How to constrain my variables
OngoingI have a three-dimensional binary variable apij[p,i,j].
When p is different, for example there are p1 and p2.
What constraints should I add to make the ixj matrix corresponding to p1 different from the ixj matrix corresponding to p2.
Looking forward to your reply.
Thank you.
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Community Moderator
Hi Fei,
I am not sure I understand your question. Could you show us the mathematical model you are trying to code (or at least the part your question relates to)?
Best regards
Jonasz0 -
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Mr.Jonasz
Thanks for your reply.
This is my code.
space=gurobipy.Model('matchpattern')
n=6
nn=15
apij=space.addVars(range(1,nn+1), range(1,n+1), range(1,n+1),vtype=gurobipy.GRB.BINARY)、space.update()
space.setObjective(quicksum(apij[p,i,j] for i in range (1,n+1) for j in range(1,n+1) for p in range(1,nn+1)),GRB.MINIMIZE)
space.addConstrs(quicksum(apij[p,i,j] for i in range(1,n+1))==1 for j in range(1,n+1) for p in range(1,nn+1))
space.addConstrs(quicksum(apij[p,i,j] for j in range(1,n+1))==1 for i in range(1,n+1) for p in range(1,nn+1))space.addConstrs(quicksum(apij[p,i,j] for p in range(1,nn+1))==3 for i in range(1,n+1) for j in range(1,n+1) if i!=j)
space.addConstrs(apij[p,i,j]==apij[p,j,i] for i in range (1,n+1) for j in range(1,n+1) for p in range(1,nn+1))
space.addConstrs(apij[p,i,i]==0 for i in range (1,n+1) for p in range(1,nn+1))
space.optimize()print(apij)
In order to make the i and j two-dimensional matrices in apij different, I added the following condition.
space.addConstrs(apij[p1,1,j1]+apij[p1,2,j2]+apij[p2,1,j1]+apij[p2,2,j2]<=3 for p1 in range(1,nn+1) for p2 in range(1,nn+1) for j1 in range(1,n+1) for j2 in range(1,n+1) if p1!=p2 if j2!=1)
When n is equal to 8, then nn becomes 105. How should the constraints be changed so that the 105 i, j matrices of apij do not repeat each other.
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I still have a difficult time understanding the constraint you are trying to implement.
Could you try to express it in mathematical terms (e.g. the way you would write down a mathematical model on a sheet of paper)?
Best regards
Jonasz0 -
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Mr.Jonasz
Thanks for your reply.
When n is 6, I want the result of variable apij to be as follows:
apij=np.array([[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]],\
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,1],[0,0,0,1,0,0]],\
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]],\
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]],\
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]],\
[[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]],\
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]],\
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]],\
[[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]],\
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0]],\
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0]],\
[[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]],\
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]],\
[[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]],\
[[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]]])0 -
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Mr.Jonasz
Thanks for your reply.
I'm doing a matching problem, please let me describe it in more detail.
When there are 6 people, there will be a matching situation like the one shown in the figure. The second column of them is called the match pattern. When n is 6, there are 15 different match patterns.
apij represents whether i and j match in the match pattern p, or 1 if they match. So for the 15 match patterns, the situation for all apij should be as follows.apij=np.array([[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]],\
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,1,0,0,1],[0,0,0,1,0,0]],\
[[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]],\
[[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]],\
[[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[0,0,0,1,0,0]],\
[[0,0,1,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,1,0,0,0,0]],\
[[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]],\
[[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0]],\
[[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]],\
[[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[1,0,0,0,0,0],[0,0,0,1,0,0]],\
[[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0]],\
[[0,0,0,0,1,0],[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0],[0,1,0,0,0,0]],\
[[0,0,0,0,0,1],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0]],\
[[0,0,0,0,0,1],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[1,0,0,0,0,0]],\
[[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]]])How can I program to get the varible apij that meet the conditions.
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