.xlsx ├── 一二表单合并对数中心化转换数据.xlsx ├── 一二表单合并数据.xlsx ├── 一二表单合并数据统计性分析.xlsx ├── 全国大学生数学建模大赛C题（C155).pdf ├── 解析方案 │ ├── 第一题 │ │ ├── 1.1 │ │ │ ├── Pearson卡方 _(类型)_(表面风化) (1).docx │ │ │ ├── Yates卡方 _(纹饰)_(表面风化) (1).docx │ │ │ ├── Yates卡方 _(颜色)_(表面风化).docx │ │ │ └── 数学建模2022C题1.1最终版.ipynb │ │ ├── 1.2 │ │ │ └── 数学建模2022国赛C代码BreakDown1.2.ipynb │ │ └── 1.3 │ │ │ └── 数学建模2022C题1.3-Copy3.ipynb │ ├── 第三题 │ │ └── 数学建模2022C题3.ipynb │ ├── 第二题 │ │ └── 数学建模2022C题2.ipynb │ └── 第四题 │ │ └── 数学建模2022C题4.ipynb └── 附件.xlsx ├── 2023年MathorCup高校数学建模挑战赛赛题 ├── 2023年MathorCup高校数学建模挑战赛承诺书（手写或者电子签名后上传）.docx ├── 2023年MathorCup高校数学建模挑战赛提交步骤.pdf ├── 2023年MathorCup高校数学建模挑战赛论文模板.doc ├── D题 │ ├── 2023年MathorCup高校数学建模挑战赛D题.pdf │ ├── 数据处理过程备份 2 │ │ ├── onedata3的生成过程.html │ │ ├── onedata3的生成过程.ipynb │ │ ├── onedata6的生成过程.html │ │ ├── onedata6的生成过程.ipynb │ │ ├── 特征重要性分析.html │ │ └── 特征重要性分析.ipynb │ ├── 第三题思路及其代码 │ │ ├── TwoData1.html │ │ ├── TwoData1.ipynb │ │ ├── TwoData2.html │ │ ├── TwoData2.ipynb │ │ └── 第三题思路说明.txt │ ├── 第二题数据处理 │ │ ├── Joystick_Position_Trend_Analysis.mlx │ │ ├── 操纵杆位置趋势分析代码.txt │ │ └── 问题2.docx │ ├── 第五题 │ │ ├── Third.html │ │ └── Third.ipynb │ ├── 论文.pdf │ └── 附件 │ │ ├── 附件1-2关键参数航段数据的字段说明.xlsx │ │ ├── 附件2：超限数据.xlsx │ │ └── 附件3 飞行参数测量数据 │ │ ├── 附件3：飞行参数测量数据.xlsx │ │ └── 飞行参数测量数据的字段说明.xls └── 第十三届MathorCup高校数学建模挑战赛论文格式及提交规范.pdf ├── README.md └── 数学建模国赛算法库 ├── 供给地与需求地的最优资源分配问题.ipynb ├── 分支定界算法求解整数规划.ipynb ├── 匈牙利算法求解整数规划.ipynb ├── 回归算法.ipynb ├── 层次分析法.ipynb ├── 拟牛顿法.ipynb ├── 插值法.ipynb ├── 灰色预测模型.ipynb ├── 粒子群算法.ipynb ├── 蚁群算法.ipynb ├── 遗传算法.ipynb └── 非线性规划函数.ipynb /2022国赛C题论文155代码复现/C题.pdf: 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特征期望计数小于5的单元格数最小期望计数期望计数小于5的单元格数的比例
0类型07.4482760.000000
1纹饰22.4827590.333333
2颜色120.4444440.750000
\n", 60 | "
" 61 | ], 62 | "text/plain": [ 63 | " 特征 期望计数小于5的单元格数 最小期望计数 期望计数小于5的单元格数的比例\n", 64 | "0 类型 0 7.448276 0.000000\n", 65 | "1 纹饰 2 2.482759 0.333333\n", 66 | "2 颜色 12 0.444444 0.750000" 67 | ] 68 | }, 69 | "execution_count": 1, 70 | "metadata": {}, 71 | "output_type": "execute_result" 72 | } 73 | ], 74 | "source": [ 75 | "import pandas as pd\n", 76 | "import numpy as np\n", 77 | "\n", 78 | "# Load data\n", 79 | "xls = pd.ExcelFile(\"E:\\\\数学建模国赛\\\\2022数学建模赛题\\\\C题\\\\附件.xlsx\")\n", 80 | "\n", 81 | "\n", 82 | "# Load all sheets in the Excel file\n", 83 | "sheets = xls.sheet_names\n", 84 | "dfs = {}\n", 85 | "for sheet in sheets:\n", 86 | " dfs[sheet] = pd.read_excel(xls, sheet)\n", 87 | "df1=dfs['表单1'].drop(columns=[\"文物编号\"])\n", 88 | "\n", 89 | "# 创建一个DataFrame来保存每个特征的计数信息\n", 90 | "count_info = pd.DataFrame(columns=['特征', '期望计数小于5的单元格数', \n", 91 | " '最小期望计数', '期望计数小于5的单元格数的比例'])\n", 92 | "\n", 93 | "# 对每个特征进行卡方检验\n", 94 | "for column in ['类型', '纹饰', '颜色']:\n", 95 | " # 删除含有空值的行\n", 96 | " df_dropped_na = df1[['表面风化', column]].dropna()\n", 97 | " \n", 98 | " # 创建列联表\n", 99 | " contingency_table = pd.crosstab(df_dropped_na['表面风化'], df_dropped_na[column])\n", 100 | " \n", 101 | " # 计算期望计数\n", 102 | " row_totals = contingency_table.sum(axis=1)\n", 103 | " col_totals = contingency_table.sum(axis=0)\n", 104 | " total = contingency_table.sum().sum()\n", 105 | " expected = np.outer(row_totals, col_totals) / total\n", 106 | " \n", 107 | " # 计算期望计数小于5的单元格数\n", 108 | " cells_with_expected_count_less_than_5 = (expected < 5).sum()\n", 109 | " \n", 110 | " # 获取最小期望计数\n", 111 | " min_expected_count = expected.min()\n", 112 | " \n", 113 | " # 计算期望计数小于5的单元格数的比例\n", 114 | " ratio_cells_with_expected_count_less_than_5 = cells_with_expected_count_less_than_5 / (contingency_table.shape[0] * contingency_table.shape[1])\n", 115 | " \n", 116 | " # 将结果保存到DataFrame\n", 117 | " count_info_to_append = pd.DataFrame({\n", 118 | " '特征': [column],\n", 119 | " '期望计数小于5的单元格数': [cells_with_expected_count_less_than_5],\n", 120 | " '最小期望计数': [min_expected_count],\n", 121 | " '期望计数小于5的单元格数的比例': [ratio_cells_with_expected_count_less_than_5]\n", 122 | " })\n", 123 | " \n", 124 | " count_info = pd.concat([count_info, count_info_to_append], ignore_index=True)\n", 125 | "\n", 126 | "# 显示计数信息\n", 127 | "count_info\n" 128 | ] 129 | }, 130 | { 131 | "cell_type": "code", 132 | "execution_count": 2, 133 | "id": "72c20404", 134 | "metadata": {}, 135 | "outputs": [ 136 | { 137 | "data": { 138 | "image/png": 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\n", 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" 141 | ] 142 | }, 143 | "metadata": {}, 144 | "output_type": "display_data" 145 | } 146 | ], 147 | "source": [ 148 | "import seaborn as sns\n", 149 | "import matplotlib.pyplot as plt\n", 150 | "plt.rcParams['font.sans-serif'] = ['SimHei']\n", 151 | "p_values = [0.009,0.084,0.507]\n", 152 | "p_values_df = pd.DataFrame({\n", 153 | " 'Feature': ['类型', '纹饰', '颜色'],\n", 154 | " 'p_value': p_values\n", 155 | "})\n", 156 | "# 创建图形\n", 157 | "plt.figure(figsize=(8, 6))\n", 158 | "bar_plot = sns.barplot(x='Feature', y='p_value', data=p_values_df)\n", 159 | "\n", 160 | "# 在条形顶部添加 p 值\n", 161 | "for i in range(p_values_df.shape[0]):\n", 162 | " bar_plot.text(i, p_values_df.p_value[i], round(p_values_df.p_value[i], 3), ha='center')\n", 163 | "\n", 164 | "# 添加 p=0.05 的参考线\n", 165 | "plt.axhline(y=0.05, color='r', linestyle='--')\n", 166 | "\n", 167 | "# 设置标题和标签\n", 168 | "plt.title('卡方检验 p值')\n", 169 | "plt.ylabel('p值')\n", 170 | "\n", 171 | "# 显示图形\n", 172 | "plt.show()\n" 173 | ] 174 | }, 175 | { 176 | "cell_type": "code", 177 | "execution_count": null, 178 | "id": "58845ae0", 179 | "metadata": {}, 180 | "outputs": [], 181 | "source": [] 182 | } 183 | ], 184 | "metadata": { 185 | "kernelspec": { 186 | "display_name": "Python 3 (ipykernel)", 187 | "language": "python", 188 | "name": "python3" 189 | }, 190 | "language_info": { 191 | "codemirror_mode": { 192 | "name": "ipython", 193 | "version": 3 194 | }, 195 | "file_extension": ".py", 196 | "mimetype": "text/x-python", 197 | "name": "python", 198 | "nbconvert_exporter": "python", 199 | "pygments_lexer": "ipython3", 200 | "version": "3.10.8" 201 | } 202 | }, 203 | "nbformat": 4, 204 | "nbformat_minor": 5 205 | } 206 | -------------------------------------------------------------------------------- /2022国赛C题论文155代码复现/解析方案/第三题/数学建模2022C题3.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "id": "8b41fd4a", 7 | "metadata": {}, 8 | "outputs": [ 9 | { 10 | "name": "stderr", 11 | "output_type": "stream", 12 | "text": [ 13 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 14 | " warnings.warn(\n", 15 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 16 | " warnings.warn(\n", 17 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 18 | " warnings.warn(\n", 19 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 20 | " warnings.warn(\n", 21 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 22 | " warnings.warn(\n", 23 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 24 | " warnings.warn(\n", 25 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 26 | " warnings.warn(\n", 27 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but DecisionTreeClassifier was fitted with feature names\n", 28 | " warnings.warn(\n" 29 | ] 30 | }, 31 | { 32 | "data": { 33 | "text/html": [ 34 | "
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文物编号表面风化预测类型
0A1无风化高钾
1A2风化铅钡
2A3无风化铅钡
3A4无风化铅钡
4A5风化铅钡
5A6风化高钾
6A7风化高钾
7A8无风化铅钡
\n", 108 | "
" 109 | ], 110 | "text/plain": [ 111 | " 文物编号 表面风化 预测类型\n", 112 | "0 A1 无风化 高钾\n", 113 | "1 A2 风化 铅钡\n", 114 | "2 A3 无风化 铅钡\n", 115 | "3 A4 无风化 铅钡\n", 116 | "4 A5 风化 铅钡\n", 117 | "5 A6 风化 高钾\n", 118 | "6 A7 风化 高钾\n", 119 | "7 A8 无风化 铅钡" 120 | ] 121 | }, 122 | "execution_count": 1, 123 | "metadata": {}, 124 | "output_type": "execute_result" 125 | } 126 | ], 127 | "source": [ 128 | "import pandas as pd\n", 129 | "from sklearn.model_selection import train_test_split\n", 130 | "from sklearn.tree import DecisionTreeClassifier\n", 131 | "from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score\n", 132 | "import matplotlib.pyplot as plt\n", 133 | "from sklearn.tree import plot_tree\n", 134 | "\n", 135 | "# 读取合并的数据\n", 136 | "data = pd.read_excel('E:\\\\数学建模国赛\\\\2022数学建模赛题\\\\C题\\\\一二表单合并数据.xlsx')\n", 137 | "\n", 138 | "# 删除无用列\n", 139 | "data.drop(columns=['Unnamed: 0'], inplace=True)\n", 140 | "\n", 141 | "# 定义函数以处理风化或未风化组的数据\n", 142 | "def process_group(data, group_condition):\n", 143 | " group_data = data[data['表面风化'] == group_condition]\n", 144 | " X = group_data.drop(columns=['类型', '表面风化', '文物采样点'])\n", 145 | " y = group_data['类型']\n", 146 | " return train_test_split(X, y, test_size=0.3, random_state=42)\n", 147 | "\n", 148 | "# 训练决策树模型\n", 149 | "def train_decision_tree(X_train, y_train):\n", 150 | " clf = DecisionTreeClassifier(random_state=42)\n", 151 | " clf.fit(X_train, y_train)\n", 152 | " return clf\n", 153 | "\n", 154 | "# 分离风化和未风化组\n", 155 | "X_train_weathered, X_test_weathered, y_train_weathered, y_test_weathered = process_group(data, '风化')\n", 156 | "X_train_unweathered, X_test_unweathered, y_train_unweathered, y_test_unweathered = process_group(data, '无风化')\n", 157 | "\n", 158 | "# 训练风化和未风化决策树模型\n", 159 | "clf_weathered = train_decision_tree(X_train_weathered, y_train_weathered)\n", 160 | "clf_unweathered = train_decision_tree(X_train_unweathered, y_train_unweathered)\n", 161 | "\n", 162 | "# 读取表单三数据\n", 163 | "uploaded_excel_path = 'E:\\\\数学建模国赛\\\\2022数学建模赛题\\\\C题\\\\附件.xlsx'\n", 164 | "new_data = pd.read_excel(uploaded_excel_path, sheet_name='表单3')\n", 165 | "new_data = new_data .fillna(0)\n", 166 | "# 分类新数据\n", 167 | "def classify_new_data(row):\n", 168 | " features = row.drop(labels=['文物编号', '表面风化'])\n", 169 | " if row['表面风化'] == '风化':\n", 170 | " return clf_weathered.predict([features])[0]\n", 171 | " else:\n", 172 | " return clf_unweathered.predict([features])[0]\n", 173 | "\n", 174 | "new_data['预测类型'] = new_data.apply(classify_new_data, axis=1)\n", 175 | "\n", 176 | "# 显示预测结果\n", 177 | "new_data[['文物编号', '表面风化', '预测类型']]\n" 178 | ] 179 | }, 180 | { 181 | "cell_type": "code", 182 | "execution_count": 2, 183 | "id": "bb0c8247", 184 | "metadata": {}, 185 | "outputs": [ 186 | { 187 | "name": "stderr", 188 | "output_type": "stream", 189 | "text": [ 190 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\cluster\\_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n", 191 | " warnings.warn(\n", 192 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1382: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n", 193 | " warnings.warn(\n" 194 | ] 195 | }, 196 | { 197 | "data": { 198 | "text/html": [ 199 | "
