Infeasible constraints: flow_1[110,310,110]
回答済みI want to implement the new constraint called solenoidality constraint in my Gurobi code and explain it in the following section:
set E within {N,N} := B union setof{(i,j) in B} (j,i);
set D within {N_L,N_L} := E_L union setof{(s,t) in E_L} (t,s);
s.t. flow_1 {(s,t) in D, i in N: i=s}:
sum{(i,j) in E} x[i,j,s,t] - sum{(j,i) in E} x[j,i,s,t] = pr[s,t];
I write the code in the Gurobi, as the following:
when I run this code, I got the following error:
Infeasible constraints: flow_1[110,310,110],
Is my code correct? how should I solve this problem, and how can I debug the following error, because in Cplex I have an answer for this constraint.
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Gurobi Staff
Hi Arsalan,
I suspect the following is what your flow_1 constraints should be:
m.addConstrs((gp.quicksum(x[i,j,s,t] for (i,j) in E_new if i == s) - gp.quicksum(x[j,i,s,t] for (j,i) in E_new if i == s) == pr[s, t] for (s, t) in D_new), "flow_1")
- Riley
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This is an ample version of the constraint which is like the following section:
s.t. flow_1 {(s,t) in D, i in N: i=s}:
sum{(i,j) in E} x[i,j,s,t] - sum{(j,i) in E} x[j,i,s,t] = pr[s,t];
s.t. flow_2 {(s,t) in D, i in N: i=t}:
sum{(i,j) in E} x[i,j,s,t] - sum{(j,i) in E} x[j,i,s,t] = -pr[s,t];
s.t. flow_3 {(s,t) in D, i in N: i<>s and i<>t}:
sum{(i,j) in E} x[i,j,s,t] - sum{(j,i) in E} x[j,i,s,t] = 0;
I implemented the following section code:
model.addConstrs((gp.quicksum(x[i,j,s,t] for (i,j) in E_0 if k == s) - gp.quicksum(x[j,i,s,t] for (j,i) in E_0 if k == s) == pr[s, t] for (s, t) in D_s_t for k in N ), "flow_1")
but it's the same error again could you define the better version?
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Hi Arsalan,
From your first post:
s.t. flow_1 {(s,t) in D, i in N: i=s}:
sum{(i,j) in E} x[i,j,s,t] - sum{(j,i) in E} x[j,i,s,t] = pr[s,t];From your second post:
s.t. flow_1 {(s,t) in D, i in N: i=s}:
sum{(i,j) in E} x[i,j,s,t] - sum{(j,i) in E} x[j,i,s,t] = pr[s,t];It seems you have posted the same question.
- Riley
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Dear Riley,
Thank you for your reply. I mean that in the following constraint:
s.t. flow_1 {(s,t) in D, i in N: i=s}: sum{(i,j) in E} x[i,j,s,t] - sum{(j,i) in E} x[j,i,s,t] = pr[s,t];should we consider the i in the set N, like this:
model.addConstrs((gp.quicksum(x[i,j,s,t] for (i,j) in E_new) - gp.quicksum(x[j,i,s,t] for (j,i) in E_new ) == pr[s, t] for (s, t) in D_new for i in N if i == s ), "flow_1")in your reply to the previous post, I did not find for loop for the i in the N set:
m.addConstrs((gp.quicksum(x[i,j,s,t] for (i,j) in E_new if i == s) - gp.quicksum(x[j,i,s,t] for (j,i) in E_new if i == s) == pr[s, t] for (s, t) in D_new), "flow_1")
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Hi Arsalan,
You don't need a loop for i. The AMPL formulation is misleading, as the for loop i is just not necessary:
{(s,t) in D, i in N: i=s}As an simpler analogy, say N is the set of numbers 1 to 100, and consider the set
{i in N: i is even}This is the set of all numbers that are between 1 and 100, and are even. This is a perfectly reasonable way to represent this set. Now consider this set
{i in N: i = 42}This is the set of all numbers between 1 and 100, that are equal to 42. I.e. the set is {42}. This is essentially the same thing that is happening with "i in N: i=s". Hopefully this makes it clear why there is no loop over i needed. The AMPL constraint should ideally be written as
s.t. flow_1 {(s,t) in D}: sum{(i,j) in E: i = s} x[i,j,s,t] - sum{(j,i) in E: i = s} x[j,i,s,t] = pr[s,t];We write it like this using gurobipy:
m.addConstrs((gp.quicksum(x[i,j,s,t] for (i,j) in E_new if i == s) - gp.quicksum(x[j,i,s,t] for (j,i) in E_new if i == s) == pr[s, t] for (s, t) in D_new), "flow_1")
because we need to make sure that (s,j) belongs to E_new in the first quicksum and (j, s) belongs to E_new in the second quicksum. If you knew these conditions were always true then you could simplify further:
m.addConstrs((gp.quicksum(x[s,j,s,t] for j in N) - gp.quicksum(x[j,s,s,t] for j in N) == pr[s, t] for (s, t) in D_new), "flow_1")
- Riley
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