Are valid inequalities worth the effort given modern solver preprocessing options?Solver rounding precision vs programming language rounding precisionWhat is the “big-M” method? And are there two of them?What are the tradeoffs between “exact” and Reinforcement Learning methods for solving optimization problemsWhy is it important to choose big-M carefully and what are the consequences of doing it badly?Why the optimal value that minimizes a function does not satisfy condition?How to select a Constraint Programming SolverRead an LP/MPS file in the PuLPHow to evaluate the performance of open source solver?Are there examples of spatially explicit MIP problems?Estimation of the size of Branch-and-Bound trees using ML
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Are valid inequalities worth the effort given modern solver preprocessing options?
Solver rounding precision vs programming language rounding precisionWhat is the “big-M” method? And are there two of them?What are the tradeoffs between “exact” and Reinforcement Learning methods for solving optimization problemsWhy is it important to choose big-M carefully and what are the consequences of doing it badly?Why the optimal value that minimizes a function does not satisfy condition?How to select a Constraint Programming SolverRead an LP/MPS file in the PuLPHow to evaluate the performance of open source solver?Are there examples of spatially explicit MIP problems?Estimation of the size of Branch-and-Bound trees using ML
$begingroup$
In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also Ch 9).
In the application-oriented literature, I've often seen authors present a MILP formulation then follow it up with VIs they have derived and found to be helpful in the problem, usually accompanied with experimental results (robust or not) to show the utility of the VI. (For clarification, I'm referring to VIs authors suggest adding to the formulation, not user-generated cuts derived and/or added during the solution procedure.)
Q: With the extensive pre-processing options available with commercial solvers like CPLEX or Gurobi, is this still worth doing? If yes, what are the best practices for testing and convincing oneself a VI (or set of VIs) is worth the trouble?
[1] Wolsey, Laurence A. 1998. Integer Programming. Wiley: New York. ISBN 0471283665.
mixed-integer-programming optimization solver valid-inequalities
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
$endgroup$
add a comment |
$begingroup$
In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also Ch 9).
In the application-oriented literature, I've often seen authors present a MILP formulation then follow it up with VIs they have derived and found to be helpful in the problem, usually accompanied with experimental results (robust or not) to show the utility of the VI. (For clarification, I'm referring to VIs authors suggest adding to the formulation, not user-generated cuts derived and/or added during the solution procedure.)
Q: With the extensive pre-processing options available with commercial solvers like CPLEX or Gurobi, is this still worth doing? If yes, what are the best practices for testing and convincing oneself a VI (or set of VIs) is worth the trouble?
[1] Wolsey, Laurence A. 1998. Integer Programming. Wiley: New York. ISBN 0471283665.
mixed-integer-programming optimization solver valid-inequalities
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
$endgroup$
$begingroup$
Valid inequalities generally do help. That's why all good MIP solvers use them. Are you asking if it's worth it to add user-generated cuts?
$endgroup$
– Austin Buchanan
7 hours ago
$begingroup$
@AustinBuchanan Latest edit should help clarify. Yes, VIs are useful during the solution procedure (we need cuts!). I'm specifically talking about the addition of VIs added to the formulation prior to passing to a solver. If this is still unclear, I'll be happy to edit.
$endgroup$
– SecretAgentMan
7 hours ago
add a comment |
$begingroup$
In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also Ch 9).
In the application-oriented literature, I've often seen authors present a MILP formulation then follow it up with VIs they have derived and found to be helpful in the problem, usually accompanied with experimental results (robust or not) to show the utility of the VI. (For clarification, I'm referring to VIs authors suggest adding to the formulation, not user-generated cuts derived and/or added during the solution procedure.)
Q: With the extensive pre-processing options available with commercial solvers like CPLEX or Gurobi, is this still worth doing? If yes, what are the best practices for testing and convincing oneself a VI (or set of VIs) is worth the trouble?