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文物编号表面风化二氧化硅(SiO2)氧化钠(Na2O)氧化钾(K2O)氧化钙(CaO)氧化镁(MgO)氧化铝(Al2O3)氧化铁(Fe2O3)氧化铜(CuO)氧化铅(PbO)氧化钡(BaO)五氧化二磷(P2O5)氧化锶(SrO)氧化锡(SnO2)二氧化硫(SO2)预测类型Cluster
0A1无风化78.450.00.006.081.867.232.152.110.000.001.060.030.000.51高钾0
1A2风化37.750.00.007.630.002.330.000.0034.300.0014.270.000.000.00铅钡1
2A3无风化31.950.01.367.190.812.937.060.2139.584.692.680.520.000.00铅钡1
3A4无风化35.470.00.792.891.057.076.450.9624.288.318.450.280.000.00铅钡1
4A5风化64.291.20.371.642.3412.750.810.9412.232.160.190.210.490.00铅钡0
5A6风化93.170.01.350.640.211.520.271.730.000.000.210.000.000.00高钾0
6A7风化90.830.00.981.120.005.060.241.170.000.000.130.000.000.11高钾0
7A8无风化51.120.00.230.890.002.120.009.0121.2411.341.460.310.002.26铅钡1
\n", 408 | "
" 409 | ], 410 | "text/plain": [ 411 | " 文物编号 表面风化 二氧化硅(SiO2) 氧化钠(Na2O) 氧化钾(K2O) 氧化钙(CaO) 氧化镁(MgO) 氧化铝(Al2O3) \\\n", 412 | "0 A1 无风化 78.45 0.0 0.00 6.08 1.86 7.23 \n", 413 | "1 A2 风化 37.75 0.0 0.00 7.63 0.00 2.33 \n", 414 | "2 A3 无风化 31.95 0.0 1.36 7.19 0.81 2.93 \n", 415 | "3 A4 无风化 35.47 0.0 0.79 2.89 1.05 7.07 \n", 416 | "4 A5 风化 64.29 1.2 0.37 1.64 2.34 12.75 \n", 417 | "5 A6 风化 93.17 0.0 1.35 0.64 0.21 1.52 \n", 418 | "6 A7 风化 90.83 0.0 0.98 1.12 0.00 5.06 \n", 419 | "7 A8 无风化 51.12 0.0 0.23 0.89 0.00 2.12 \n", 420 | "\n", 421 | " 氧化铁(Fe2O3) 氧化铜(CuO) 氧化铅(PbO) 氧化钡(BaO) 五氧化二磷(P2O5) 氧化锶(SrO) 氧化锡(SnO2) \\\n", 422 | "0 2.15 2.11 0.00 0.00 1.06 0.03 0.00 \n", 423 | "1 0.00 0.00 34.30 0.00 14.27 0.00 0.00 \n", 424 | "2 7.06 0.21 39.58 4.69 2.68 0.52 0.00 \n", 425 | "3 6.45 0.96 24.28 8.31 8.45 0.28 0.00 \n", 426 | "4 0.81 0.94 12.23 2.16 0.19 0.21 0.49 \n", 427 | "5 0.27 1.73 0.00 0.00 0.21 0.00 0.00 \n", 428 | "6 0.24 1.17 0.00 0.00 0.13 0.00 0.00 \n", 429 | "7 0.00 9.01 21.24 11.34 1.46 0.31 0.00 \n", 430 | "\n", 431 | " 二氧化硫(SO2) 预测类型 Cluster \n", 432 | "0 0.51 高钾 0 \n", 433 | "1 0.00 铅钡 1 \n", 434 | "2 0.00 铅钡 1 \n", 435 | "3 0.00 铅钡 1 \n", 436 | "4 0.00 铅钡 0 \n", 437 | "5 0.00 高钾 0 \n", 438 | "6 0.11 高钾 0 \n", 439 | "7 2.26 铅钡 1 " 440 | ] 441 | }, 442 | "execution_count": 2, 443 | "metadata": {}, 444 | "output_type": "execute_result" 445 | } 446 | ], 447 | "source": [ 448 | "from sklearn.cluster import KMeans\n", 449 | "from sklearn.preprocessing import StandardScaler\n", 450 | "\n", 451 | "# 提取数值特征\n", 452 | "numeric_features = new_data.select_dtypes(include=['number'])\n", 453 | "\n", 454 | "# 标准化数据\n", 455 | "scaler = StandardScaler()\n", 456 | "standardized_data = scaler.fit_transform(numeric_features)\n", 457 | "\n", 458 | "# 执行K均值聚类\n", 459 | "kmeans = KMeans(n_clusters=2, random_state=42)\n", 460 | "clusters = kmeans.fit_predict(standardized_data)\n", 461 | "\n", 462 | "# 将聚类结果添加到新数据表中\n", 463 | "new_data['Cluster'] = clusters\n", 464 | "\n", 465 | "# 显示带有聚类结果的前几行数据\n", 466 | "new_data" 467 | ] 468 | }, 469 | { 470 | "cell_type": "code", 471 | "execution_count": null, 472 | "id": "648662d4", 473 | "metadata": {}, 474 | "outputs": [], 475 | "source": [] 476 | } 477 | ], 478 | "metadata": { 479 | "kernelspec": { 480 | "display_name": "Python 3 (ipykernel)", 481 | "language": "python", 482 | "name": "python3" 483 | }, 484 | "language_info": { 485 | "codemirror_mode": { 486 | "name": "ipython", 487 | "version": 3 488 | }, 489 | "file_extension": ".py", 490 | "mimetype": "text/x-python", 491 | "name": "python", 492 | "nbconvert_exporter": "python", 493 | "pygments_lexer": "ipython3", 494 | "version": "3.10.8" 495 | } 496 | }, 497 | "nbformat": 4, 498 | "nbformat_minor": 5 499 | } 500 | -------------------------------------------------------------------------------- /2022国赛C题论文155代码复现/附件.xlsx: -------------------------------------------------------------------------------- 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ALTITUDE (1013)Inertial Vertical SpeedRADIO ALTCOMPUTED AIR SPDGROUNDSPEEDGEAR SELECT DOWNROLL ATTROLL ATT.1N1 SELTED-LN1 SELTED-R...DEPARTURE_AIRPORT_5DEPARTURE_AIRPORT_68DEPARTURE_AIRPORT_73DEPARTURE_AIRPORT_117DEPARTURE_AIRPORT_118DESTINATION_AIRPORTT_5DESTINATION_AIRPORTT_68DESTINATION_AIRPORTT_73DESTINATION_AIRPORTT_117DESTINATION_AIRPORTT_118
0135-5-830.08.0000.08790.087921.421.4...0100000010
1136-9-830.08.2500.08790.087921.421.5...0100000010
2136-12-830.08.2500.08790.087921.421.5...0100000010
3135-4-830.08.2500.08790.087921.421.5...0100000010
4136-3-830.08.5000.08790.087921.421.5...0100000010
\n", 176 | "

5 rows × 49 columns

\n", 177 | "
" 178 | ], 179 | "text/plain": [ 180 | " ALTITUDE (1013) Inertial Vertical Speed RADIO ALT COMPUTED AIR SPD \\\n", 181 | "0 135 -5 -8 30.0 \n", 182 | "1 136 -9 -8 30.0 \n", 183 | "2 136 -12 -8 30.0 \n", 184 | "3 135 -4 -8 30.0 \n", 185 | "4 136 -3 -8 30.0 \n", 186 | "\n", 187 | " GROUNDSPEED GEAR SELECT DOWN ROLL ATT ROLL ATT.1 N1 SELTED-L \\\n", 188 | "0 8.00 0 0.0879 0.0879 21.4 \n", 189 | "1 8.25 0 0.0879 0.0879 21.4 \n", 190 | "2 8.25 0 0.0879 0.0879 21.4 \n", 191 | "3 8.25 0 0.0879 0.0879 21.4 \n", 192 | "4 8.50 0 0.0879 0.0879 21.4 \n", 193 | "\n", 194 | " N1 SELTED-R ... DEPARTURE_AIRPORT_5 DEPARTURE_AIRPORT_68 \\\n", 195 | "0 21.4 ... 0 1 \n", 196 | "1 21.5 ... 0 1 \n", 197 | "2 21.5 ... 0 1 \n", 198 | "3 21.5 ... 0 1 \n", 199 | "4 21.5 ... 0 1 \n", 200 | "\n", 201 | " DEPARTURE_AIRPORT_73 DEPARTURE_AIRPORT_117 DEPARTURE_AIRPORT_118 \\\n", 202 | "0 0 0 0 \n", 203 | "1 0 0 0 \n", 204 | "2 0 0 0 \n", 205 | "3 0 0 0 \n", 206 | "4 0 0 0 \n", 207 | "\n", 208 | " DESTINATION_AIRPORTT_5 DESTINATION_AIRPORTT_68 DESTINATION_AIRPORTT_73 \\\n", 209 | "0 0 0 0 \n", 210 | "1 0 0 0 \n", 211 | "2 0 0 0 \n", 212 | "3 0 0 0 \n", 213 | "4 0 0 0 \n", 214 | "\n", 215 | " DESTINATION_AIRPORTT_117 DESTINATION_AIRPORTT_118 \n", 216 | "0 1 0 \n", 217 | "1 1 0 \n", 218 | "2 1 0 \n", 219 | "3 1 0 \n", 220 | "4 1 0 \n", 221 | "\n", 222 | "[5 rows x 49 columns]" 223 | ] 224 | }, 225 | "execution_count": 1, 226 | "metadata": {}, 227 | "output_type": "execute_result" 228 | } 229 | ], 230 | "source": [ 231 | "from sklearn.cluster import KMeans\n", 232 | "from sklearn.datasets import make_blobs\n", 233 | "from sklearn.feature_selection import mutual_info_classif\n", 234 | "from sklearn.feature_selection import chi2\n", 235 | "import numpy as np\n", 236 | "import pandas as pd\n", 237 | "\n", 238 | "# 读取 Excel 文件\n", 239 | "df6 = pd.read_excel('D:\\mathercup\\OneData6.xlsx')\n", 240 | "\n", 241 | "# 显示前几行数据+-\n", 242 | "df6.head()" 243 | ] 244 | }, 245 | { 246 | "cell_type": "code", 247 | "execution_count": 2, 248 | "id": "9e1c1fa1", 249 | "metadata": { 250 | "scrolled": true 251 | }, 252 | "outputs": [ 253 | { 254 | "name": "stderr", 255 | "output_type": "stream", 256 | "text": [ 257 | "D:\\py1.1\\envs\\pytorch\\lib\\site-packages\\sklearn\\cluster\\_kmeans.py:870: FutureWarning: The default value of `n_init` will change from 10 to 'auto' in 1.4. Set the value of `n_init` explicitly to suppress the warning\n", 258 | " warnings.warn(\n" 259 | ] 260 | }, 261 | { 262 | "data": { 263 | "text/html": [ 264 | "
KMeans(n_clusters=3, random_state=42)
