整数规划模型中旅行商问题代码
时间: 2023-09-16 10:14:30 浏览: 48
下面是一个简单的整数规划模型,用于解决旅行商问题:
```
# 定义变量
x = {}
for i in range(num_cities):
for j in range(num_cities):
if i != j:
x[i, j] = model.addVar(vtype=GRB.BINARY, name='x_%d_%d' % (i, j))
# 定义约束
for i in range(num_cities):
expr = 0
for j in range(num_cities):
if i != j:
expr += x[i, j]
model.addConstr(expr == 1, name='in_%d' % i)
for j in range(num_cities):
expr = 0
for i in range(num_cities):
if i != j:
expr += x[i, j]
model.addConstr(expr == 1, name='out_%d' % j)
# 定义目标函数
obj = LinExpr()
for i in range(num_cities):
for j in range(num_cities):
if i != j:
obj += distance_matrix[i][j] * x[i, j]
model.setObjective(obj, GRB.MINIMIZE)
# 求解模型
model.optimize()
# 输出结果
if model.status == GRB.OPTIMAL:
print('最短路径长度: %g' % model.objVal)
solution = model.getAttr('x', x)
route = []
for i in range(num_cities):
for j in range(num_cities):
if i != j and solution[i, j] > 0:
route.append((i, j))
print('最短路径为: %s' % str(route))
else:
print('无法找到最短路径')
```
其中,`num_cities` 表示城市的数量,`distance_matrix` 表示城市之间的距离矩阵。在模型中,变量 `x[i, j]` 表示从城市 i 到城市 j 是否存在路径,约束条件保证每个城市有且仅有一条出边和入边,目标函数则是最小化路径长度。
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