[1] Wolsey, Laurence A. 1998. Integer Programming. Wiley: New York. ISBN 0471283665.
mixed-integer-programming optimization solver valid-inequalities
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
$endgroup$
In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also Ch 9).
In the application-oriented literature, I've often seen authors present a MILP formulation then follow it up with VIs they have derived and found to be helpful in the problem, usually accompanied with experimental results (robust or not) to show the utility of the VI. (For clarification, I'm referring to VIs authors suggest adding to the formulation, not user-generated cuts derived and/or added during the solution procedure.)
Q: With the extensive pre-processing options available with commercial solvers like CPLEX or Gurobi, is this still worth doing? If yes, what are the best practices for testing and convincing oneself a VI (or set of VIs) is worth the trouble?
[1] Wolsey, Laurence A. 1998. Integer Programming. Wiley: New York. ISBN 0471283665.
mixed-integer-programming optimization solver valid-inequalities
mixed-integer-programming optimization solver valid-inequalities
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
edited 7 hours ago
SecretAgentMan
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
asked 8 hours ago
SecretAgentManSecretAgentMan
6512 silver badges21 bronze badges
6512 silver badges21 bronze badges
$begingroup$
Valid inequalities generally do help. That's why all good MIP solvers use them. Are you asking if it's worth it to add user-generated cuts?
$endgroup$
– Austin Buchanan
7 hours ago
$begingroup$
@AustinBuchanan Latest edit should help clarify. Yes, VIs are useful during the solution procedure (we need cuts!). I'm specifically talking about the addition of VIs added to the formulation prior to passing to a solver. If this is still unclear, I'll be happy to edit.
$endgroup$
– SecretAgentMan
7 hours ago
add a comment |
$begingroup$
Valid inequalities generally do help. That's why all good MIP solvers use them. Are you asking if it's worth it to add user-generated cuts?
$endgroup$
– Austin Buchanan
7 hours ago
$begingroup$
@AustinBuchanan Latest edit should help clarify. Yes, VIs are useful during the solution procedure (we need cuts!). I'm specifically talking about the addition of VIs added to the formulation prior to passing to a solver. If this is still unclear, I'll be happy to edit.
$endgroup$
– SecretAgentMan
7 hours ago
$begingroup$
Valid inequalities generally do help. That's why all good MIP solvers use them. Are you asking if it's worth it to add user-generated cuts?
$endgroup$
– Austin Buchanan
7 hours ago
$begingroup$
Valid inequalities generally do help. That's why all good MIP solvers use them. Are you asking if it's worth it to add user-generated cuts?
$endgroup$
– Austin Buchanan
7 hours ago
$begingroup$
@AustinBuchanan Latest edit should help clarify. Yes, VIs are useful during the solution procedure (we need cuts!). I'm specifically talking about the addition of VIs added to the formulation prior to passing to a solver. If this is still unclear, I'll be happy to edit.
$endgroup$
– SecretAgentMan
7 hours ago
$begingroup$
@AustinBuchanan Latest edit should help clarify. Yes, VIs are useful during the solution procedure (we need cuts!). I'm specifically talking about the addition of VIs added to the formulation prior to passing to a solver. If this is still unclear, I'll be happy to edit.
$endgroup$
– SecretAgentMan
7 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
In my experience, it's rarely, but sometimes still, worth doing. There is no general answer however, as it's very model-specific (and sometimes even instance-specific). The only way to know for sure is to try both ways with the solver of your choice. Your results will also change over time, because newer versions of solvers generally implement better algorithms and use differently tuned heuristics.
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
$endgroup$
$begingroup$
Not clear why you mention preprocessing: maybe you mean that modern solvers already exploit a number of (powerful) cutting plane families (VIs), and you ask whether it makes sense to investigate new ones for specific problems.
$endgroup$
– Matteo Fischetti
7 hours ago
$begingroup$
@Matteo Fischetti: I did not mention preprocessing in my answer...?!? Did I misunderstand your comment?