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" 265 | ], 266 | "text/plain": [ 267 | "KMeans(n_clusters=3, random_state=42)" 268 | ] 269 | }, 270 | "execution_count": 2, 271 | "metadata": {}, 272 | "output_type": "execute_result" 273 | } 274 | ], 275 | "source": [ 276 | "kmeans = KMeans(n_clusters=3, random_state=42)\n", 277 | "kmeans.fit(df6)" 278 | ] 279 | }, 280 | { 281 | "cell_type": "code", 282 | "execution_count": 3, 283 | "id": "6225ac76", 284 | "metadata": {}, 285 | "outputs": [ 286 | { 287 | "data": { 288 | "text/plain": [ 289 | "array([1, 1, 1, ..., 0, 0, 0])" 290 | ] 291 | }, 292 | "execution_count": 3, 293 | "metadata": {}, 294 | "output_type": "execute_result" 295 | } 296 | ], 297 | "source": [ 298 | "labels = kmeans.labels_\n", 299 | "labels" 300 | ] 301 | }, 302 | { 303 | "cell_type": "code", 304 | "execution_count": 8, 305 | "id": "5947b80e", 306 | "metadata": {}, 307 | "outputs": [], 308 | "source": [ 309 | "mutual_info_scores = mutual_info_classif(df6, labels)" 310 | ] 311 | }, 312 | { 313 | "cell_type": "code", 314 | "execution_count": 16, 315 | "id": "83d8009a", 316 | "metadata": {}, 317 | "outputs": [ 318 | { 319 | "name": "stdout", 320 | "output_type": "stream", 321 | "text": [ 322 | "Feature 0 Mutual Information: 0.6162\n", 323 | "Feature 1 Mutual Information: 0.0917\n", 324 | "Feature 2 Mutual Information: 0.1129\n", 325 | "Feature 3 Mutual Information: 0.3990\n", 326 | "Feature 4 Mutual Information: 0.2289\n", 327 | "Feature 5 Mutual Information: 0.0479\n", 328 | "Feature 6 Mutual Information: 0.0536\n", 329 | "Feature 7 Mutual Information: 0.0581\n", 330 | "Feature 8 Mutual Information: 0.3063\n", 331 | "Feature 9 Mutual Information: 0.3056\n", 332 | "Feature 10 Mutual Information: 0.7034\n", 333 | "Feature 11 Mutual Information: 0.1503\n", 334 | "Feature 12 Mutual Information: 0.0957\n", 335 | "Feature 13 Mutual Information: 0.0423\n", 336 | "Feature 14 Mutual Information: 0.0530\n", 337 | "Feature 15 Mutual Information: 0.4664\n", 338 | "Feature 16 Mutual Information: 0.4658\n", 339 | "Feature 17 Mutual Information: 0.4695\n", 340 | "Feature 18 Mutual Information: 0.4703\n", 341 | "Feature 19 Mutual Information: 0.0338\n", 342 | "Feature 20 Mutual Information: 0.0153\n", 343 | "Feature 21 Mutual Information: 0.0172\n", 344 | "Feature 22 Mutual Information: 1.0772\n", 345 | "Feature 23 Mutual Information: 0.0011\n", 346 | "Feature 24 Mutual Information: 0.0431\n", 347 | "Feature 25 Mutual Information: 0.0382\n", 348 | "Feature 26 Mutual Information: 0.0448\n", 349 | "Feature 27 Mutual Information: 0.1615\n", 350 | "Feature 28 Mutual Information: 0.1609\n", 351 | "Feature 29 Mutual Information: 0.0251\n", 352 | "Feature 30 Mutual Information: 0.3589\n", 353 | "Feature 31 Mutual Information: 0.0243\n", 354 | "Feature 32 Mutual Information: 0.0425\n", 355 | "Feature 33 Mutual Information: 0.0310\n", 356 | "Feature 34 Mutual Information: 0.0538\n", 357 | "Feature 35 Mutual Information: 0.0416\n", 358 | "Feature 36 Mutual Information: 0.1099\n", 359 | "Feature 37 Mutual Information: 0.1582\n", 360 | "Feature 38 Mutual Information: 0.0905\n", 361 | "Feature 39 Mutual Information: 0.0516\n", 362 | "Feature 40 Mutual Information: 0.0154\n", 363 | "Feature 41 Mutual Information: 0.0371\n", 364 | "Feature 42 Mutual Information: 0.0203\n", 365 | "Feature 43 Mutual Information: 0.0160\n", 366 | "Feature 44 Mutual Information: 0.0483\n", 367 | "Feature 45 Mutual Information: 0.0158\n", 368 | "Feature 46 Mutual Information: 0.0324\n", 369 | "Feature 47 Mutual Information: 0.0090\n", 370 | "Feature 48 Mutual Information: 0.0459\n" 371 | ] 372 | } 373 | ], 374 | "source": [ 375 | "for i in range(df6.shape[1]):\n", 376 | " print(\"Feature {} Mutual Information: {:.4f}\".format(i, mutual_info_scores[i]))" 377 | ] 378 | }, 379 | { 380 | "cell_type": "code", 381 | "execution_count": 12, 382 | "id": "e443783a", 383 | "metadata": {}, 384 | "outputs": [ 385 | { 386 | "name": "stdout", 387 | "output_type": "stream", 388 | "text": [ 389 | "Selected Features Indices: [22, 10, 0, 18, 17, 15, 16, 3, 30, 8]\n" 390 | ] 391 | } 392 | ], 393 | "source": [ 394 | "# 排序并选择前10个互信息值最大的特征\n", 395 | "selected_features_indices = sorted(range(df6.shape[1]), key=lambda i: mutual_info_scores[i], reverse=True)[:10]\n", 396 | "\n", 397 | "# 输出选择的特征索引\n", 398 | "print(\"Selected Features Indices: \", selected_features_indices)" 399 | ] 400 | }, 401 | { 402 | "cell_type": "code", 403 | "execution_count": 15, 404 | "id": "2dbac333", 405 | "metadata": {}, 406 | "outputs": [ 407 | { 408 | "name": "stdout", 409 | "output_type": "stream", 410 | "text": [ 411 | "Feature names from file: ['ALTITUDE (1013)', 'Inertial Vertical Speed', 'RADIO ALT', 'COMPUTED AIR SPD', 'GROUNDSPEED', ' GEAR SELECT DOWN', 'ROLL ATT', 'ROLL ATT.1', 'N1 SELTED-L', 'N1 SELTED-R', 'MAGNETIC HEADING', 'WIND DIR(ADIRU)', 'WIND SPD(ADIRU)', 'A/T ENGAGED', 'ANY A/P ENGAGED', 'TRA-L', 'TRA-L.1', 'TRA-R', 'TRA-R.1', 'RUDD POSN', 'PITCH ATT RATE', 'PITCH ATT RATE.1', 'FMF GROSS WEIGHT', 'WOW INDICATE INAIR_STD', 'WOW INDICATE INAIR_MEAN', 'COG NORM ACCEL_STD', 'COG NORM ACCEL_MEAN', 'RMS_LOCALIZER', 'RMS_GLIDESLOPE', 'PITCH ATTL_STD', 'PITCH ATT_MEAN', 'CAP CLM 1 POSN_STD', 'CAP CLM 1 POSN_MEAN', 'CAP WHL 1 POSN_STD', 'CAP WHL 1 POSN_MEAN', 'DATE: DAY_7', 'DATE: DAY_8', 'DATE: DAY_9', 'DATE: DAY_10', 'DEPARTURE_AIRPORT_5', 'DEPARTURE_AIRPORT_68', 'DEPARTURE_AIRPORT_73', 'DEPARTURE_AIRPORT_117', 'DEPARTURE_AIRPORT_118', 'DESTINATION_AIRPORTT_5', 'DESTINATION_AIRPORTT_68', 'DESTINATION_AIRPORTT_73', 'DESTINATION_AIRPORTT_117', 'DESTINATION_AIRPORTT_118']\n" 412 | ] 413 | } 414 | ], 415 | "source": [ 416 | "\n", 417 | "# 获取特征名称列表\n", 418 | "feature_names = df6.columns.tolist()\n", 419 | "print(\"Feature names from file: \", feature_names)\n" 420 | ] 421 | }, 422 | { 423 | "cell_type": "code", 424 | "execution_count": 18, 425 | "id": "b156dddf", 426 | "metadata": {}, 427 | "outputs": [ 428 | { 429 | "data": { 430 | "text/plain": [ 431 | "{'FMF GROSS WEIGHT': 1.0772040072225644,\n", 432 | " 'MAGNETIC HEADING': 0.7033938576718883,\n", 433 | " 'ALTITUDE (1013)': 0.6161810329581932,\n", 434 | " 'TRA-R.1': 0.4702851787321869,\n", 435 | " 'TRA-R': 0.46954438749493677,\n", 436 | " 'TRA-L': 0.4664298446926787,\n", 437 | " 'TRA-L.1': 0.4658418133645956,\n", 438 | " 'COMPUTED AIR SPD': 0.398997384815331,\n", 439 | " 'PITCH ATT_MEAN': 0.3588688236763906,\n", 440 | " 'N1 SELTED-L': 0.30631984567708614}" 441 | ] 442 | }, 443 | "execution_count": 18, 444 | "metadata": {}, 445 | "output_type": "execute_result" 446 | } 447 | ], 448 | "source": [ 449 | "mutual_info_dict = {feature_names[i]: mutual_info_scores[i] for i in selected_features_indices}\n", 450 | "mutual_info_dict" 451 | ] 452 | }, 453 | { 454 | "cell_type": "code", 455 | "execution_count": null, 456 | "id": "9d72e2df", 457 | "metadata": {}, 458 | "outputs": [], 459 | "source": [] 460 | } 461 | ], 462 | "metadata": { 463 | "kernelspec": { 464 | "display_name": "Python 3 (ipykernel)", 465 | "language": "python", 466 | "name": "python3" 467 | }, 468 | "language_info": { 469 | "codemirror_mode": { 470 | "name": "ipython", 471 | "version": 3 472 | }, 473 | "file_extension": ".py", 474 | "mimetype": "text/x-python", 475 | "name": "python", 476 | "nbconvert_exporter": "python", 477 | "pygments_lexer": "ipython3", 478 | "version": "3.10.8" 479 | } 480 | }, 481 | "nbformat": 4, 482 | "nbformat_minor": 5 483 | } 484 | -------------------------------------------------------------------------------- /2023年MathorCup高校数学建模挑战赛赛题/D题/第三题思路及其代码/TwoData2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "id": "0319a55f", 7 | "metadata": { 8 | "scrolled": false 9 | }, 10 | "outputs": [ 11 | { 12 | "data": { 13 | "text/html": [ 14 | "
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\n", 563 | "
" 564 | ], 565 | "text/plain": [ 566 | " EVENT_NAME(超限名称) ARN（机号）_100号机 ARN（机号）_101号机 ARN（机号）_102号机 \\\n", 567 | "0 50英尺至接地距离远 0 0 0 \n", 568 | "1 50英尺至接地距离远 0 0 0 \n", 569 | "2 GPWS警告(sink rate) 0 0 0 \n", 570 | "3 下降率大400-50ft 0 0 0 \n", 571 | "4 50英尺至接地距离远 0 0 0 \n", 572 | "... ... ... ... ... \n", 573 | "44098 爬升速度大35-1000ft 0 0 0 \n", 574 | "44099 爬升速度大35-1000ft 0 0 0 \n", 575 | "44100 爬升速度大35-1000ft 0 0 0 \n", 576 | "44101 50英尺至接地距离远 0 0 0 \n", 577 | "44102 接地速度小 0 0 0 \n", 578 | "\n", 579 | " ARN（机号）_103号机 ARN（机号）_104号机 ARN（机号）_105号机 ARN（机号）_106号机 \\\n", 580 | "0 0 0 0 0 \n", 581 | "1 0 0 0 0 \n", 582 | "2 0 0 0 0 \n", 583 | "3 0 0 0 0 \n", 584 | "4 0 0 0 0 \n", 585 | "... ... ... ... ... \n", 586 | "44098 0 0 0 0 \n", 587 | "44099 0 0 0 0 \n", 588 | "44100 0 0 0 0 \n", 589 | "44101 0 0 0 0 \n", 590 | "44102 0 0 0 0 \n", 591 | "\n", 592 | " ARN（机号）_107号机 ARN（机号）_108号机 ... DEP（起飞机场）_107 DEP（起飞机场）_108 \\\n", 593 | "0 0 0 ... 0 0 \n", 594 | "1 0 0 ... 0 0 \n", 595 | "2 0 0 ... 0 0 \n", 596 | "3 0 0 ... 0 0 \n", 597 | "4 0 0 ... 0 0 \n", 598 | "... ... ... ... ... ... \n", 599 | "44098 0 0 ... 0 0 \n", 600 | "44099 0 0 ... 0 0 \n", 601 | "44100 0 0 ... 0 0 \n", 602 | "44101 0 0 ... 0 0 \n", 603 | "44102 0 0 ... 0 0 \n", 604 | "\n", 605 | " DEP（起飞机场）_109 DEP（起飞机场）_110 DEP（起飞机场）_111 DEP（起飞机场）_112 \\\n", 606 | "0 0 0 0 0 \n", 607 | "1 0 0 0 0 \n", 608 | "2 0 0 0 0 \n", 609 | "3 0 0 0 0 \n", 610 | "4 0 0 0 0 \n", 611 | "... ... ... ... ... \n", 612 | "44098 0 0 0 0 \n", 613 | "44099 0 0 0 0 \n", 614 | "44100 0 0 0 0 \n", 615 | "44101 0 0 0 0 \n", 616 | "44102 0 0 0 0 \n", 617 | "\n", 618 | " DEP（起飞机场）_113 DEP（起飞机场）_114 DEP（起飞机场）_115 DEP（起飞机场）_116 \n", 619 | "0 0 0 0 0 \n", 620 | "1 0 0 0 0 \n", 621 | "2 0 0 0 0 \n", 622 | "3 0 0 0 0 \n", 623 | "4 0 0 0 0 \n", 624 | "... ... ... ... ... \n", 625 | "44098 0 0 1 0 \n", 626 | "44099 0 0 1 0 \n", 627 | "44100 0 0 1 0 \n", 628 | "44101 0 0 0 1 \n", 629 | "44102 0 0 0 1 \n", 630 | "\n", 631 | "[44103 rows x 378 columns]" 632 | ] 633 | }, 634 | "execution_count": 10, 635 | "metadata": {}, 636 | "output_type": "execute_result" 637 | } 638 | ], 639 | "source": [ 640 | "data=data.drop(columns=['ALERT（警告级别）_2', 'ALERT（警告级别）_3'])\n", 641 | "data" 642 | ] 643 | }, 644 | { 645 | "cell_type": "code", 646 | "execution_count": 20, 647 | "id": "298792d7", 648 | "metadata": {}, 649 | "outputs": [ 650 | { 651 | "name": "stdout", 652 | "output_type": "stream", 653 | "text": [ 654 | "标签\t\t前三列名称\n", 655 | "50英尺至接地距离近\t\tDEP（起飞机场）_46, ARR（目的机场）_76, ARR（目的机场）_24\n", 656 | "50英尺至接地距离远\t\tARR（目的机场）_107, ARR（目的机场）_53, ARR（目的机场）_13\n", 657 | "GPWS警告(sink rate)\t\tDEP（起飞机场）_1, ARR（目的机场）_76, ARR（目的机场）_24\n", 658 | "GPWS警告(windshear)\t\tDEP（起飞机场）_22, ARR（目的机场）_24, ARR（目的机场）_76\n", 659 | "High normal accel with flap (in