MIP: Adding a Variable to Indicate Equality
I am trying to build a MIP model in the OR Tools Python API. I have two expressions x and y and want to make a variable b that is equal to 1 when x == y and 0 otherwise. What I've tried doing so far is adding the constraint that -M(1 - b) <= x - y <= M(1 - b) for some big value of M, which forces b to be 0 if x != y. Where I am stuck is adding a constraint that forces b to be 1 if x == y. I think I would want something such as x - y >= 1 - b or y - x >= 1 - b, but I don't know how to logically combine constraints like this. Any suggestions on how to do this? Or for some totally different approach?
python or-tools mixed-integer-programming
asked Jan 18 at 21:47
jacobjacob
362
add a comment |
I am trying to build a MIP model in the OR Tools Python API. I have two expressions x and y and want to make a variable b that is equal to 1 when x == y and 0 otherwise. What I've tried doing so far is adding the constraint that -M(1 - b) <= x - y <= M(1 - b) for some big value of M, which forces b to be 0 if x != y. Where I am stuck is adding a constraint that forces b to be 1 if x == y. I think I would want something such as x - y >= 1 - b or y - x >= 1 - b, but I don't know how to logically combine constraints like this. Any suggestions on how to do this? Or for some totally different approach?
python or-tools mixed-integer-programming
asked Jan 18 at 21:47
jacobjacob
362
Important to know about the bools:False == 0 && True == 1
– JacobIRR
Jan 18 at 21:49
Do you mean that I should just sayb = x == y? I don't think I am able to add a constraint in that form to the model.
– jacob
Jan 18 at 23:17
I mean that the boolean value True is literally equal to the number 1 and the boolean value False is literally equal to the number 0.
– JacobIRR
Jan 18 at 23:19
add a comment |
I am trying to build a MIP model in the OR Tools Python API. I have two expressions x and y and want to make a variable b that is equal to 1 when x == y and 0 otherwise. What I've tried doing so far is adding the constraint that -M(1 - b) <= x - y <= M(1 - b) for some big value of M, which forces b to be 0 if x != y. Where I am stuck is adding a constraint that forces b to be 1 if x == y. I think I would want something such as x - y >= 1 - b or y - x >= 1 - b, but I don't know how to logically combine constraints like this. Any suggestions on how to do this? Or for some totally different approach?
python or-tools mixed-integer-programming
asked Jan 18 at 21:47
jacobjacob
362
I am trying to build a MIP model in the OR Tools Python API. I have two expressions x and y and want to make a variable b that is equal to 1 when x == y and 0 otherwise. What I've tried doing so far is adding the constraint that -M(1 - b) <= x - y <= M(1 - b) for some big value of M, which forces b to be 0 if x != y. Where I am stuck is adding a constraint that forces b to be 1 if x == y. I think I would want something such as x - y >= 1 - b or y - x >= 1 - b, but I don't know how to logically combine constraints like this. Any suggestions on how to do this? Or for some totally different approach?
python or-tools mixed-integer-programming
python or-tools mixed-integer-programming
asked Jan 18 at 21:47
jacobjacob
362
asked Jan 18 at 21:47
jacobjacob
362
asked Jan 18 at 21:47
jacobjacob
362
asked Jan 18 at 21:47
jacobjacob
362
asked Jan 18 at 21:47
jacobjacob
362
362
Important to know about the bools:False == 0 && True == 1
– JacobIRR
Jan 18 at 21:49
Do you mean that I should just sayb = x == y? I don't think I am able to add a constraint in that form to the model.
– jacob
Jan 18 at 23:17
I mean that the boolean value True is literally equal to the number 1 and the boolean value False is literally equal to the number 0.
– JacobIRR
Jan 18 at 23:19
add a comment |
Important to know about the bools:False == 0 && True == 1
– JacobIRR
Jan 18 at 21:49
Do you mean that I should just sayb = x == y? I don't think I am able to add a constraint in that form to the model.
– jacob
Jan 18 at 23:17
I mean that the boolean value True is literally equal to the number 1 and the boolean value False is literally equal to the number 0.
– JacobIRR
Jan 18 at 23:19
Important to know about the bools:
False == 0 && True == 1– JacobIRR
Jan 18 at 21:49
Important to know about the bools:
False == 0 && True == 1– JacobIRR
Jan 18 at 21:49
Do you mean that I should just say
b = x == y? I don't think I am able to add a constraint in that form to the model.– jacob
Jan 18 at 23:17
Do you mean that I should just say
b = x == y? I don't think I am able to add a constraint in that form to the model.– jacob
Jan 18 at 23:17
I mean that the boolean value True is literally equal to the number 1 and the boolean value False is literally equal to the number 0.
– JacobIRR
Jan 18 at 23:19
I mean that the boolean value True is literally equal to the number 1 and the boolean value False is literally equal to the number 0.
– JacobIRR
Jan 18 at 23:19
add a comment |
2 Answers
2
active
oldest
votes
I think the following expressions would work for you:
b <= x - y + 1
b <= y - x + 1
b >= 1-x + 1-y - 1
b >= y + x - 1
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
Sorry, I should have mentioned thatxandyare integer variables and not necessarily binary, and I think this only works when they are binary.
– jacob
Jan 19 at 18:17
add a comment |
Please note that depending on the nature of the model, the CP-SAT solver could prove competitive. And it provides reification and half-reification natively.
