archieve: homework5

2025-05-19 10:23:14 +08:00
parent 802976f4a2
commit 7d234c0163
17 changed files with 372 additions and 0 deletions
@@ -0,0 +1,165 @@
+import numpy as np
+import random
+import matplotlib.pyplot as plt
+import copy
+
+# 各个城市的坐标
+# City_Map = [[106.54,29.59]
+# ,[91.11,29.97]
+# ,[87.68,43.77]
+# ,[106.27,38.47]
+# ,[111.65,40.82]
+# ,[108.33,22.84]
+# ,[126.63,45.75]
+# ,[125.35,43.88]
+# ,[123.38,41.8]
+# ,[114.48,38.03]
+# ,[112.53,37.87]
+# ,[101.74,36.56]
+# ,[117,36.65]
+# ,[113.6,34.76]
+# ,[118.78,32.04]
+# ,[117.27,31.86]]
+
+City_Map = 100 * np.random.rand(20, 2)  # 随机产生20个城市
+
+DNA_SIZE = len(City_Map)  # 编码长度
+POP_SIZE = 200  # 种群大小
+CROSS_RATE = 0.6  # 交叉率
+MUTA_RATE = 0.2  # 变异率
+Iterations = 1000  # 迭代次数
+
+
+def distance(DNA):  # 根据DNA的路线计算距离
+    dis = 0
+    temp = City_Map[DNA[0]]
+    for i in DNA[1:]:
+        dis = dis + ((City_Map[i][0] - temp[0]) ** 2 + (City_Map[i][1] - temp[1]) ** 2) ** 0.5
+        temp = City_Map[i]
+    return dis + ((temp[0] - City_Map[DNA[0]][0]) ** 2 + (temp[1] - City_Map[DNA[0]][1]) ** 2) ** 0.5
+
+
+def getfitness(pop):  # 计算种群适应度，这里适应度用距离的倒数表示
+    temp = []
+    for i in range(len(pop)):
+        temp.append(1 / (distance(pop[i])))
+    return temp - np.min(temp)
+
+
+def select(pop, fitness):  # 根据适应度选择，以赌轮盘的形式，适应度越大的个体被选中的概率越大
+    s = fitness.sum()
+    temp = np.random.choice(np.arange(len(pop)), size=POP_SIZE, replace=True, p=(fitness / s))
+    p = []
+    for i in temp:
+        p.append(pop[i])
+    return p
+
+
+def mutation(DNA, MUTA_RATE):  # 进行变异
+    if np.random.rand() < MUTA_RATE:  # 以MUTA_RATE的概率进行变异
+        mutate_point1 = np.random.randint(0, DNA_SIZE)  # 随机产生一个实数，代表要变异基因的位置
+        mutate_point2 = np.random.randint(0, DNA_SIZE)  # 随机产生一个实数，代表要变异基因的位置
+        while (mutate_point1 == mutate_point2):  # 保证2个所选位置不相等
+            mutate_point2 = np.random.randint(0, DNA_SIZE)
+        DNA[mutate_point1], DNA[mutate_point2] = DNA[mutate_point2], DNA[mutate_point1]  # 2个所选位置进行互换
+
+
+def crossmuta(pop, CROSS_RATE):  # 交叉变异
+    new_pop = []
+    for i in range(len(pop)):  # 遍历种群中的每一个个体，将该个体作为父代
+        n = np.random.rand()
+        if n >= CROSS_RATE:  # 大于交叉概率时不发生变异，该子代直接进入下一代
+            temp = pop[i].copy()
+            new_pop.append(temp)
+
+        if n < CROSS_RATE:  # 小于交叉概率时发生变异
+            list1 = pop[i].copy()
+            list2 = pop[np.random.randint(POP_SIZE)].copy()  # 选取种群中另一个个体进行交叉
+            status = True
+            while status:  # 产生2个不相等的节点，中间部分作为交叉段，采用部分匹配交叉
+                k1 = random.randint(0, len(list1) - 1)
+                k2 = random.randint(0, len(list2) - 1)
+                if k1 < k2:
+                    status = False
+
+            k11 = k1
+
+            fragment1 = list1[k1: k2]
+            fragment2 = list2[k1: k2]
+
+            list1[k1: k2] = fragment2
+            list2[k1: k2] = fragment1
+
+            del list1[k1: k2]
+            left1 = list1
+
+            offspring1 = []
+            for pos in left1:
+                if pos in fragment2:
+                    pos = fragment1[fragment2.index(pos)]
+                    while pos in fragment2:
+                        pos = fragment1[fragment2.index(pos)]
+                    offspring1.append(pos)
+                    continue
+                offspring1.append(pos)
+            for i in range(0, len(fragment2)):
+                offspring1.insert(k11, fragment2[i])
+                k11 += 1
+            temp = offspring1.copy()
+            mutation(temp, MUTA_RATE)
+
+            new_pop.append(temp)  # 把部分匹配交叉后形成的合法个体加入到下一代种群
+
+    return new_pop
+
+
+def print_info(pop):  # 用于输出结果
+    fitness = getfitness(pop)
+    maxfitness = np.argmax(fitness)  # 得到种群中最大适应度个体的索引
+    # 打印结果
+    print("最优的基因型：", pop[maxfitness])
+    print("最短距离：", distance(pop[maxfitness]))
+    # 按最优结果顺序把地图上的点加入到best_map列表中
+    best_map = []
+    for i in pop[maxfitness]:
+        best_map.append(City_Map[i])
+    best_map.append(City_Map[pop[maxfitness][0]])
+    X = np.array((best_map))[:, 0]
+    Y = np.array((best_map))[:, 1]
+    # 绘制地图以及路线
+    plt.figure()
+    plt.rcParams['font.sans-serif'] = ['SimHei']
+    plt.scatter(X, Y)
+    for dot in range(len(X) - 1):
+        plt.annotate(pop[maxfitness][dot], xy=(X[dot], Y[dot]), xytext=(X[dot], Y[dot]))
+    plt.annotate('start', xy=(X[0], Y[0]), xytext=(X[0] + 1, Y[0]))
+    plt.plot(X, Y)
+
+
+if __name__ == "__main__":  # 主循环
+    # 生成初代种群pop
+    pop = []
+    list = list(range(DNA_SIZE))
+    for i in range(POP_SIZE):
+        random.shuffle(list)
+        l = list.copy()
+        pop.append(l)
+    best_dis = []
+    # 进行选择，交叉，变异，并把每代的最优个体保存在best_dis中
+    for i in range(Iterations):  # 迭代N代
+        pop = crossmuta(pop, CROSS_RATE)
+        fitness = getfitness(pop)
+        maxfitness = np.argmax(fitness)
+        best_dis.append(distance(pop[maxfitness]))
+        pop = select(pop, fitness)  # 选择生成新的种群
+
+    print_info(pop)  # 打印信息
+
+    print('逐代的最小距离：', best_dis)
+
+# 画图
+plt.figure()
+plt.plot(range(Iterations), best_dis)
+plt.show()
+plt.close()
+