flight)\t\tARN（机号）_48号机, ARN（机号）_6号机, DEP（起飞机场）_113\n", 660 | "Left of centreline below 1000ft\t\t月份_201506, 月份_201507, 月份_201606\n", 661 | "TCAS RA 警告\t\tDEP（起飞机场）_93, ARR（目的机场）_76, ARR（目的机场）_24\n", 662 | "下滑道警告\t\tARN（机号）_68号机, ARN（机号）_91号机, DEP（起飞机场）_113\n", 663 | "下降率大1000-400(含)ft\t\tARR（目的机场）_65, ARR（目的机场）_36, DEP（起飞机场）_113\n", 664 | "下降率大2000-1000（含）ft\t\tDEP（起飞机场）_23, ARR（目的机场）_76, ARR（目的机场）_24\n", 665 | "下降率大400-50ft\t\tDEP（起飞机场）_60, ARR（目的机场）_76, ARR（目的机场）_24\n", 666 | "低于下滑道\t\tARN（机号）_32号机, ARN（机号）_47号机, ARN（机号）_98号机\n", 667 | "低空大速度2500ft以下\t\t月份_201505, 月份_201502, 月份_201602\n", 668 | "坡度大400/1500ft以上\t\tARR（目的机场）_95, ARR（目的机场）_49, DEP（起飞机场）_113\n", 669 | "复飞\t\t月份_201609, 月份_201608, 月份_201611\n", 670 | "抬前轮速度大\t\tDEP（起飞机场）_83, ARR（目的机场）_76, ARR（目的机场）_24\n", 671 | "抬前轮速度小\t\t月份_201507, 月份_201604, 月份_201508\n", 672 | "抬头速率大\t\t月份_201607, 月份_201602, DEP（起飞机场）_113\n", 673 | "抬头速率小\t\tDEP（起飞机场）_114, ARR（目的机场）_24, ARR（目的机场）_76\n", 674 | "接地速度小\t\t月份_201507, 月份_201501, 月份_201505\n", 675 | "收反推晚\t\tARR（目的机场）_107, ARR（目的机场）_65, DEP（起飞机场）_113\n", 676 | "放起落架晚\t\tDEP（起飞机场）_6, ARR（目的机场）_24, ARR（目的机场）_76\n", 677 | "未知\t\tARR（目的机场）_20, ARR（目的机场）_76, ARR（目的机场）_24\n", 678 | "爬升坡度大35-400(含)ft\t\t月份_201609, 月份_201608, 月份_201507\n", 679 | "爬升速度大35-1000ft\t\tARN（机号）_65号机, ARN（机号）_64号机, DEP（起飞机场）_113\n", 680 | "爬升速度小35-1000ft\t\tARR（目的机场）_98, ARR（目的机场）_91, DEP（起飞机场）_113\n", 681 | "直线滑行速度大\t\tARR（目的机场）_17, ARR（目的机场）_76, ARR（目的机场）_24\n", 682 | "着陆俯仰角大\t\tARR（目的机场）_103, ARR（目的机场）_88, DEP（起飞机场）_113\n", 683 | "着陆俯仰角小\t\tPHASE（飞行阶段）_6, PHASE（飞行阶段）_5, PHASE（飞行阶段）_0\n", 684 | "着陆垂直载荷大\t\tDEP（起飞机场）_49, ARR（目的机场）_76, ARR（目的机场）_24\n", 685 | "着陆襟翼到位晚\t\tDEP（起飞机场）_91, ARR（目的机场）_24, ARR（目的机场）_76\n", 686 | "着陆重、跳着陆\t\tDEP（起飞机场）_45, ARR（目的机场）_24, ARR（目的机场）_76\n", 687 | "离地仰角大\t\tPHASE（飞行阶段）_2, PHASE（飞行阶段）_4, PHASE（飞行阶段）_3\n", 688 | "离地速度大\t\tARR（目的机场）_63, ARR（目的机场）_101, DEP（起飞机场）_113\n", 689 | "离地速度小\t\tDEP（起飞机场）_105, ARR（目的机场）_24, ARR（目的机场）_76\n", 690 | "空中过载\t\tARR（目的机场）_30, ARR（目的机场）_9, DEP（起飞机场）_113\n", 691 | "起飞EGT超限\t\tDEP（起飞机场）_50, ARR（目的机场）_24, ARR（目的机场）_76\n", 692 | "起飞坡度大0-35（含）ft\t\tDEP（起飞机场）_91, ARR（目的机场）_24, ARR（目的机场）_76\n", 693 | "起飞收起落架晚\t\tPHASE（飞行阶段）_7, PHASE（飞行阶段）_3, PHASE（飞行阶段）_0\n", 694 | "起飞滑跑方向不稳定\t\tARR（目的机场）_108, ARR（目的机场）_36, ARR（目的机场）_13\n", 695 | "超襟翼限制速度Vfe\t\tDEP（起飞机场）_51, ARR（目的机场）_24, ARR（目的机场）_76\n", 696 | "转弯滑行速度大\t\tARN（机号）_80号机, ARN（机号）_111号机, ARN（机号）_31号机\n", 697 | "进近坡度大1500-500（含）ft\t\tDEP（起飞机场）_63, ARR（目的机场）_76, ARR（目的机场）_24\n", 698 | "进近坡度大200-50（含）ft\t\tDEP（起飞机场）_101, ARR（目的机场）_76, ARR（目的机场）_24\n", 699 | "进近坡度大500-200（含）ft\t\tARR（目的机场）_56, ARR（目的机场）_76, ARR（目的机场）_24\n", 700 | "进近坡度大50ft以下\t\tDEP（起飞机场）_48, ARR（目的机场）_76, ARR（目的机场）_24\n", 701 | "进近速度大50 ft以下\t\tARN（机号）_63号机, ARN（机号）_83号机, DEP（起飞机场）_113\n", 702 | "进近速度大500-50（含）ft\t\tARR（目的机场）_21, ARR（目的机场）_17, ARR（目的机场）_109\n", 703 | "进近速度小500 ft以下\t\t月份_201509, 月份_201505, DEP（起飞机场）_113\n", 704 | "高于下滑道\t\tDEP（起飞机场）_31, ARR（目的机场）_24, ARR（目的机场）_76\n" 705 | ] 706 | } 707 | ], 708 | "source": [ 709 | "import pandas as pd\n", 710 | "from sklearn.linear_model import LinearRegression\n", 711 | "\n", 712 | "\n", 713 | "# 对标签列进行独热编码\n", 714 | "labels = data.iloc[:, 0]\n", 715 | "labels_encoded = pd.get_dummies(labels)\n", 716 | "\n", 717 | "# 提取其他 n 列数据作为特征\n", 718 | "n = data.shape[1] - 1 # 计算特征列数\n", 719 | "features = data.iloc[:, 1:] # 提取特征数据\n", 720 | "\n", 721 | "# 执行多元线性回归\n", 722 | "mdl = LinearRegression()\n", 723 | "mdl.fit(features, labels_encoded) # 使用 LinearRegression 进行多元线性回归\n", 724 | "\n", 725 | "# 提取回归模型的回归系数\n", 726 | "coefs = mdl.coef_\n", 727 | "\n", 728 | "# 初始化存储结果的字典\n", 729 | "top5_cols = {}\n", 730 | "\n", 731 | "# 遍历每个标签，找出对应的前三列影响最大的因子\n", 732 | "for i, label in enumerate(labels_encoded.columns):\n", 733 | " idx = coefs[i].argsort()[-3:] # 找出最大的三个系数的索引\n", 734 | "''' \n", 735 | " 这段代码使用了 NumPy 库中的 argpartition 函数来找出一个一维数组中绝对值最大的五个数值对应的索引。\n", 736 | "具体解析如下：\n", 737 | "\n", 738 | "coefs[i]：表示一维数组 coefs 中的第 i 个元素，其中 coefs 可能是一个二维数组，i 表示其中的某一行。\n", 739 | "np.abs(coefs[i])：表示取 coefs[i] 中各元素的绝对值，得到一个与 coefs[i] 相同大小的新数组。\n", 740 | "np.argpartition(np.abs(coefs[i]), -5)：表示对绝对值数组进行分区操作，将绝对值最大的五个数值的索引放在数组的末尾，这里使用了 -5 表示倒数第五个位置。\n", 741 | "[-5:]：表示取分区后数组末尾的五个索引，即绝对值最大的五个系数的索引。\n", 742 | "最终，idx 变量将保存绝对值最大的五个系数在 coefs[i] 中对应的索引，用于后续的处理。\n", 743 | "'''\n", 744 | " top5_cols[label] = features.columns[idx] # 存储对应的列名称\n", 745 | "\n", 746 | "# 输出结果\n", 747 | "print('标签\\t\\t前三列名称')\n", 748 | "for label, cols in top5_cols.items():\n", 749 | " print(f'{label}\\t\\t{\", \".join(cols)}')\n" 750 | ] 751 | }, 752 | { 753 | "cell_type": "code", 754 | "execution_count": 21, 755 | "id": "8cb1f9ca", 756 | "metadata": {}, 757 | "outputs": [ 758 | { 759 | "name": "stdout", 760 | "output_type": "stream", 761 | "text": [ 762 | "标签\t\t前三列名称\n", 763 | "50英尺至接地距离近\t\tDEP（起飞机场）_46, ARN（机号）_33号机, ARR（目的机场）_109\n", 764 | "50英尺至接地距离远\t\tARN（机号）_90号机, ARN（机号）_24号机, PHASE（飞行阶段）_6\n", 765 | "GPWS警告(sink rate)\t\tARN（机号）_9号机, ARR（目的机场）_54, ARR（目的机场）_65\n", 766 | "GPWS警告(windshear)\t\tARR（目的机场）_74, DEP（起飞机场）_106, DEP（起飞机场）_22\n", 767 | "High normal accel with flap (in flight)\t\tARR（目的机场）_4, DEP（起飞机场）_19, ARN（机号）_6号机\n", 768 | "Left of centreline below 1000ft\t\t月份_201606, ARR（目的机场）_16, ARN（机号）_3号机\n", 769 | "TCAS RA 警告\t\t月份_201608, ARR（目的机场）_78, ARN（机号）_82号机\n", 770 | "下滑道警告\t\tARN（机号）_68号机, ARN（机号）_91号机, ARR（目的机场）_95\n", 771 | "下降率大1000-400(含)ft\t\tARR（目的机场）_69, ARR（目的机场）_65, ARR（目的机场）_36\n", 772 | "下降率大2000-1000（含）ft\t\tARR（目的机场）_64, PHASE（飞行阶段）_5, ARR（目的机场）_84\n", 773 | "下降率大400-50ft\t\tARN（机号）_11号机, ARN（机号）_31号机, PHASE（飞行阶段）_5\n", 774 | "低于下滑道\t\tDEP（起飞机场）_72, ARR（目的机场）_80, PHASE（飞行阶段）_5\n", 775 | "低空大速度2500ft以下\t\tARN（机号）_90号机, ARR（目的机场）_67, ARN（机号）_94号机\n", 776 | "坡度大400/1500ft以上\t\tARN（机号）_55号机, ARN（机号）_36号机, ARR（目的机场）_49\n", 777 | "复飞\t\tARR（目的机场）_93, ARN（机号）_95号机, ARN（机号）_107号机\n", 778 | "抬前轮速度大\t\tARN（机号）_28号机, ARR（目的机场）_101, PHASE（飞行阶段）_2\n", 779 | "抬前轮速度小\t\tARR（目的机场）_98, ARR（目的机场）_44, PHASE（飞行阶段）_2\n", 780 | "抬头速率大\t\tDEP（起飞机场）_16, ARN（机号）_69号机, PHASE（飞行阶段）_2\n", 781 | "抬头速率小\t\tARN（机号）_84号机, ARN（机号）_77号机, PHASE（飞行阶段）_0\n", 782 | "接地速度小\t\tARR（目的机场）_9, DEP（起飞机场）_24, PHASE（飞行阶段）_6\n", 783 | "收反推晚\t\tARR（目的机场）_107, ARR（目的机场）_65, PHASE（飞行阶段）_7\n", 784 | "放起落架晚\t\tARR（目的机场）_4, DEP（起飞机场）_6, ARR（目的机场）_22\n", 785 | "未知\t\tARN（机号）_97号机, ARN（机号）_22号机, PHASE（飞行阶段）_0\n", 786 | "爬升坡度大35-400(含)ft\t\t月份_201507, ARN（机号）_18号机, ARR（目的机场）_99\n", 787 | "爬升速度大35-1000ft\t\tARR（目的机场）_66, DEP（起飞机场）_115, PHASE（飞行阶段）_4\n", 788 | "爬升速度小35-1000ft\t\tARR（目的机场）_30, ARR（目的机场）_98, ARR（目的机场）_91\n", 789 | "直线滑行速度大\t\tDEP（起飞机场）_49, ARN（机号）_95号机, PHASE（飞行阶段）_1\n", 790 | "着陆俯仰角大\t\tARR（目的机场）_88, DEP（起飞机场）_83, PHASE（飞行阶段）_7\n", 791 | "着陆俯仰角小\t\tARR（目的机场）_31, ARR（目的机场）_91, ARR（目的机场）_25\n", 792 | "着陆垂直载荷大\t\tARR（目的机场）_75, ARR（目的机场）_82, PHASE（飞行阶段）_7\n", 793 | "着陆襟翼到位晚\t\tARN（机号）_68号机, ARR（目的机场）_101, ARR（目的机场）_96\n", 794 | "着陆重、跳着陆\t\tDEP（起飞机场）_45, PHASE（飞行阶段）_7, ARN（机号）_108号机\n", 795 | "离地仰角大\t\tARN（机号）_82号机, ARN（机号）_97号机, ARN（机号）_57号机\n", 796 | "离地速度大\t\tARR（目的机场）_101, ARR（目的机场）_63, PHASE（飞行阶段）_3\n", 797 | "离地速度小\t\tARR（目的机场）_99, ARN（机号）_84号机, PHASE（飞行阶段）_3\n", 798 | "空中过载\t\tDEP（起飞机场）_84, DEP（起飞机场）_48, ARR（目的机场）_9\n", 799 | "起飞EGT超限\t\tARN（机号）_49号机, DEP（起飞机场）_50, ARR（目的机场）_4\n", 800 | "起飞坡度大0-35（含）ft\t\tARR（目的机场）_46, ARN（机号）_84号机, ARN（机号）_111号机\n", 801 | "起飞收起落架晚\t\tDEP（起飞机场）_43, PHASE（飞行阶段）_0, ARN（机号）_93号机\n", 802 | "起飞滑跑方向不稳定\t\tARN（机号）_60号机, PHASE（飞行阶段）_2, DEP（起飞机场）_108\n", 803 | "超襟翼限制速度Vfe\t\tARR（目的机场）_23, ARN（机号）_66号机, ARN（机号）_9号机\n", 804 | "转弯滑行速度大\t\tDEP（起飞机场）_1, ARR（目的机场）_83, PHASE（飞行阶段）_1\n", 805 | "进近坡度大1500-500（含）ft\t\tARN（机号）_85号机, ARR（目的机场）_104, ARR（目的机场）_21\n", 806 | "进近坡度大200-50（含）ft\t\tARR（目的机场）_67, ARN（机号）_104号机, ARR（目的机场）_31\n", 807 | "进近坡度大500-200（含）ft\t\tARR（目的机场）_69, ARR（目的机场）_54, ARR（目的机场）_56\n", 808 | "进近坡度大50ft以下\t\tARN（机号）_79号机, ARR（目的机场）_25, PHASE（飞行阶段）_5\n", 809 | "进近速度大50 ft以下\t\tARN（机号）_83号机, ARN（机号）_63号机, PHASE（飞行阶段）_5\n", 810 | "进近速度大500-50（含）ft\t\tDEP（起飞机场）_71, ARR（目的机场）_109, ARN（机号）_118号机\n", 811 | "进近速度小500 ft以下\t\t月份_201505, ARN（机号）_42号机, DEP（起飞机场）_86\n", 812 | "高于下滑道\t\tPHASE（飞行阶段）_0, ARN（机号）_27号机, ARR（目的机场）_87\n" 813 | ] 814 | } 815 | ], 816 | "source": [ 817 | "import pandas as pd\n", 818 | "from sklearn.linear_model import Ridge\n", 819 | "\n", 820 | "# 对标签列进行独热编码\n", 821 | "labels = data.iloc[:, 0]\n", 822 | "labels_encoded = pd.get_dummies(labels)\n", 823 | "\n", 824 | "# 提取其他 n 列数据作为特征\n", 825 | "n = data.shape[1] - 1 # 计算特征列数\n", 826 | "features = data.iloc[:, 1:] # 提取特征数据\n", 827 | "\n", 828 | "# 执行岭回归\n", 829 | "alpha = 1.0 # 设置岭回归的超参数 alpha\n", 830 | "mdl = Ridge(alpha=alpha)\n", 831 | "mdl.fit(features, labels_encoded) # 使用 Ridge 进行岭回归\n", 832 | "\n", 833 | "# 提取回归模型的回归系数\n", 834 | "coefs = mdl.coef_\n", 835 | "\n", 836 | "# 初始化存储结果的字典\n", 837 | "top5_cols = {}\n", 838 | "\n", 839 | "# 遍历每个标签，找出对应的前三列影响最大的因子\n", 840 | "for i, label in enumerate(labels_encoded.columns):\n", 841 | " idx = coefs[i].argsort()[-3:] # 找出最大的三个系数的索引\n", 842 | " top5_cols[label] = features.columns[idx] # 存储对应的列名称\n", 843 | "\n", 844 | "# 输出结果\n", 845 | "print('标签\\t\\t前三列名称')\n", 846 | "for label, cols in top5_cols.items():\n", 847 | " print(f'{label}\\t\\t{\", \".join(cols)}')\n" 848 | ] 849 | }, 850 | { 851 | "cell_type": "code", 852 | "execution_count": 22, 853 | "id": "65b16b5e", 854 | "metadata": {}, 855 | "outputs": [ 856 | { 857 | "name": "stdout", 858 | "output_type": "stream", 859 | "text": [ 860 | "岭回归模型的每折交叉验证的均方误差,平均均方误差\n", 861 | "Mean Squared Error for each fold: [0.00798278 0.00807174 0.00807823 0.00803226 0.00817225]\n", 862 | "Mean Squared Error (MSE): 0.00806745195165686\n" 863 | ] 864 | } 865 | ], 866 | "source": [ 867 | "from sklearn.model_selection import train_test_split, cross_val_score\n", 868 | "from sklearn.linear_model import Ridge\n", 869 | "\n", 870 | "X=features\n", 871 | "y=labels_encoded\n", 872 | "# 将数据集划分为训练集和测试集\n", 873 | "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", 874 | "\n", 875 | "# 创建岭回归模型\n", 876 | "ridge_model = Ridge(alpha=1.0)\n", 877 | "\n", 878 | "# 训练岭回归模型\n", 879 | "ridge_model.fit(X_train, y_train)\n", 880 | "\n", 881 | "# 使用交叉验证对模型进行评估\n", 882 | "cv_scores = cross_val_score(ridge_model, X_train, y_train, cv=5, scoring='neg_mean_squared_error')\n", 883 | "\n", 884 | "# 将负均方误差转换为正值\n", 885 | "mse_scores = -cv_scores\n", 886 | "print(\"岭回归模型的每折交叉验证的均方误差,平均均方误差\")\n", 887 | "# 输出每折交叉验证的均方误差\n", 888 | "print(\"Mean Squared Error for each fold:\", mse_scores)\n", 889 | "\n", 890 | "# 输出平均均方误差\n", 891 | "print(\"Mean Squared Error (MSE):\", mse_scores.mean())\n" 892 | ] 893 | }, 894 | { 895 | "cell_type": "code", 896 | "execution_count": 23, 897 | "id": "b6b95855", 898 | "metadata": {}, 899 | "outputs": [ 900 | { 901 | "name": "stdout", 902 | "output_type": "stream", 903 | "text": [ 904 | "线性回归模型的每折交叉验证的均方误差,平均均方误差\n", 905 | "Mean Squared Error for each fold: [1.85519468e+20 8.12605321e+19 1.27686951e+16 3.69909206e+18\n", 906 | " 2.24166621e+19]\n", 907 | "Mean Squared Error (MSE): 5.8581704657836474e+19\n" 908 | ] 909 | } 910 | ], 911 | "source": [ 912 | "import pandas as pd\n", 913 | "from sklearn.model_selection import train_test_split\n", 914 | "from sklearn.linear_model import LinearRegression\n", 915 | "from sklearn.model_selection import cross_val_score\n", 916 | "from sklearn.metrics import mean_squared_error\n", 917 | "\n", 918 | "\n", 919 | "X=features\n", 920 | "y=labels_encoded\n", 921 | "\n", 922 | "# 划分训练集和测试集\n", 923 | "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n", 924 | "\n", 925 | "# 创建线性回归模型\n", 926 | "lr_model = LinearRegression()\n", 927 | "\n", 928 | "# 在训练集上拟合线性回归模型\n", 929 | "lr_model.fit(X_train, y_train)\n", 930 | "\n", 931 | "# 进行5折交叉验证，计算均方误差\n", 932 | "mse_scores = -cross_val_score(lr_model, X_train, y_train, cv=5, scoring='neg_mean_squared_error')\n", 933 | "print(\"线性回归模型的每折交叉验证的均方误差,平均均方误差\")\n", 934 | "# 输出每折交叉验证的均方误差\n", 935 | "print(\"Mean Squared Error for each fold:\", mse_scores)\n", 936 | "\n", 937 | "# 计算平均均方误差\n", 938 | "mse_mean = mse_scores.mean()\n", 939 | "print(\"Mean Squared Error (MSE):\", mse_mean)\n" 940 | ] 941 | }, 942 | { 943 | "cell_type": "code", 944 | "execution_count": null, 945 | "id": "b5562c9b", 946 | "metadata": {}, 947 | "outputs": [], 948 | "source": [] 949 | } 950 | ], 951 | "metadata": { 952 | "kernelspec": { 953 | "display_name": "Python 3 (ipykernel)", 954 | "language": "python", 955 | "name": "python3" 956 | }, 957 | "language_info": { 958 | "codemirror_mode": { 959 | "name": "ipython", 960 | "version": 3 961 | }, 962 | "file_extension": ".py", 963 | "mimetype": "text/x-python", 964 | "name": "python", 965 | "nbconvert_exporter": "python", 966 | "pygments_lexer": "ipython3", 967 | "version": "3.10.8" 968 | } 969 | }, 970 | "nbformat": 4, 971 | "nbformat_minor": 5 972 | } 973 | -------------------------------------------------------------------------------- /2023年MathorCup高校数学建模挑战赛赛题/D题/第三题思路及其代码/第三题思路说明.txt: -------------------------------------------------------------------------------- 1 | 实现思路和流程如下： 2 | 3 | 数据加载：使用Pandas库加载附件2的数据，得到一个包含所有数据的DataFrame。 4 | 数据预处理：对数据进行清洗和处理，包括处理缺失值、将非数值列进行独热编码、提取特征等。 5 | 特征工程：通过对数据的探索性分析，提取和分析不同超限的基本特征，如航线、机场等。 6 | 模型训练：使用岭回归算法对处理后的数据进行建模，并于线性回归模型做了比较。岭回归是一种正则化线性回归方法，可以在处理多重共线性问题时有效。可以使用Scikit-learn库中的Ridge模型进行训练。 7 | 模型评估：使用交叉验证等方法对模型进行评估，评估模型的性能和预测效果。 8 | 结果解释：根据训练得到的模型参数和特征重要性，对不同超限的基本特征进行解释和分析，得出结论。 9 | 10 | 11 | 12 | 使用岭回归相对于线性回归的优点包括： 13 | 14 | 解决多重共线性问题：岭回归通过引入正则化项，可以有效处理数据中存在的多重共线性问题，避免模型过于依赖某个特征，提高模型的稳定性和可靠性。 15 | 控制模型复杂度：岭回归通过正则化项控制模型的复杂度，可以防止过拟合，提高模型的泛化能力。 16 | 对异常值具有鲁棒性：岭回归对异常值的影响较小，能够在存在少量异常值的情况下依然获得较好的拟合效果。 17 | 可调节的超参数：岭回归通过调节超参数（正则化强度）来控制模型的拟合效果，可以根据实际情况进行调优。 18 | 通过以上实现思路和使用岭回归的方法，可以对附件2中的数据进行分析，研究不同超限的基本特征，如航线、机场等，并得出结论。同时，独热编码和岭回归方法可以在处理非数值列和解决多重共线性问题时提供有效的解决方案，从而得到更稳定和可靠的分析结果。 19 | 20 | 21 | 线性回归结果和岭回归的结果相比孰优孰劣： 22 | 23 | 根据给出的结果，线性回归的均方误差（MSE）明显较大，为5.8581704657836474e+19，而岭回归的均方误差（MSE）较小，为0.00806745195165686。因此，从评估指标MSE的角度来看，岭回归模型在这个数据集上的表现更好，因为其均方误差较小。 24 | 25 | MSE是评估模型预测效果的一种常用指标，其值越小表示模型预测效果越好。在这里，线性回归模型的MSE值较大，说明模型在训练集上的预测效果较差，可能存在过拟合的情况。而岭回归模型的MSE值较小，说明模型在训练集上的预测效果较好，相对来说更具有泛化能力，可以更好地应对新数据的预测。因此，从MSE指标来看，岭回归模型优于线性回归模型。 -------------------------------------------------------------------------------- /2023年MathorCup高校数学建模挑战赛赛题/D题/第二题数据处理/Joystick_Position_Trend_Analysis.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/WindowBird/MathModel-with-python/0ac0a57f5dffd4e43a7229442c6d50a1eda80148/2023年MathorCup高校数学建模挑战赛赛题/D题/第二题数据处理/Joystick_Position_Trend_Analysis.mlx -------------------------------------------------------------------------------- /2023年MathorCup高校数学建模挑战赛赛题/D题/第二题数据处理/操纵杆位置趋势分析代码.txt: -------------------------------------------------------------------------------- 1 | % 提取杆量数据 2 | stick_position = OneData(:, 1:5); % 操纵杆位置数据，假设在第1列到第5列 3 | 4 | % 滑动窗口参数 5 | window_size = 5; % 滑动窗口大小，表示每秒记录的次数 6 | stride = 1; % 滑动窗口的步长 7 | 8 | % 初始化趋势线系数矩阵 9 | order = 1; % 多项式拟合的阶数，这里选择1表示线性拟合 10 | coeffs = zeros(order + 1, size(stick_position, 2)); % 初始化系数矩阵 11 | 12 | % 滑动窗口趋势分析 13 | for i = 1:size(stick_position, 2) 14 | for j = 1:stride:(size(stick_position, 1) - window_size + 1) 15 | window_data = stick_position(j:(j + window_size - 1), i); % 提取滑动窗口内的数据 16 | time = (j:(j + window_size - 1)) / window_size; % 时间，假设每秒记录5次 17 | coeffs(:, i) = coeffs(:, i) + polyfit(time, window_data, order)'; % 对滑动窗口内的数据进行多项式拟合并累加系数 18 | end 19 | coeffs(:, i) = coeffs(:, i) / ((size(stick_position, 1) - window_size + 1) / stride); % 求平均系数 20 | end 21 | 22 | % 数据可视化 23 | figure; 24 | plot(stick_position); 25 | xlabel('样本索引'); 26 | ylabel('操纵杆位置'); 27 | title('操纵杆位置趋势分析'); 28 | 29 | % 绘制趋势线 30 | hold on; 31 | for i = 1:size(stick_position, 2) 32 | time = (1:size(stick_position, 1)) / window_size; % 计算时间 33 | y_fit = polyval(coeffs(:, i), time); % 计算拟合后的值 34 | plot(time, y_fit, 'r'); % 绘制趋势线 35 | end 36 | legend('杆量1', '杆量2', '杆量3', '杆量4', '杆量5', '趋势线'); -------------------------------------------------------------------------------- /2023年MathorCup高校数学建模挑战赛赛题/D题/第二题数据处理/问题2.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/WindowBird/MathModel-with-python/0ac0a57f5dffd4e43a7229442c6d50a1eda80148/2023年MathorCup高校数学建模挑战赛赛题/D题/第二题数据处理/问题2.docx -------------------------------------------------------------------------------- /2023年MathorCup高校数学建模挑战赛赛题/D题/论文.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/WindowBird/MathModel-with-python/0ac0a57f5dffd4e43a7229442c6d50a1eda80148/2023年MathorCup高校数学建模挑战赛赛题/D题/论文.pdf -------------------------------------------------------------------------------- /2023年MathorCup高校数学建模挑战赛赛题/D题/附件/附件1-2关键参数航段数据的字段说明.xlsx: 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### Hi there 👋 2 | 数学建模python备战数据库 3 | 仅做数据分析类题目 4 | 5 | 6 | 7 | - 🔭 I’m currently working on 复现往年国赛论文中的数据，图表 8 | - [2022国赛C题论文复现](https://github.com/WindowBird/MathModel-with-python/tree/a524059d85a514793ff3dfccea017e4b913560ea/C%E9%A2%98) 9 | 10 | - 🌱 I’m currently learning 数学建模 11 | - [数学建模算法实现](https://github.com/WindowBird/MathModel-with-python/tree/e5efea19de5948718b1f9d19e014ec76c212fc73/1a%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1%E5%9B%BD%E8%B5%9B%E7%AE%97%E6%B3%95%E5%BA%93) 12 | - 🤔 竞赛经历 13 | - [2022mothercupD题三等奖](https://github.com/WindowBird/MathModel-with-python/tree/d4b974008024290fa61f411da0abbe03b06d9963/2023%E5%B9%B4MathorCup%E9%AB%98%E6%A0%A1%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1%E6%8C%91%E6%88%98%E8%B5%9B%E8%B5%9B%E9%A2%98) 14 | - [2023数学建模国赛C题代码实现](https://github.com/WindowBird/MathModel-with-python/tree/main/2023%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1c%E9%A2%98) 15 | - 💬 Ask me about ... 16 | - 📫 How to reach me: ... 17 | 18 | 19 | 20 | -------------------------------------------------------------------------------- /数学建模国赛算法库/供给地与需求地的最优资源分配问题.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "id": "99e2997f", 7 | "metadata": {}, 8 | "outputs": [ 9 | { 10 | "name": "stdout", 11 | "output_type": "stream", 12 | "text": [ 13 | "资源分配方案：\n", 14 | "[[ 3. 5. 0. 7. 0. 1.]\n", 15 | " [ 0. 0. 4. 0. 6. 10.]]