numpyでのattributeエラー

前提・実現したいこと

非線形最適化のコードでエラーが出てしまいます

発生している問題・エラーメッセージ

---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<ipython-input-34-fbf3d37a6f72> in <module>
     14 
     15 #目的関数
---> 16 model.obj=Objective( expr=sum( model.y[i,t]*u_ij[i,j]*log(model.x[j,t])+model.y[i,t]*(1-u_ij[i,j])*log(1-model.x[j,t]) for i in model.Candidate for j in model.Item for t in  model.Class ))
     17 
     18 

<ipython-input-34-fbf3d37a6f72> in <genexpr>(.0)
     14 
     15 #目的関数
---> 16 model.obj=Objective( expr=sum( model.y[i,t]*u_ij[i,j]*log(model.x[j,t])+model.y[i,t]*(1-u_ij[i,j])*log(1-model.x[j,t]) for i in model.Candidate for j in model.Item for t in  model.Class ))
     17 
     18 

pyomo/core/expr/numvalue.pyx in pyomo.core.expr.numvalue.NumericValue.__mul__()

pyomo/core/expr/numeric_expr.pyx in pyomo.core.expr.numeric_expr._generate_mul_expression()

AttributeError: 'numpy.str_' object has no attribute 'is_expression_type'

該当のソースコード

python
1u_ij=np.array(u)
2u_ij[0]
3
4"""
5array(['0', '0', '0', '0', '0', '0', '0', '1', '0', '0', '0', '0', '0',
6       '0', '0', '0', '1', '1', '0', '0', '0', '0', '0', '0', '0', '0',
7       '0', '0', '0', '1'], dtype='<U1')
8"""
9
10
11from pyomo.environ import *
12
13I=100
14J=30
15T=10
16
17model=ConcreteModel()
18model.Candidate=range(I)
19model.Item=range(J)
20model.Class=range(T)
21
22model.x=Var(model.Item,model.Class,bounds=(0.0,1.0))
23model.y=Var(model.Candidate,model.Class,within=Binary)
24
25#目的関数
26model.obj=Objective( expr=sum( model.y[i,t]*u_ij[i,j]*log(model.x[j,t])+model.y[i,t]*(1-u_ij[i,j])*log(1-model.x[j,t]) for i in model.Candidate for j in model.Item for t in  model.Class ))
27                              
28                              
29#制約条件1
30model.mono=ConstraintList()
31for j in model.Item:
32    for t in model.Class:
33        model.mono.add( model.x[j,t] <= model.x[j,t+1])
34
35#制約条件2                              
36model.single_y=ConstraintList()                              
37for i in model.Candidate:
38    model.single_y.add( sum( model.y[i,t] for t in model.Class ) == 1)
39                              
40opt = SolverFactory("ipopt")
41solver.solve(model)
42model.pprint()                                      
43