已知路网每个路段的阻抗函数,在路网总阻抗最小的目标下,约束条件包括交通流守恒定律,路径流量满足非负约束,用python语言求解
时间: 2024-03-27 12:38:11 浏览: 127
这是一个典型的线性规划问题,可以使用Python中的PuLP模块来求解。
以下是一个简单的Python代码示例,可以帮助你求解该问题:
```
import pulp
# 定义路段阻抗函数
def impedance(x):
return 1 + 0.15*x + 0.0005*x**2
# 创建线性规划问题
problem = pulp.LpProblem("Minimize Total Impedance", pulp.LpMinimize)
# 定义变量
x1 = pulp.LpVariable('x1', lowBound=0, cat='Continuous')
x2 = pulp.LpVariable('x2', lowBound=0, cat='Continuous')
x3 = pulp.LpVariable('x3', lowBound=0, cat='Continuous')
x4 = pulp.LpVariable('x4', lowBound=0, cat='Continuous')
x5 = pulp.LpVariable('x5', lowBound=0, cat='Continuous')
# 定义目标函数
problem += impedance(x1) + impedance(x2) + impedance(x3) + impedance(x4) + impedance(x5)
# 定义流量守恒约束
problem += x1 == x2 + x3
problem += x2 + x4 == x5
problem += x3 + x4 == x5
# 定义路径流量非负约束
problem += x1 >= 0
problem += x2 >= 0
problem += x3 >= 0
problem += x4 >= 0
problem += x5 >= 0
# 求解问题
status = problem.solve()
# 输出结果
print("Status:", pulp.LpStatus[status])
print("Minimum Total Impedance:", pulp.value(problem.objective))
print("x1 =", pulp.value(x1))
print("x2 =", pulp.value(x2))
print("x3 =", pulp.value(x3))
print("x4 =", pulp.value(x4))
print("x5 =", pulp.value(x5))
```
在上面的示例代码中,我们假设路网有5个路段,每个路段的阻抗函数已知。通过定义PuLP变量和约束条件,我们可以求解该问题并输出结果。
请注意,这只是一个简单的示例,实际问题可能更加复杂。你需要根据具体情况来修改代码。
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