\n", 16 | "最小距离与资源运载量之积： 135.28154179067644\n" 17 | ] 18 | } 19 | ], 20 | "source": [ 21 | "import numpy as np\n", 22 | "from scipy.optimize import linprog\n", 23 | "\n", 24 | "def distance(point1, point2):\n", 25 | " # 计算两点之间的距离，这里可以根据实际情况选择合适的距离计算方法\n", 26 | " return np.sqrt((point1[0] - point2[0])**2 + (point1[1] - point2[1])**2)\n", 27 | "\n", 28 | "def resource_allocation_optimization(ci, dj, supply_locations, demand_locations):\n", 29 | " n = len(ci) # 供给地数目\n", 30 | " m = len(dj) # 需求地数目\n", 31 | "\n", 32 | " # 构建目标函数系数向量 c\n", 33 | " c = np.zeros(n * m)\n", 34 | " for i, supply_loc in enumerate(supply_locations):\n", 35 | " for j, demand_loc in enumerate(demand_locations):\n", 36 | " c[i*m + j] = distance(supply_loc, demand_loc)\n", 37 | "\n", 38 | " # 构建等式约束矩阵 A_eq 和右侧常数向量 b_eq\n", 39 | " A_eq = np.zeros((m, n*m))\n", 40 | " b_eq = dj\n", 41 | " for i in range(m):\n", 42 | " A_eq[i, i::m] = 1\n", 43 | "\n", 44 | " # 构建不等式约束矩阵 A_ub 和右侧常数向量 b_ub\n", 45 | " A_ub = np.zeros((n, n*m))\n", 46 | " b_ub = ci\n", 47 | " for i in range(n):\n", 48 | " A_ub[i, i*m:(i+1)*m] = 1\n", 49 | "\n", 50 | " # 定义变量的上下界\n", 51 | " bounds = [(0, None) for _ in range(n*m)]\n", 52 | "\n", 53 | " # 使用线性规划求解问题\n", 54 | " result = linprog(c, A_eq=A_eq, b_eq=b_eq, A_ub=A_ub, b_ub=b_ub, bounds=bounds)\n", 55 | "\n", 56 | " # 输出结果\n", 57 | " xij = result.x.reshape(n, m)\n", 58 | " total_cost = result.fun\n", 59 | "\n", 60 | " return xij, total_cost\n", 61 | "\n", 62 | "# 示例输入数据\n", 63 | "ci = np.array([20,20]) # 供给地的资源量\n", 64 | "dj = np.array([3,5,4,7,6,11]) # 需求地的资源需求量\n", 65 | "supply_locations = [(5,1), (2,7)] # 供给地的地理位置\n", 66 | "demand_locations = [(1.25,1.25),(8.75,0.75),(0.5,4.75),(5.75,5),(3,6.5),(7.25,7.25)] # 需求地的地理位置\n", 67 | "\n", 68 | "# 求解资源分配问题\n", 69 | "xij, total_cost = resource_allocation_optimization(ci, dj, supply_locations, demand_locations)\n", 70 | "\n", 71 | "print(\"资源分配方案：\")\n", 72 | "print(xij)\n", 73 | "print(\"最小距离与资源运载量之积：\", total_cost)\n" 74 | ] 75 | }, 76 | { 77 | "cell_type": "code", 78 | "execution_count": 2, 79 | "id": "95f10cf2", 80 | "metadata": {}, 81 | "outputs": [ 82 | { 83 | "name": "stdout", 84 | "output_type": "stream", 85 | "text": [ 86 | "最优解: [3.00000000e+00 5.00000000e+00 4.00000000e+00 7.00000000e+00\n", 87 | " 1.00000000e+00 3.33429701e-15 8.63389187e-16 5.83928713e-16\n", 88 | " 1.22840006e-14 8.27021532e-16 5.00000000e+00 1.10000000e+01\n", 89 | " 5.69415991e+00 4.92569771e+00 7.24999995e+00 7.74999997e+00]\n", 90 | "最小成本: 89.88348555736768\n" 91 | ] 92 | } 93 | ], 94 | "source": [ 95 | "#更改供给地位置，对资源分配进行进一步优化\n", 96 | "import numpy as np\n", 97 | "from scipy.optimize import minimize\n", 98 | "\n", 99 | "def nsd(x):\n", 100 | " a = np.array([1.25, 8.75, 0.5, 5.75, 3, 7.25])\n", 101 | " b = np.array([1.25, 0.75, 4.75, 5, 6.5, 7.75])\n", 102 | " #s = np.zeros(12)\n", 103 | " f1 = sum([np.sqrt((x[12] - a[i])**2 + (x[13] - b[i])**2) * x[i] for i in range(6)])\n", 104 | " f2 = sum([np.sqrt((x[14] - a[i])**2 + (x[15] - b[i])**2) * x[i+6] for i in range(6)])\n", 105 | " return f1 + f2\n", 106 | "\n", 107 | "x0 = np.array([3, 5, 0, 7, 0, 1, 0, 0, 4, 0, 6, 10, 5, 1, 2, 7])\n", 108 | "bounds = [(0, None)]*12 + [(None, None)]*4\n", 109 | "\n", 110 | "A = np.array([[1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n", 111 | " [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]])\n", 112 | "\n", 113 | "B = np.array([20, 20])\n", 114 | "\n", 115 | "Aeq = np.zeros((6, 16))\n", 116 | "for i in range(6):\n", 117 | " Aeq[i, i] = 1\n", 118 | " Aeq[i, i+6] = 1\n", 119 | "\n", 120 | "beq = np.array([3, 5, 4, 7, 6, 11])\n", 121 | "\n", 122 | "constraints = [{'type': 'eq', 'fun': lambda x, i=i : Aeq[i] @ x - beq[i]} for i in range(Aeq.shape[0])]\n", 123 | "constraints += [{'type': 'ineq', 'fun': lambda x, i=i : B[i] - A[i] @ x} for i in range(A.shape[0])]\n", 124 | "\n", 125 | "res = minimize(nsd, x0, bounds=bounds, constraints=constraints)\n", 126 | "\n", 127 | "print('最优解:', res.x)\n", 128 | "print('最小成本:', res.fun)" 129 | ] 130 | }, 131 | { 132 | "cell_type": "code", 133 | "execution_count": null, 134 | "id": "8cda0368", 135 | "metadata": {}, 136 | "outputs": [], 137 | "source": [] 138 | } 139 | ], 140 | "metadata": { 141 | "kernelspec": { 142 | "display_name": "Python 3 (ipykernel)", 143 | "language": "python", 144 | "name": "python3" 145 | }, 146 | "language_info": { 147 | "codemirror_mode": { 148 | "name": "ipython", 149 | "version": 3 150 | }, 151 | "file_extension": ".py", 152 | "mimetype": "text/x-python", 153 | "name": "python", 154 | "nbconvert_exporter": "python", 155 | "pygments_lexer": "ipython3", 156 | "version": "3.10.8" 157 | } 158 | }, 159 | "nbformat": 4, 160 | "nbformat_minor": 5 161 | } 162 | -------------------------------------------------------------------------------- /数学建模国赛算法库/分支定界算法求解整数规划.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": null, 6 | "id": "4890e981", 7 | "metadata": {}, 8 | "outputs": [], 9 | "source": [ 10 | "#我们可以先使用线性规划方法求解整数规划问题的松弛线性规划问题，\n", 11 | "#然后根据线性规划的结果来确定整数规划问题的整数变量的上下界，\n", 12 | "#再使用分支定界法进行求解整数规划问题。下面是完整的函数实现：" 13 | ] 14 | }, 15 | { 16 | "cell_type": "code", 17 | "execution_count": 1, 18 | "id": "31cbd36a", 19 | "metadata": {}, 20 | "outputs": [ 21 | { 22 | "name": "stdout", 23 | "output_type": "stream", 24 | "text": [ 25 | "最优目标函数值： -9.0\n", 26 | "最优解： [3. 1.]\n" 27 | ] 28 | } 29 | ], 30 | "source": [ 31 | "from scipy.optimize import linprog\n", 32 | "\n", 33 | "def branch_and_bound_integer_programming(c, A, b, integer_indices):\n", 34 | " \"\"\"\n", 35 | " 分支定界法求解整数规划问题\n", 36 | "\n", 37 | " 参数:\n", 38 | " c (list): 目标函数的系数向量\n", 39 | " A (list): 约束条件的系数矩阵\n", 40 | " b (list): 约束条件的右侧常数向量\n", 41 | " integer_indices (list): 整数变量的索引列表\n", 42 | "\n", 43 | " 返回:\n", 44 | " best_objective (float): 最优目标函数值\n", 45 | " best_solution (list): 最优解，即使没有找到整数解，也返回一个最接近整数解的非整数解\n", 46 | " \"\"\"\n", 47 | " def integer_solution(x):\n", 48 | " return all(abs(x[i] - round(x[i])) < 1e-6 for i in integer_indices)\n", 49 | "\n", 50 | " def branch_and_bound(c, A, b, integer_indices, integer_bounds, current_objective, current_solution):\n", 51 | " nonlocal best_objective, best_solution\n", 52 | "\n", 53 | " # 判断是否为整数解\n", 54 | " if integer_solution(current_solution):\n", 55 | " # 更新最优解\n", 56 | " if current_objective > best_objective:\n", 57 | " best_objective = current_objective\n", 58 | " best_solution = current_solution\n", 59 | " return\n", 60 | "\n", 61 | " # 选择一个整数变量进行分支\n", 62 | " branch_index = None\n", 63 | " for idx in integer_indices:\n", 64 | " if abs(current_solution[idx] - round(current_solution[idx])) >= 1e-6:\n", 65 | " branch_index = idx\n", 66 | " break\n", 67 | "\n", 68 | " # 如果所有整数变量都已经是整数解，则说明问题无解\n", 69 | " if branch_index is None:\n", 70 | " return\n", 71 | "\n", 72 | " # 对当前分支变量的两个取值进行递归分支\n", 73 | " lower_bound, upper_bound = integer_bounds[branch_index]\n", 74 | " branch_value = round(current_solution[branch_index])\n", 75 | "\n", 76 | " # 分支：当前分支变量取下界\n", 77 | " A_branch = A.copy()\n", 78 | " b_branch = b.copy()\n", 79 | " A_branch.append([0] * len(c))\n", 80 | " A_branch[-1][branch_index] = 1\n", 81 | " b_branch.append(lower_bound)\n", 82 | " lp_result = linprog(c, A_ub=A_branch, b_ub=b_branch)\n", 83 | " if lp_result.success and lp_result.fun > best_objective:\n", 84 | " branch_and_bound(c, A_branch, b_branch, integer_indices, integer_bounds,\n", 85 | " lp_result.fun, lp_result.x)\n", 86 | "\n", 87 | " # 分支：当前分支变量取上界\n", 88 | " A_branch = A.copy()\n", 89 | " b_branch = b.copy()\n", 90 | " A_branch.append([0] * len(c))\n", 91 | " A_branch[-1][branch_index] = -1\n", 92 | " b_branch.append(-upper_bound)\n", 93 | " lp_result = linprog(c, A_ub=A_branch, b_ub=b_branch)\n", 94 | " if lp_result.success and lp_result.fun > best_objective:\n", 95 | " branch_and_bound(c, A_branch, b_branch, integer_indices, integer_bounds,\n", 96 | " lp_result.fun, lp_result.x)\n", 97 | "\n", 98 | " best_objective = float('-inf')\n", 99 | " best_solution = None\n", 100 | "\n", 101 | " # 先使用线性规划方法求解整数规划问题的松弛线性规划问题\n", 102 | " lp_result = linprog(c, A_ub=A, b_ub=b)\n", 103 | " if lp_result.success:\n", 104 | " # 根据线性规划结果来确定整数规划问题的整数变量的上下界\n", 105 | " integer_bounds = [(int(lp_result.x[i]), int(lp_result.x[i])) if i in integer_indices else (0, None) for i in range(len(c))]\n", 106 | "\n", 107 | " # 使用分支定界法求解整数规划问题\n", 108 | " branch_and_bound(c, A, b, integer_indices, integer_bounds, lp_result.fun, lp_result.x)\n", 109 | "\n", 110 | " return best_objective, best_solution\n", 111 | "\n", 112 | "# 测试例子\n", 113 | "c = [-2, -3]\n", 114 | "A = [[3, 2], [1, 4]]\n", 115 | "b = [12, 8]\n", 116 | "integer_indices = [0, 1]\n", 117 | "\n", 118 | "# 使用分支定界法求解整数规划问题\n", 119 | "best_objective, best_solution = branch_and_bound_integer_programming(c, A, b, integer_indices)\n", 120 | "\n", 121 | "print(\"最优目标函数值：\", best_objective)\n", 122 | "print(\"最优解：\", best_solution)" 123 | ] 124 | }, 125 | { 126 | "cell_type": "code", 127 | "execution_count": null, 128 | "id": "4fe1b414", 129 | "metadata": {}, 130 | "outputs": [], 131 | "source": [] 132 | } 133 | ], 134 | "metadata": { 135 | "kernelspec": { 136 | "display_name": "Python 3 (ipykernel)", 137 | "language": "python", 138 | "name": "python3" 139 | }, 140 | "language_info": { 141 | "codemirror_mode": { 142 | "name": "ipython", 143 | "version": 3 144 | }, 145 | "file_extension": ".py", 146 | "mimetype": "text/x-python", 147 | "name": "python", 148 | "nbconvert_exporter": "python", 149 | "pygments_lexer": "ipython3", 150 | "version": "3.10.8" 151 | } 152 | }, 153 | "nbformat": 4, 154 | "nbformat_minor": 5 155 | } 156 | -------------------------------------------------------------------------------- /数学建模国赛算法库/匈牙利算法求解整数规划.