$endgroup$
– Simon
6 hours ago
$begingroup$
@Simon Perhaps this was intended as a comment on the question? I'll wait for the commenter to clarify before I edit the question to address.
$endgroup$
– SecretAgentMan
4 hours ago
add a comment |
$begingroup$
It is, at least sometimes, still very useful.
I have a short note (link) on a problem in quay crane scheduling in which adding a single - rather uninspired - family of valid inequalities greatly reduced solution times.
My understanding is that you make the most out of enumerated valid inequalities when the linear relaxation of the MIP is poor, as they can quickly improve the dual bound.
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
$endgroup$
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
$begingroup$
In my experience, it's rarely, but sometimes still, worth doing. There is no general answer however, as it's very model-specific (and sometimes even instance-specific). The only way to know for sure is to try both ways with the solver of your choice. Your results will also change over time, because newer versions of solvers generally implement better algorithms and use differently tuned heuristics.
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
$endgroup$
$begingroup$
Not clear why you mention preprocessing: maybe you mean that modern solvers already exploit a number of (powerful) cutting plane families (VIs), and you ask whether it makes sense to investigate new ones for specific problems.
$endgroup$
– Matteo Fischetti
7 hours ago
$begingroup$
@Matteo Fischetti: I did not mention preprocessing in my answer...?!? Did I misunderstand your comment?
$endgroup$
– Simon
6 hours ago
$begingroup$
@Simon Perhaps this was intended as a comment on the question? I'll wait for the commenter to clarify before I edit the question to address.
$endgroup$
– SecretAgentMan
4 hours ago
add a comment |
$begingroup$
In my experience, it's rarely, but sometimes still, worth doing. There is no general answer however, as it's very model-specific (and sometimes even instance-specific). The only way to know for sure is to try both ways with the solver of your choice. Your results will also change over time, because newer versions of solvers generally implement better algorithms and use differently tuned heuristics.
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
$endgroup$
$begingroup$
Not clear why you mention preprocessing: maybe you mean that modern solvers already exploit a number of (powerful) cutting plane families (VIs), and you ask whether it makes sense to investigate new ones for specific problems.
$endgroup$
– Matteo Fischetti
7 hours ago
$begingroup$
@Matteo Fischetti: I did not mention preprocessing in my answer...?!? Did I misunderstand your comment?
$endgroup$
– Simon
6 hours ago
$begingroup$
@Simon Perhaps this was intended as a comment on the question? I'll wait for the commenter to clarify before I edit the question to address.
$endgroup$
– SecretAgentMan
4 hours ago
add a comment |
$begingroup$
In my experience, it's rarely, but sometimes still, worth doing. There is no general answer however, as it's very model-specific (and sometimes even instance-specific). The only way to know for sure is to try both ways with the solver of your choice. Your results will also change over time, because newer versions of solvers generally implement better algorithms and use differently tuned heuristics.
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
$endgroup$
In my experience, it's rarely, but sometimes still, worth doing. There is no general answer however, as it's very model-specific (and sometimes even instance-specific). The only way to know for sure is to try both ways with the solver of your choice. Your results will also change over time, because newer versions of solvers generally implement better algorithms and use differently tuned heuristics.
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
edited 6 hours ago
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
answered 8 hours ago
SimonSimon
5721 silver badge13 bronze badges
5721 silver badge13 bronze badges
$begingroup$
Not clear why you mention preprocessing: maybe you mean that modern solvers already exploit a number of (powerful) cutting plane families (VIs), and you ask whether it makes sense to investigate new ones for specific problems.
$endgroup$
– Matteo Fischetti
7 hours ago
$begingroup$
@Matteo Fischetti: I did not mention preprocessing in my answer...?!? Did I misunderstand your comment?
$endgroup$
– Simon
6 hours ago
$begingroup$
@Simon Perhaps this was intended as a comment on the question? I'll wait for the commenter to clarify before I edit the question to address.
