我正在尝试使用 Gurobi 解决复杂的装箱问题。
我有一个解决问题的模型,但我遇到了类型错误。
我的代码是:
from gurobipy import GRB, Model
import numpy as np
"""
Create data
"""
items = np.arange(50)
radii = 0.2 * np.ones_like(items)
areas = np.pi * radii ** 2 # Areas of items in m2
min_dist = np.add.outer(radii, radii)
pallet_length = 1.2 # x-dimension of pallet in m
pallet_width = 0.8 # y-dimension of pallet in m
pallet_area = pallet_length * pallet_width # pallet area in m2
def master(patterns, vtype):
m = Model()
x = m.addMVar(patterns.shape[1], lb=0, obj=1, vtype=vtype)
contraints = m.addConstr(patterns @ x >= 1)
m.optimize()
if vtype == GRB.CONTINUOUS:
return m.objVal, contraints.pi
else:
return m.objVal, x.X
def sub(duals):
m = Model()
m.setParam("NonConvex", 2)
x = m.addMVar((len(items)), lb=0, obj=-duals, vtype=GRB.BINARY, name="x")
cx = m.addMVar((len(items)), lb=radii, ub=pallet_length - radii, name="cx")
cy = m.addMVar((len(items)), lb=radii, ub=pallet_width - radii, name="cy")
# Pallet size constraint, the area of packed stacks cannot exceed the pallet area.
m.addConstr(areas @ x <= pallet_area, name=f"area")
for i in range(len(radii) - 1):
for j in range(i + 1, len(radii)):
lhs = (cx[i] - cx[j])** 2 + (cy[i] - cy[j]) ** 2
rhs = (x[i] + x[j] - 1) * min_dist[i, j] ** 2
m.addConstr(lhs >= rhs, name=f"overlap[{i},{j}]")
def callback(model, where):
if where == GRB.Callback.MIPNODE:
if model.cbGet(GRB.Callback.MIPNODE_OBJBST) < -1:
model.terminate()
m.optimize(callback)
return x.X if m.objVal < -1 else None
# Initial pattern: put every item on its own pallet.
patterns = np.eye(len(items))
num_pallets, duals = master(patterns, GRB.CONTINUOUS)
while (new_pattern := sub(duals)) is not None:
print("Current number of pallets needed (LP):", num_pallets)
# Check if we already have this pattern. If so, we are done as well.
if any(np.allclose(new_pattern, column) for column in patterns.T):
break
patterns = np.column_stack((patterns, new_pattern))
num_pallets, duals = master(patterns, GRB.CONTINUOUS)
min_pallets, used_patterns = master(patterns, GRB.BINARY)
unused = set(items)
print("Number of pallets needed (IP):", min_pallets)
for idx, used in enumerate(used_patterns):
if used:
on_pallet = items[patterns[:, idx].astype(bool)]
on_pallet = {item for item in on_pallet if item in unused}
unused -= on_pallet
print(f"Put items {on_pallet} on same pallet.")
我得到的错误是
lhs = (cx[i] - cx[j])** 2 + (cy[i] - cy[j]) ** 2
~~~~~~~~~~~~~~^^~~~
TypeError: unsupported operand type(s) for ** or pow(): 'MLinExpr' and 'int'
所以我知道不可能对两个变量进行减法并获取它们的幂。我应该如何解决这个问题或改变我的模型以便我能够进行比较?
我使用的是 Gurobi v.10.0.1
最佳答案
而不是
lhs = (cx[i] - cx[j])** 2 + (cy[i] - cy[j]) ** 2
尝试:
lhs = (cx[i] - cx[j])*(cx[i] - cx[j]) + (cy[i] - cy[j])*(cy[i] - cy[j])
(请参阅以下示例: https://www.gurobi.com/documentation/10.0/refman/py_qex.html )
关于python - 类型错误 : unsupported operand type(s) for ** or pow(): 'MLinExpr' and 'int' ,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/76089678/