软件工具 | Python调用运筹优化求解器（一）：以CVRP&VRPTW为例

软件工具、Python调用运筹优化求解器、CVRP、VRPTW

在 Python 中调用运筹优化求解器可以通过 Pyomo 库实现。以下是一个以解决车辆路径问题 (Vehicle Routing Problem, VRP) 为例的示例代码：

```python
from pyomo.environ import *

# 构建模型对象
model = AbstractModel()

# 定义数据集
model.NUM_CUSTOMERS = Param(within=PositiveIntegers)
model.Customers = RangeSet(1, model.NUM_CUSTOMERS)
model.Demand = Param(model.Customers, within=PositiveIntegers)
model.xCoord = Param(model.Customers, within=Reals)
model.yCoord = Param(model.Customers, within=Reals)
model.Capacity = Param(within=PositiveIntegers)

# 定义变量
model.y = Var(model.Customers, model.Customers, within=Binary)
model.u = Var(model.Customers, within=NonNegativeReals)

# 定义目标函数
def total_distance_rule(model):
return sum(sqrt((model.xCoord[i]-model.xCoord[j])**2 + (model.yCoord[i]-model.yCoord[j])**2) * model.y[i,j] \
for i in model.Customers for j in model.Customers if i != j)
model.total_distance = Objective(rule=total_distance_rule, sense=minimize)

# 定义约束条件
def demand_constraint_rule(model, i):
return sum(model.Demand[j] * model.y[i,j] for j in model.Customers if i != j) <= model.u[i]
model.demand_constraint = Constraint(model.Customers, rule=demand_constraint_rule)

def vehicle_capacity_constraint_rule(model):
return sum(model.Demand[i] * model.y[i,j] for i in model.Customers for j in model.Customers if i != j) <= model.Capacity
model.vehicle_capacity_constraint = Constraint(rule=vehicle_capacity_constraint_rule)

# 使用求解器求解问题
solver = SolverFactory('glpk')
data = {'NUM_CUSTOMERS': 10,
'Demand': {1:50, 2:19, 3:30, 4:16, 5:23, 6:11, 7:31, 8:15, 9:28, 10:33},
'xCoord': {1:40, 2:45, 3:45, 4:20, 5:20, 6:35, 7:30, 8:10, 9:25, 10:45},
'yCoord': {1:50, 2:68, 3:70, 4:65, 5:35, 6:52, 7:55, 8:45, 9:30, 10:10},
'Capacity': 100}
instance = model.create_instance(data)
results = solver.solve(instance)

print("Objective value: ", instance.total_distance())
print("Route: ")
for i in instance.Customers:
for j in instance.Customers:
if instance.y[i,j]() == 1:
print(i, "->", j)
```

这段代码通过 Pyomo 库构建 VRP 模型，并使用 GLPK 求解器求解问题。你可以根据自己的需求调整数据集和约束条件，并选择不同的求解器。