Please have a look at
- [Specific answer] https://github.com/google/or-tools/blob/master/ortools/sat/doc/channeling.md
- [Introduction] https://developers.google.com/optimization/cp/cp_solver#cp-sat_example
- [CP-SAT recipes] https://github.com/google/or-tools/blob/master/ortools/sat/doc/index.md
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
The reason I am using OR-tools is to be able to plug my model into lots of different solvers in order to compare them. Does CP-SAT also support this?
– jacob
Jan 19 at 18:19
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
I think the following expressions would work for you:
b <= x - y + 1
b <= y - x + 1
b >= 1-x + 1-y - 1
b >= y + x - 1
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
Sorry, I should have mentioned thatxandyare integer variables and not necessarily binary, and I think this only works when they are binary.
– jacob
Jan 19 at 18:17
add a comment |
I think the following expressions would work for you:
b <= x - y + 1
b <= y - x + 1
b >= 1-x + 1-y - 1
b >= y + x - 1
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
Sorry, I should have mentioned thatxandyare integer variables and not necessarily binary, and I think this only works when they are binary.
– jacob
Jan 19 at 18:17
add a comment |
I think the following expressions would work for you:
b <= x - y + 1
b <= y - x + 1
b >= 1-x + 1-y - 1
b >= y + x - 1
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
I think the following expressions would work for you:
b <= x - y + 1
b <= y - x + 1
b >= 1-x + 1-y - 1
b >= y + x - 1
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
answered Jan 19 at 8:31
Magnus ÅhlanderMagnus Åhlander
4612
4612
Sorry, I should have mentioned thatxandyare integer variables and not necessarily binary, and I think this only works when they are binary.
– jacob
Jan 19 at 18:17
add a comment |
Sorry, I should have mentioned thatxandyare integer variables and not necessarily binary, and I think this only works when they are binary.
– jacob
Jan 19 at 18:17
Sorry, I should have mentioned that
x and y are integer variables and not necessarily binary, and I think this only works when they are binary.– jacob
Jan 19 at 18:17
Sorry, I should have mentioned that
x and y are integer variables and not necessarily binary, and I think this only works when they are binary.– jacob
Jan 19 at 18:17
add a comment |
Please note that depending on the nature of the model, the CP-SAT solver could prove competitive. And it provides reification and half-reification natively.
Please have a look at
- [Specific answer] https://github.com/google/or-tools/blob/master/ortools/sat/doc/channeling.md
- [Introduction] https://developers.google.com/optimization/cp/cp_solver#cp-sat_example
- [CP-SAT recipes] https://github.com/google/or-tools/blob/master/ortools/sat/doc/index.md
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
The reason I am using OR-tools is to be able to plug my model into lots of different solvers in order to compare them. Does CP-SAT also support this?
– jacob
Jan 19 at 18:19
add a comment |
Please note that depending on the nature of the model, the CP-SAT solver could prove competitive. And it provides reification and half-reification natively.
Please have a look at
- [Specific answer] https://github.com/google/or-tools/blob/master/ortools/sat/doc/channeling.md
- [Introduction] https://developers.google.com/optimization/cp/cp_solver#cp-sat_example
- [CP-SAT recipes] https://github.com/google/or-tools/blob/master/ortools/sat/doc/index.md
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
The reason I am using OR-tools is to be able to plug my model into lots of different solvers in order to compare them. Does CP-SAT also support this?
– jacob
Jan 19 at 18:19
add a comment |
Please note that depending on the nature of the model, the CP-SAT solver could prove competitive. And it provides reification and half-reification natively.
Please have a look at
- [Specific answer] https://github.com/google/or-tools/blob/master/ortools/sat/doc/channeling.md
- [Introduction] https://developers.google.com/optimization/cp/cp_solver#cp-sat_example
- [CP-SAT recipes] https://github.com/google/or-tools/blob/master/ortools/sat/doc/index.md
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
Please note that depending on the nature of the model, the CP-SAT solver could prove competitive. And it provides reification and half-reification natively.
Please have a look at
- [Specific answer] https://github.com/google/or-tools/blob/master/ortools/sat/doc/channeling.md
- [Introduction] https://developers.google.com/optimization/cp/cp_solver#cp-sat_example
- [CP-SAT recipes] https://github.com/google/or-tools/blob/master/ortools/sat/doc/index.md
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
edited Jan 19 at 14:38
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
answered Jan 19 at 14:19
Laurent PerronLaurent Perron
2266
2266
The reason I am using OR-tools is to be able to plug my model into lots of different solvers in order to compare them. Does CP-SAT also support this?
– jacob
Jan 19 at 18:19
add a comment |
The reason I am using OR-tools is to be able to plug my model into lots of different solvers in order to compare them. Does CP-SAT also support this?
– jacob
Jan 19 at 18:19
The reason I am using OR-tools is to be able to plug my model into lots of different solvers in order to compare them. Does CP-SAT also support this?
– jacob
Jan 19 at 18:19
The reason I am using OR-tools is to be able to plug my model into lots of different solvers in order to compare them. Does CP-SAT also support this?
– jacob
Jan 19 at 18:19
add a comment |
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Important to know about the bools:
False == 0 && True == 1– JacobIRR
Jan 18 at 21:49
Do you mean that I should just say
b = x == y? I don't think I am able to add a constraint in that form to the model.– jacob
Jan 18 at 23:17
I mean that the boolean value True is literally equal to the number 1 and the boolean value False is literally equal to the number 0.
– JacobIRR
Jan 18 at 23:19