Update public notes

Author: actions-user

content/杂七杂八/数学/解桂林四日游设计最优旅游路线的整数规划.md

@@ -37,3 +37,109 @@ $X$ 需要满足以下约束：
 
 $$max\ S=\sum_{i,j}^{2,8}x_{ij}*A_{i 2}$$
 
+代码：
+```python
+import pulp as lp  
+import numpy as np  
+  
+# ===================== 工具函数 ====================  
+  
+NAME_DICT = {  
+    0: "象鼻山", 1: "漓江", 2: "阳朔西街", 3: "遇龙河", 4: "十里画廊",  
+    5: "银子岩", 6: "龙脊梯田", 7: "靖江王城", 8: "两江四湖"  
+}  
+  
+  
+def idx_to_name(idx):  
+    return NAME_DICT[idx]  
+  
+  
+# ===================== 导入数据 ====================  
+NUM_DAYS = 3  
+A = [  
+    [1.5, 60, 8],  
+    [4.5, 250, 10],  
+    [2, 0, 7],  
+    [2, 180, 9],  
+    [3, 40, 8],  
+    [2, 80, 7],  
+    [8, 100, 9],  
+    [2.5, 120, 6],  
+    [1.5, 180, 8],  
+]  
+  
+A = np.asarray(A)  
+  
+NUM_POINTS = A.shape[0]  
+  
+print(A)  
+  
+print(f'共有{NUM_POINTS}个景点, 需要游玩{NUM_DAYS}天')  
+  
+# ===================== 建模 ====================  
+  
+prob = lp.LpProblem("GuilinTravelOptProb", lp.LpMaximize)  
+  
+X = {}  
+for i in range(NUM_DAYS):  
+    for j in range(NUM_POINTS):  
+        X[(i, j)] = lp.LpVariable(f'x_{i}_{j}', 0, 1, lp.LpBinary)  
+  
+## 添加目标  
+prob += lp.lpSum([X[(i, j)] * A[j][2] for i in range(NUM_DAYS) for j in range(NUM_POINTS)]), "total s"  
+  
+##  添加约束  
+  
+# 次数约束  
+for j in range(NUM_POINTS):  
+    prob += lp.lpSum([X[(i, j)] for i in range(NUM_DAYS)]) <= 1  
+  
+# 时间约束  
+for i in range(NUM_DAYS):  
+    prob += lp.lpSum([X[(i, j)] * A[j][0] for j in range(NUM_POINTS)]) <= 10  
+  
+# 费用约束  
+prob += lp.lpSum([X[(i, j)] * A[j][1] for i in range(NUM_DAYS) for j in range(NUM_POINTS)]) <= 800  
+  
+# 地理约束  
+for i in range(NUM_DAYS):  
+    prob += lp.lpSum([X[(i, j)] for j in range(NUM_POINTS)]) <= 1 + NUM_POINTS * (1 - X[(i, 6)])  
+  
+for i in range(NUM_DAYS):  
+    prob += lp.lpSum([X[(i, j)] for j in range(2, 6)]) >= X[(i, 1)]  
+    prob += lp.lpSum([X[(i, 0)]]) <= 1 - X[(i, 1)]  
+    prob += lp.lpSum([X[(i, 7)]]) <= 1 - X[(i, 1)]  
+  
+# ===================== 求解 ====================  
+  
+prob.solve(lp.PULP_CBC_CMD(msg=False))  # 用编译的 cbc 求解器  
+  
+print("== 求解结果 ==")  
+print(f"求解状态：{lp.LpStatus[prob.status]}")  
+print(f"最大总兴趣度：{lp.value(prob.objective):.0f}")  
+  
+# 统计总数据  
+total_cost = 0  
+total_time = 0  
+total_s = 0  
+  
+# 输出每天行程  
+for i in range(NUM_DAYS):  
+    selected_j = [j for j in range(NUM_POINTS) if X[(i, j)].varValue == 1]  
+    selected_names = [idx_to_name(j) for j in selected_j]  
+  
+    # 计算当天费用  
+    day_cost = sum([A[j][1] for j in selected_j])  
+    total_cost += day_cost  
+    total_time += sum([A[j][0] for j in selected_j])  
+    total_s += sum([A[j][2] for j in selected_j])  
+  
+    # 计算当天游玩时间  
+    day_time = sum([A[j][0] for j in selected_j])  
+    print(f"\n第{i + 1}天：")  
+    print(f"  游玩景点：{selected_names}")  
+    print(f"  游玩时间：{day_time}小时 | 当天费用：{day_cost}元 | 兴趣度： {total_s}")  
+  
+print(f"总用时：{total_time} 小时 | 总费用：{total_cost}元 | 总兴趣度：{total_s}")
+```
+