$endgroup$
– SecretAgentMan
4 hours ago
add a comment |
$begingroup$
Not clear why you mention preprocessing: maybe you mean that modern solvers already exploit a number of (powerful) cutting plane families (VIs), and you ask whether it makes sense to investigate new ones for specific problems.
$endgroup$
– Matteo Fischetti
7 hours ago
$begingroup$
@Matteo Fischetti: I did not mention preprocessing in my answer...?!? Did I misunderstand your comment?
$endgroup$
– Simon
6 hours ago
$begingroup$
@Simon Perhaps this was intended as a comment on the question? I'll wait for the commenter to clarify before I edit the question to address.
$endgroup$
– SecretAgentMan
4 hours ago
$begingroup$
Not clear why you mention preprocessing: maybe you mean that modern solvers already exploit a number of (powerful) cutting plane families (VIs), and you ask whether it makes sense to investigate new ones for specific problems.
$endgroup$
– Matteo Fischetti
7 hours ago
$begingroup$
Not clear why you mention preprocessing: maybe you mean that modern solvers already exploit a number of (powerful) cutting plane families (VIs), and you ask whether it makes sense to investigate new ones for specific problems.
$endgroup$
– Matteo Fischetti
7 hours ago
$begingroup$
@Matteo Fischetti: I did not mention preprocessing in my answer...?!? Did I misunderstand your comment?
$endgroup$
– Simon
6 hours ago
$begingroup$
@Matteo Fischetti: I did not mention preprocessing in my answer...?!? Did I misunderstand your comment?
$endgroup$
– Simon
6 hours ago
$begingroup$
@Simon Perhaps this was intended as a comment on the question? I'll wait for the commenter to clarify before I edit the question to address.
$endgroup$
– SecretAgentMan
4 hours ago
$begingroup$
@Simon Perhaps this was intended as a comment on the question? I'll wait for the commenter to clarify before I edit the question to address.
$endgroup$
– SecretAgentMan
4 hours ago
add a comment |
$begingroup$
It is, at least sometimes, still very useful.
I have a short note (link) on a problem in quay crane scheduling in which adding a single - rather uninspired - family of valid inequalities greatly reduced solution times.
My understanding is that you make the most out of enumerated valid inequalities when the linear relaxation of the MIP is poor, as they can quickly improve the dual bound.
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
$endgroup$
add a comment |
$begingroup$
It is, at least sometimes, still very useful.
I have a short note (link) on a problem in quay crane scheduling in which adding a single - rather uninspired - family of valid inequalities greatly reduced solution times.
My understanding is that you make the most out of enumerated valid inequalities when the linear relaxation of the MIP is poor, as they can quickly improve the dual bound.
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
$endgroup$
add a comment |
$begingroup$
It is, at least sometimes, still very useful.
I have a short note (link) on a problem in quay crane scheduling in which adding a single - rather uninspired - family of valid inequalities greatly reduced solution times.
My understanding is that you make the most out of enumerated valid inequalities when the linear relaxation of the MIP is poor, as they can quickly improve the dual bound.
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
$endgroup$
It is, at least sometimes, still very useful.
I have a short note (link) on a problem in quay crane scheduling in which adding a single - rather uninspired - family of valid inequalities greatly reduced solution times.
My understanding is that you make the most out of enumerated valid inequalities when the linear relaxation of the MIP is poor, as they can quickly improve the dual bound.
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
answered 1 hour ago
Alberto SantiniAlberto Santini
6413 silver badges6 bronze badges
6413 silver badges6 bronze badges
add a comment |
add a comment |
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$begingroup$
Valid inequalities generally do help. That's why all good MIP solvers use them. Are you asking if it's worth it to add user-generated cuts?
$endgroup$
– Austin Buchanan
7 hours ago
$begingroup$
@AustinBuchanan Latest edit should help clarify. Yes, VIs are useful during the solution procedure (we need cuts!). I'm specifically talking about the addition of VIs added to the formulation prior to passing to a solver. If this is still unclear, I'll be happy to edit.
$endgroup$
– SecretAgentMan
7 hours ago