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "id": "7e6a7caa", 7 | "metadata": {}, 8 | "outputs": [ 9 | { 10 | "name": "stdout", 11 | "output_type": "stream", 12 | "text": [ 13 | "最优指派方案： [(1, 0), (0, 1), (2, 2)]\n" 14 | ] 15 | } 16 | ], 17 | "source": [ 18 | "def hungarian_algorithm(cost_matrix):\n", 19 | " \"\"\"\n", 20 | " 使用匈牙利算法解决指派问题\n", 21 | "\n", 22 | " 参数:\n", 23 | " cost_matrix (list of lists): 成本矩阵，表示指派每个任务到每个工人的成本\n", 24 | "\n", 25 | " 返回:\n", 26 | " assignments (list of tuples): 最优指派方案，每个元组表示一个指派 (worker, task)\n", 27 | " \"\"\"\n", 28 | " rows = len(cost_matrix)\n", 29 | " cols = len(cost_matrix[0])\n", 30 | "\n", 31 | " def find_assignment(worker):\n", 32 | " for task in range(cols):\n", 33 | " if not assigned[task] and cost_matrix[worker][task] == 0:\n", 34 | " assigned[task] = True\n", 35 | " if worker_matches[task] is None or find_assignment(worker_matches[task]):\n", 36 | " worker_matches[task] = worker\n", 37 | " return True\n", 38 | " return False\n", 39 | "\n", 40 | " # 在每一行中找到最小成本并将其减去，使得每一行都有至少一个零元素\n", 41 | " for i in range(rows):\n", 42 | " min_cost = min(cost_matrix[i])\n", 43 | " for j in range(cols):\n", 44 | " cost_matrix[i][j] -= min_cost\n", 45 | "\n", 46 | " # 在每一列中找到最小成本并将其减去，使得每一列都有至少一个零元素\n", 47 | " for j in range(cols):\n", 48 | " min_cost = min(cost_matrix[i][j] for i in range(rows))\n", 49 | " for i in range(rows):\n", 50 | " cost_matrix[i][j] -= min_cost\n", 51 | "\n", 52 | " assigned = [False] * cols\n", 53 | " worker_matches = [None] * cols\n", 54 | "\n", 55 | " for worker in range(rows):\n", 56 | " assigned = [False] * cols\n", 57 | " find_assignment(worker)\n", 58 | "\n", 59 | " assignments = [(worker_matches[task], task) for task in range(cols) if worker_matches[task] is not None]\n", 60 | " return assignments\n", 61 | "\n", 62 | "# 示例\n", 63 | "cost_matrix = [\n", 64 | " [9, 11, 14],\n", 65 | " [6, 15, 13],\n", 66 | " [12, 13, 8]\n", 67 | "]\n", 68 | "\n", 69 | "assignments = hungarian_algorithm(cost_matrix)\n", 70 | "print(\"最优指派方案：\", assignments)\n", 71 | "\n" 72 | ] 73 | }, 74 | { 75 | "cell_type": "code", 76 | "execution_count": null, 77 | "id": "e707e4e4", 78 | "metadata": {}, 79 | "outputs": [], 80 | "source": [] 81 | } 82 | ], 83 | "metadata": { 84 | "kernelspec": { 85 | "display_name": "Python 3 (ipykernel)", 86 | "language": "python", 87 | "name": "python3" 88 | }, 89 | "language_info": { 90 | "codemirror_mode": { 91 | "name": "ipython", 92 | "version": 3 93 | }, 94 | "file_extension": ".py", 95 | "mimetype": "text/x-python", 96 | "name": "python", 97 | "nbconvert_exporter": "python", 98 | "pygments_lexer": "ipython3", 99 | "version": "3.10.8" 100 | } 101 | }, 102 | "nbformat": 4, 103 | "nbformat_minor": 5 104 | } 105 | -------------------------------------------------------------------------------- /数学建模国赛算法库/回归算法.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 3, 6 | "id": "bfe51a8f", 7 | "metadata": {}, 8 | "outputs": [ 9 | { 10 | "ename": "SyntaxError", 11 | "evalue": "unterminated string literal (detected at line 1) (3865750220.py, line 1)", 12 | "output_type": "error", 13 | "traceback": [ 14 | "\u001b[1;36m Cell \u001b[1;32mIn [3], line 1\u001b[1;36m\u001b[0m\n\u001b[1;33m '回归分析和插值都是根据已知数据进行预测的方法，但它们之间存在一些关键区别：()\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m unterminated string literal (detected at line 1)\n" 15 | ] 16 | } 17 | ], 18 | "source": [ 19 | "/'回归分析和插值都是根据已知数据进行预测的方法，但它们之间存在一些关键区别：\n", 20 | "\n", 21 | "回归分析：\n", 22 | "\n", 23 | "回归分析是一种统计方法，旨在了解两种或多种变量之间的关系。最常见的类型是线性回归，\n", 24 | "它试图找到一条直线最好地描述两个变量之间的关系。\n", 25 | "回归分析对数据中的噪声和异常值有一定的鲁棒性，因为它不是精确地通过每个数据点，\n", 26 | "而是试图找到一条最适合所有数据点的线或曲线。\n", 27 | "回归分析可以用于外推（预测范围在已知数据范围之外的点）。\n", 28 | "插值：\n", 29 | "\n", 30 | "插值是一种数学方法，用于在已知数据点之间估计新的数据点。插值算法会精确地通过每个已知数据点。\n", 31 | "插值对数据中的噪声和异常值非常敏感，因为它会精确地通过每个数据点，如果数据点有噪声或异常值，\n", 32 | "插值的结果也可能有大的偏差。\n", 33 | "插值主要用于内插（预测范围在已知数据范围之内的点），如果用于外推，可能会导致不准确的结果。\n", 34 | "综上所述，选择回归分析还是插值主要取决于你的应用场景。如果你的数据可能包含噪声或异常值，\n", 35 | "并且你对预测范围在已知数据范围之外的点感兴趣，\n", 36 | "那么回归分析可能是一个更好的选择。如果你的数据非常准确，并且你只对预测范围在已知数据范围之内的点感兴趣，\n", 37 | "那么插值可能是一个更好的选择。''/" 38 | ] 39 | }, 40 | { 41 | "cell_type": "code", 42 | "execution_count": 4, 43 | "id": "468589d7", 44 | "metadata": {}, 45 | "outputs": [ 46 | { 47 | "data": { 48 | "image/png": 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\n", 49 | "text/plain": [ 50 | "
" 51 | ] 52 | }, 53 | "metadata": {}, 54 | "output_type": "display_data" 55 | } 56 | ], 57 | "source": [ 58 | "import matplotlib.pyplot as plt\n", 59 | "import numpy as np\n", 60 | "from sklearn.linear_model import LinearRegression\n", 61 | "\n", 62 | "# 创建数据\n", 63 | "x = np.array([5, 15, 25, 35, 45, 55]).reshape((-1, 1))\n", 64 | "y = np.array([5, 20, 14, 32, 22, 38])\n", 65 | "\n", 66 | "# 创建线性回归模型\n", 67 | "model = LinearRegression()\n", 68 | "\n", 69 | "# 训练模型\n", 70 | "model.fit(x, y)\n", 71 | "\n", 72 | "# 得到预测值\n", 73 | "y_pred = model.predict(x)\n", 74 | "\n", 75 | "# 绘制散点图和拟合线\n", 76 | "plt.scatter(x, y, color='blue')\n", 77 | "plt.plot(x, y_pred, color='red')\n", 78 | "plt.show()\n" 79 | ] 80 | }, 81 | { 82 | "cell_type": "code", 83 | "execution_count": null, 84 | "id": "bd8dd3b1", 85 | "metadata": {}, 86 | "outputs": [], 87 | "source": [] 88 | } 89 | ], 90 | "metadata": { 91 | "kernelspec": { 92 | "display_name": "Python 3 (ipykernel)", 93 | "language": "python", 94 | "name": "python3" 95 | }, 96 | "language_info": { 97 | "codemirror_mode": { 98 | "name": "ipython", 99 | "version": 3 100 | }, 101 | "file_extension": ".py", 102 | "mimetype": "text/x-python", 103 | "name": "python", 104 | "nbconvert_exporter": "python", 105 | "pygments_lexer": "ipython3", 106 | "version": "3.10.8" 107 | } 108 | }, 109 | "nbformat": 4, 110 | "nbformat_minor": 5 111 | } 112 | -------------------------------------------------------------------------------- /数学建模国赛算法库/层次分析法.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "id": "32ac797e", 7 | "metadata": {}, 8 | "outputs": [ 9 | { 10 | "name": "stdout", 11 | "output_type": "stream", 12 | "text": [ 13 | "==========准则层==========\n", 14 | "最大特征值5.072084,CR=0.014533,检验通过\n", 15 | "准则层权重 = [0.47583538 0.26360349 0.0538146 0.09806829 0.10867824]\n", 16 | "\n", 17 | "==========方案层==========\n", 18 | " 方案0 方案1 方案2 最大特征值 CR 一致性检验\n", 19 | "准则0 0.081935 0.236341 0.681725 3.001542 8.564584e-04 True\n", 20 | "准则1 0.595379 0.276350 0.128271 3.005535 3.075062e-03 True\n", 21 | "准则2 0.428571 0.428571 0.142857 3.000000 -4.934325e-16 True\n", 22 | "准则3 0.633708 0.191921 0.174371 3.009203 5.112618e-03 True\n", 23 | "准则4 0.344545 0.108525 0.546931 3.053622 2.978976e-02 True\n", 24 | "\n", 25 | "==========目标层==========\n", 26 | "[[0.318586 0.23898522 0.44242878]]\n", 27 | "最优选择是方案2\n" 28 | ] 29 | } 30 | ], 31 | "source": [ 32 | "from AHP import AHP\n", 33 | "import numpy as np\n", 34 | "\n", 35 | "# 准则重要性矩阵\n", 36 | "criteria = np.array([[1, 2, 7, 5, 5],\n", 37 | " [1 / 2, 1, 4, 3, 3],\n", 38 | " [1 / 7, 1 / 4, 1, 1 / 2, 1 / 3],\n", 39 | " [1 / 5, 1 / 3, 2, 1, 1],\n", 40 | " [1 / 5, 1 / 3, 3, 1, 1]])\n", 41 | "\n", 42 | "# 对每个准则，方案优劣排序\n", 43 | "b1 = np.array([[1, 1 / 3, 1 / 8], [3, 1, 1 / 3], [8, 3, 1]])\n", 44 | "b2 = np.array([[1, 2, 5], [1 / 2, 1, 2], [1 / 5, 1 / 2, 1]])\n", 45 | "b3 = np.array([[1, 1, 3], [1, 1, 3], [1 / 3, 1 / 3, 1]])\n", 46 | "b4 = np.array([[1, 3, 4], [1 / 3, 1, 1], [1 / 4, 1, 1]])\n", 47 | "b5 = np.array([[1, 4, 1 / 2], [1 / 4, 1, 1 / 4], [2, 4, 1]])\n", 48 | "\n", 49 | "b = [b1, b2, b3, b4, b5]\n", 50 | "a = AHP(criteria, b).run()" 51 | ] 52 | }, 53 | { 54 | "cell_type": "code", 55 | "execution_count": null, 56 | "id": "552fc97f", 57 | "metadata": {}, 58 | "outputs": [], 59 | "source": [] 60 | } 61 | ], 62 | "metadata": { 63 | "kernelspec": { 64 | "display_name": "Python 3 (ipykernel)", 65 | "language": "python", 66 | "name": "python3" 67 | }, 68 | "language_info": { 69 | "codemirror_mode": { 70 | "name": "ipython", 71 | "version": 3 72 | }, 73 | "file_extension": ".py", 74 | "mimetype": "text/x-python", 75 | "name": "python", 76 | "nbconvert_exporter": "python", 77 | "pygments_lexer": "ipython3", 78 | "version": "3.10.8" 79 | } 80 | }, 81 | "nbformat": 4, 82 | "nbformat_minor": 5 83 | } 84 | -------------------------------------------------------------------------------- /数学建模国赛算法库/拟牛顿法.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": null, 6 | "id": "16dba65c", 7 | "metadata": {}, 8 | "outputs": [], 9 | "source": [ 10 | "\"\"\"粒子群优化（PSO）：\n", 11 | "\n", 12 | "优点：\n", 13 | "\n", 14 | "简单易实现，参数调整较为容易。\n", 15 | "由于其并行性，能够同时搜索解空间的多个区域，因此具有较好的全局优化能力。\n", 16 | "对于复杂的、非线性的、多模态的、高维度的问题有较好的适应性。\n", 17 | "缺点：\n", 18 | "\n", 19 | "对于一些复杂的、需要精确解的问题，粒子群优化可能无法找到最精确的解。\n", 20 | "可能会陷入局部最优，尤其是在处理高复杂度、高维度的问题时。\n", 21 | "拟牛顿法：\n", 22 | "\n", 23 | "优点：\n", 24 | "\n", 25 | "通常能够快速地收敛到最优解，尤其是在问题是凸的或近似凸的情况下。\n", 26 | "不需要提供目标函数的二阶导数，只需要一阶导数，计算成本相对较低。\n", 27 | "缺点：\n", 28 | "\n", 29 | "需要计算目标函数的梯度，对于一些不可微或者梯度难以求解的问题，可能无法使用。\n", 30 | "通常只能找到局部最优解，不一定能找到全局最优解。\n", 31 | "对于非凸、复杂的问题可能表现不佳。\"\"\"" 32 | ] 33 | }, 34 | { 35 | "cell_type": "code", 36 | "execution_count": 1, 37 | "id": "b4fe58eb", 38 | "metadata": {}, 39 | "outputs": [ 40 | { 41 | "name": "stdout", 42 | "output_type": "stream", 43 | "text": [ 44 | "Optimized parameters: [-5.84891567e-09 -5.84891567e-09]\n", 45 | "Minimum function value: 1.0053918284590435\n" 46 | ] 47 | }, 48 | { 49 | "data": { 50 | "image/png": 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\n", 51 | "text/plain": [ 52 | "
