How to define the constraints with accumulation of one index?
AnsweredWe conduct a constraint below:
where the variables in red are decision variables, others are known constants. how do i define this constraint? I tried to write it, but I couldn't achieve accumulate the index i.
for v in range(1,3):
model.addConstr(e[v,0] == E,"l7a")
for m in range(1,3):
name = 'l7_' + str(v) + '0' + str(m)
model.addConstr(th[v,0,m] == 0, name=name) #gurantee thv0m=0
for j in range(1,4):
for i in range(3):
if i < j:
model.addGenConstrAnd(sth,[s[v, i, j],th[v, i, m]],'andconstr') # s and th are both decision variables
expr = QuadExpr((E-e[v,i])*sth+(e[v,i]-Econsumption[j])*s[v,i,j]) # e is also a decision variable
model.addConstr(expr == e[v,j],"l7")
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Official comment
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Hi Yaoyao,
I think you've got the right idea, which is to introduce an auxiliary variable for the multiplication of s and theta variables.
\[z^v_{ijm} = s^{v}_{ij}\theta^v_{im}\]
\[e^v_j = \sum_{i \in S_0} Ez^v_{ijm} + s^{v}_{ij}e^v_i - e^v_iz^v_{ijm} - u_j\]The And constraint would only work if s and th are binary variables, which I'll assume they are and also define sth as binary, but I'd suggest an equality constraint linking the sth with the multiplication of s and th is more readable.
V = range(1,3) F = range(1,3) S = range(1,4)
for v in V:
for m in F:
for j in S:
expr = gp.QuadExpr()
for i in S:
if i != j:
sth = model.addVar(vtype="B")
model.addConstr(sth == s[v, i, j]*th[v, i, m])
expr += E*sth + e[v,i]*s[v,i,j] + e[v,i]*sth - Econsumption[j]
model.addConstr(expr == e[v,j],"l7")You could also structure this slightly differently, so that the code is not as nested, with the help of itertools.product:
from itertools import product
V = range(1,3)
F = range(1,3)
S = range(1,4)
model.addConstrs((e[v,0] == E for v in V),"l7a")
model.addConstrs((th[v,0,m] == 0 for v, m in product(V,F)), name="l7_")
z_indices = [(v,i,j,m) for v,i,j,m in product(V, S, S, F) if i != j]
z = model.addVars(z_indices, vtype="B")
model.addConstrs(z[v,i,j,m] == s[v, i, j]*th[v, i, m] for v,i,j,m in z_indices)
for v,m,j in product(V,F,S):
m.addConstr(e[v,j] == gp.quicksum(
E*z[v,i,j,m] + e[v,i]*s[v,i,j] + e[v,i]*z[v,i,j,m] - Econsumption[j]
for i in S if i != j
))- Riley
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Thanks, Riley. I got it!
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Hi, Riley:
I'm sorry to bother you, I met problems again. when i want to introduce another auxiliary variable rth[v,i,j,m]for the multiplication of r[v,j] and (1-th[v,i,m]) variables, i try the structure you proposed, but as the index of the product is same to sth, it outputs "KeyError: 'Duplicate keys in Model.addVars()'".
The code of defining rth is as follow. How can i deal with the definition of sth and rth?
rth_indices = [(v,i,j,m) for v,i,j,m in product(range(1,V+1), range(S), range(1,S+1),range(1,F+1)) if i < j]
rth = model.addVars(rth_indices, vtype=GRB.BINARY, name='rth')
model.addConstrs(rth[v,i,j,m] == r[v, j] * (1-th[v, i, m]) for v,i,j,m in rth_indices)
for m in vrange(1,F+1):
for v in range(1, V + 1):
for i in range(S):
for j in range(i+1,S+1):
name = 'C16_mvij' + str(m) + str(v) + str(i) + str(j)
model.addConstr(st[i] + RT[i] + t + th[d,i,m] * q * (E - e[v,i]) + rth[v,i,j,m]*h[v,j] <= st[j] + BigM * (1 - s[v,i,j]), name=name)0 -
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And how can i continue calling sth as an auxiliary variable in another constraint, it seems to be wrong as well, which also outputs"KeyError: 'Duplicate keys in Model.addVars()'"?
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Hi Ariel,
No problem, can you show me the values of V, S, F, and paste the full error message including stacktrace?
- Riley
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Difinitely! The values of V,S,F are the same as above.
V = range(1,3) F = range(1,3) S = range(1,4)
The full error message is as follow, the definition of sth referred to your answer about 'product' structure:
Traceback (most recent call last):
File "D:\Python_installment\Pythoncode\Research\writing2\Driver_bind_VehicleMode\Model1_Driver_bind_VehicleMode.py", line 183, in <module>
sth = model.addVars(sth_indices, vtype=GRB.BINARY, name='sth')
File "src\gurobipy\model.pxi", line 2991, in gurobipy.Model.addVars
KeyError: 'Duplicate keys in Model.addVars()'
Set parameter IntegralityFocus to value 1Thanks, Riley!
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Hi Ariel,
Any chance it's V,F,S = 3,3,4? The code you pasted is incompatible with the ranges. I.e. this doesn't work
V = range(1,3)
...
range(1,V+1)Since the stack trace is pointing to the definition of the sth variables we'll need you to paste the code for that, not the rth variables.
- Riley
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Sorry, Riley. Waste your time. When I just revisited my code, I found typo. It can work with two similar index. Thank you!
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No worries, good luck!
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