在docplex python中实现TSP

from docplex.mp.model import Model

model = Model(name='TSP')

# 城市数量
num_cities = 5

# 城市索引
cities = range(num_cities)

# 距离矩阵
distances = [[0, 10, 15, 20, 25],
             [10, 0, 35, 25, 20],
             [15, 35, 0, 30, 10],
             [20, 25, 30, 0, 15],
             [25, 20, 10, 15, 0]]

# 创建二进制变量表示是否访问了某个城市
x = {(i, j): model.binary_var(name='x_{0}_{1}'.format(i, j)) for i in cities for j in cities if i != j}

# 每个城市只能被访问一次
for i in cities:
    model.add_constraint(model.sum(x[(i, j)] for j in cities if i != j) == 1)

# 每个城市必须从另一个城市出发
for j in cities:
    model.add_constraint(model.sum(x[(i, j)] for i in cities if i != j) == 1)

# 定义目标函数，最小化总距离
model.minimize(model.sum(distances[i][j] * x[(i, j)] for i in cities for j in cities if i != j))

# 求解模型
solution = model.solve()

# 输出结果
if solution:
    print('最短路径距离：', solution.objective_value)
    print('最短路径：')
    for i in cities:
        for j in cities:
            if i != j and solution[x[(i, j)]]:
                print('从城市', i, '到城市', j)
else:
    print('未找到可行解')