" 53 | ] 54 | }, 55 | "metadata": {}, 56 | "output_type": "display_data" 57 | } 58 | ], 59 | "source": [ 60 | "from scipy.optimize import minimize\n", 61 | "import numpy as np\n", 62 | "import matplotlib.pyplot as plt\n", 63 | "\n", 64 | "def func(x):\n", 65 | " # x输入粒子位置\n", 66 | " # y 粒子适应度值\n", 67 | " if (x[0]==0)&(x[1]==0):\n", 68 | " y = np.exp((np.cos(2*np.pi*x[0])+np.cos(2*np.pi*x[1]))/2)-2.71289\n", 69 | " else:\n", 70 | " y = np.sin(np.sqrt(x[0]**2+x[1]**2))/np.sqrt(x[0]**2+x[1]**2)+np.exp((np.cos(2*np.pi*x[0])+np.cos(2*np.pi*x[1]))/2)-2.71289\n", 71 | " return -y \n", 72 | "\n", 73 | "def store_values(x):\n", 74 | " store_values.f_values.append(-func(x))\n", 75 | "\n", 76 | "store_values.f_values = []\n", 77 | "\n", 78 | "x0 = np.array([0, 0])\n", 79 | "\n", 80 | "res = minimize(func, x0, method='BFGS', callback=store_values)\n", 81 | "\n", 82 | "print('Optimized parameters: ', res.x)\n", 83 | "print('Minimum function value: ', -res.fun)\n", 84 | "\n", 85 | "plt.plot(store_values.f_values)\n", 86 | "plt.xlabel('Iteration')\n", 87 | "plt.ylabel('Function value')\n", 88 | "plt.show()" 89 | ] 90 | }, 91 | { 92 | "cell_type": "code", 93 | "execution_count": null, 94 | "id": "34e32d7a", 95 | "metadata": {}, 96 | "outputs": [], 97 | "source": [] 98 | } 99 | ], 100 | "metadata": { 101 | "kernelspec": { 102 | "display_name": "Python 3 (ipykernel)", 103 | "language": "python", 104 | "name": "python3" 105 | }, 106 | "language_info": { 107 | "codemirror_mode": { 108 | "name": "ipython", 109 | "version": 3 110 | }, 111 | "file_extension": ".py", 112 | "mimetype": "text/x-python", 113 | "name": "python", 114 | "nbconvert_exporter": "python", 115 | "pygments_lexer": "ipython3", 116 | "version": "3.10.8" 117 | } 118 | }, 119 | "nbformat": 4, 120 | "nbformat_minor": 5 121 | } 122 | -------------------------------------------------------------------------------- /数学建模国赛算法库/粒子群算法.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "id": "276207fe", 7 | "metadata": {}, 8 | "outputs": [ 9 | { 10 | "data": { 11 | "image/png": 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\n", 12 | "text/plain": [ 13 | "
" 14 | ] 15 | }, 16 | "metadata": {}, 17 | "output_type": "display_data" 18 | } 19 | ], 20 | "source": [ 21 | "# -*- coding:utf-8 -*-\n", 22 | "import numpy as np\n", 23 | "import matplotlib.pyplot as plt\n", 24 | "import math\n", 25 | "\n", 26 | "def getweight():\n", 27 | " # 惯性权重\n", 28 | " weight = 1\n", 29 | " return weight\n", 30 | "\n", 31 | "def getlearningrate():\n", 32 | " # 分别是粒子的个体和社会的学习因子，也称为加速常数\n", 33 | " lr = (0.49445,1.49445)\n", 34 | " return lr\n", 35 | "\n", 36 | "def getmaxgen():\n", 37 | " # 最大迭代次数\n", 38 | " maxgen = 20\n", 39 | " return maxgen\n", 40 | "\n", 41 | "def getsizepop():\n", 42 | " # 种群规模\n", 43 | " sizepop = 50\n", 44 | " return sizepop\n", 45 | "\n", 46 | "def getrangepop():\n", 47 | " # 粒子的位置的范围限制,x、y方向的限制相同\n", 48 | " rangepop = (-2*math.pi , 2*math.pi)\n", 49 | " #rangepop = (-2,2)\n", 50 | " return rangepop\n", 51 | "\n", 52 | "def getrangespeed():\n", 53 | " # 粒子的速度范围限制\n", 54 | " rangespeed = (-0.5,0.5)\n", 55 | " return rangespeed\n", 56 | "\n", 57 | "def func(x):\n", 58 | " # x输入粒子位置\n", 59 | " # y 粒子适应度值\n", 60 | " if (x[0]==0)&(x[1]==0):\n", 61 | " y = np.exp((np.cos(2*np.pi*x[0])+np.cos(2*np.pi*x[1]))/2)-2.71289\n", 62 | " else:\n", 63 | " y = np.sin(np.sqrt(x[0]**2+x[1]**2))/np.sqrt(x[0]**2+x[1]**2)+np.exp((np.cos(2*np.pi*x[0])+np.cos(2*np.pi*x[1]))/2)-2.71289\n", 64 | " return y\n", 65 | "\n", 66 | "def initpopvfit(sizepop):\n", 67 | " pop = np.zeros((sizepop,2))\n", 68 | " v = np.zeros((sizepop,2))\n", 69 | " fitness = np.zeros(sizepop)\n", 70 | "\n", 71 | " for i in range(sizepop):\n", 72 | " pop[i] = [(np.random.rand()-0.5)*rangepop[0]*2,(np.random.rand()-0.5)*rangepop[1]*2]\n", 73 | " v[i] = [(np.random.rand()-0.5)*rangepop[0]*2,(np.random.rand()-0.5)*rangepop[1]*2]\n", 74 | " fitness[i] = func(pop[i])\n", 75 | " return pop,v,fitness\n", 76 | "\n", 77 | "def getinitbest(fitness,pop):\n", 78 | " # 群体最优的粒子位置及其适应度值\n", 79 | " gbestpop,gbestfitness = pop[fitness.argmax()].copy(),fitness.max()\n", 80 | " #个体最优的粒子位置及其适应度值,使用copy()使得对pop的改变不影响pbestpop，pbestfitness类似\n", 81 | " pbestpop,pbestfitness = pop.copy(),fitness.copy()\n", 82 | "\n", 83 | " return gbestpop,gbestfitness,pbestpop,pbestfitness \n", 84 | "\n", 85 | "w = getweight()\n", 86 | "lr = getlearningrate()\n", 87 | "maxgen = getmaxgen()\n", 88 | "sizepop = getsizepop()\n", 89 | "rangepop = getrangepop()\n", 90 | "rangespeed = getrangespeed()\n", 91 | "\n", 92 | "pop,v,fitness = initpopvfit(sizepop)\n", 93 | "gbestpop,gbestfitness,pbestpop,pbestfitness = getinitbest(fitness,pop)\n", 94 | "\n", 95 | "result = np.zeros(maxgen)\n", 96 | "for i in range(maxgen):\n", 97 | " t=0.5\n", 98 | " #速度更新\n", 99 | " for j in range(sizepop):\n", 100 | " v[j] += lr[0]*np.random.rand()*(pbestpop[j]-pop[j])+lr[1]*np.random.rand()*(gbestpop-pop[j])\n", 101 | " v[vrangespeed[1]] = rangespeed[1]\n", 103 | "\n", 104 | " #粒子位置更新\n", 105 | " for j in range(sizepop):\n", 106 | " #pop[j] += 0.5*v[j]\n", 107 | " pop[j] = t*(0.5*v[j])+(1-t)*pop[j]\n", 108 | " pop[poprangepop[1]] = rangepop[1]\n", 110 | "\n", 111 | " #适应度更新\n", 112 | " for j in range(sizepop):\n", 113 | " fitness[j] = func(pop[j])\n", 114 | "\n", 115 | " for j in range(sizepop):\n", 116 | " if fitness[j] > pbestfitness[j]:\n", 117 | " pbestfitness[j] = fitness[j]\n", 118 | " pbestpop[j] = pop[j].copy()\n", 119 | "\n", 120 | " if pbestfitness.max() > gbestfitness :\n", 121 | " gbestfitness = pbestfitness.max()\n", 122 | " gbestpop = pop[pbestfitness.argmax()].copy()\n", 123 | "\n", 124 | " result[i] = gbestfitness\n", 125 | "\n", 126 | "\n", 127 | "plt.plot(result)\n", 128 | "plt.show()" 129 | ] 130 | }, 131 | { 132 | "cell_type": "code", 133 | "execution_count": 2, 134 | "id": "d28922c0", 135 | "metadata": {}, 136 | "outputs": [ 137 | { 138 | "data": { 139 | "text/plain": [ 140 | "array([0.51744368, 0.51744368, 0.51744368, 0.98885325, 0.98885325,\n", 141 | " 0.98885325, 0.98885325, 1.00363772, 1.00363772, 1.00435015,\n", 142 | " 1.00435015, 1.00498527, 1.00498527, 1.0052142 , 1.00537065,\n", 143 | " 1.00537065, 1.005382 , 1.00538932, 1.00538932, 1.00539142])" 144 | ] 145 | }, 146 | "execution_count": 2, 147 | "metadata": {}, 148 | "output_type": "execute_result" 149 | } 150 | ], 151 | "source": [ 152 | "result" 153 | ] 154 | }, 155 | { 156 | "cell_type": "code", 157 | "execution_count": null, 158 | "id": "ef005a77", 159 | "metadata": {}, 160 | "outputs": [], 161 | "source": [] 162 | } 163 | ], 164 | "metadata": { 165 | "kernelspec": { 166 | "display_name": "Python 3 (ipykernel)", 167 | "language": "python", 168 | "name": "python3" 169 | }, 170 | "language_info": { 171 | "codemirror_mode": { 172 | "name": "ipython", 173 | "version": 3 174 | }, 175 | "file_extension": ".py", 176 | "mimetype": "text/x-python", 177 | "name": "python", 178 | "nbconvert_exporter": "python", 179 | "pygments_lexer": "ipython3", 180 | "version": "3.10.8" 181 | } 182 | }, 183 | "nbformat": 4, 184 | "nbformat_minor": 5 185 | } 186 | -------------------------------------------------------------------------------- /数学建模国赛算法库/非线性规划函数.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "id": "868f0d3d", 7 | "metadata": {}, 8 | "outputs": [ 9 | { 10 | "name": "stdout", 11 | "output_type": "stream", 12 | "text": [ 13 | "最优目标函数值： 10.651091840572583\n", 14 | "最优解： [0.55216734 1.20325918 0.94782404]\n" 15 | ] 16 | } 17 | ], 18 | "source": [ 19 | "# 等式约束意味着约束函数结果为零，而不等式意味着约束函数结果为非负。请注意，COBYLA 仅支持不等式约束。\n", 20 | "import numpy as np\n", 21 | "from scipy.optimize import minimize\n", 22 | "\n", 23 | "def objective_function(x):\n", 24 | " return x[0]**2 + x[1]**2+x[2]**2+8\n", 25 | "\n", 26 | "def constraint1(x):\n", 27 | " return x[0]**2 - x[1]+x[2]**2\n", 28 | "\n", 29 | "def constraint2(x):\n", 30 | " return -x[0] - x[1]**2-x[2]**2+20\n", 31 | "\n", 32 | "def constraint3(x):\n", 33 | " return -x[0] - x[1]**2+2\n", 34 | "\n", 35 | "def constraint4(x):\n", 36 | " return x[1]+2*x[2]**2-3\n", 37 | "\n", 38 | "# 定义初始猜测值\n", 39 | "x0 = [0, 0,0]\n", 40 | "\n", 41 | "bounds = [(0, None), (0, None), (0, None)]\n", 42 | "\n", 43 | "# 定义约束条件\n", 44 | "constraint1_args = {'type': 'ineq', 'fun': constraint1}\n", 45 | "constraint2_args = {'type': 'ineq', 'fun': constraint2}\n", 46 | "constraint3_args = {'type': 'eq', 'fun': constraint3}\n", 47 | "constraint4_args = {'type': 'eq', 'fun': constraint4}\n", 48 | "\n", 49 | "# 定义约束条件列表\n", 50 | "constraints = [constraint1_args, constraint2_args,constraint3_args, constraint4_args]\n", 51 | "\n", 52 | "# 使用minimize函数求解非线性规划问题\n", 53 | "result = minimize(objective_function, x0, method='SLSQP', constraints=constraints,bounds=bounds)\n", 54 | "\n", 55 | "# 输出结果\n", 56 | "print(\"最优目标函数值：\", result.fun)\n", 57 | "print(\"最优解：\", result.x)\n" 58 | ] 59 | }, 60 | { 61 | "cell_type": "code", 62 | "execution_count": null, 63 | "id": "b2353d2f", 64 | "metadata": {}, 65 | "outputs": [], 66 | "source": [] 67 | } 68 | ], 69 | "metadata": { 70 | "kernelspec": { 71 | "display_name": "Python 3 (ipykernel)", 72 | "language": "python", 73 | "name": "python3" 74 | }, 75 | "language_info": { 76 | "codemirror_mode": { 77 | "name": "ipython", 78 | "version": 3 79 | }, 80 | "file_extension": ".py", 81 | "mimetype": "text/x-python", 82 | "name": "python", 83 | "nbconvert_exporter": "python", 84 | "pygments_lexer": "ipython3", 85 | "version": "3.10.8" 86 | } 87 | }, 88 | "nbformat": 4, 89 | "nbformat_minor": 5 90 | } 91 | --------------------------------------------------------------------------------