Difference between Chance constraints and logical constraintsSingle reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc?What is the “big-M” method? And are there two of them?What is the difference between integer programming and constraint programming?Symmetry-breaking ILP constraints for square binary matrixDealing with non-overlapping constraintsHow to handle real-world (soft) constraints in an optimization problem?Conditional constraint formulationHow to formulate this scheduling problem efficiently?How to reformulate (linearize/convexify) a budgeted assignment problem?Soft constraints and hard constraints
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Difference between Chance constraints and logical constraints
Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc?What is the “big-M” method? And are there two of them?What is the difference between integer programming and constraint programming?Symmetry-breaking ILP constraints for square binary matrixDealing with non-overlapping constraintsHow to handle real-world (soft) constraints in an optimization problem?Conditional constraint formulationHow to formulate this scheduling problem efficiently?How to reformulate (linearize/convexify) a budgeted assignment problem?Soft constraints and hard constraints
$begingroup$
A logical constraint combines linear constraints using
logical operators, such as logical-and, logical-or, negation (that is, not), conditional statements (that is, if ... then ...) to express complex relations between linear constraints.
About chance constraints, it is desired to specify that a certain constraint be satisfied with a given probability.
beginequation
Pleft[sum_j a_j x_j leq bright] geq beta
endequation
According to the above definitions, Is there any difference between Logical constraints and chance constraints?
modeling logical-constraints chance-constraints
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
$endgroup$
add a comment |
$begingroup$
A logical constraint combines linear constraints using
logical operators, such as logical-and, logical-or, negation (that is, not), conditional statements (that is, if ... then ...) to express complex relations between linear constraints.
About chance constraints, it is desired to specify that a certain constraint be satisfied with a given probability.
beginequation
Pleft[sum_j a_j x_j leq bright] geq beta
endequation
According to the above definitions, Is there any difference between Logical constraints and chance constraints?
modeling logical-constraints chance-constraints
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
$endgroup$
2
$begingroup$
Out of curiosity, can you explain why/how these two types of constraints are related?
$endgroup$
– David M.
Aug 3 at 2:57
1
$begingroup$
@DavidM., some days ago, I saw a comment on the forum of one of the optimization solvers that, I can use logical constraints to deal with chance constraints.
$endgroup$
– abbas omidi
Aug 3 at 4:24
$begingroup$
Can you provide a link to or extract from the comment?
$endgroup$
– Mark L. Stone
Aug 3 at 11:50
add a comment |
$begingroup$
A logical constraint combines linear constraints using
logical operators, such as logical-and, logical-or, negation (that is, not), conditional statements (that is, if ... then ...) to express complex relations between linear constraints.
About chance constraints, it is desired to specify that a certain constraint be satisfied with a given probability.
beginequation
Pleft[sum_j a_j x_j leq bright] geq beta
endequation
According to the above definitions, Is there any difference between Logical constraints and chance constraints?
modeling logical-constraints chance-constraints
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
$endgroup$
A logical constraint combines linear constraints using
logical operators, such as logical-and, logical-or, negation (that is, not), conditional statements (that is, if ... then ...) to express complex relations between linear constraints.
About chance constraints, it is desired to specify that a certain constraint be satisfied with a given probability.
beginequation
Pleft[sum_j a_j x_j leq bright] geq beta
endequation
According to the above definitions, Is there any difference between Logical constraints and chance constraints?
modeling logical-constraints chance-constraints
modeling logical-constraints chance-constraints
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
asked Aug 2 at 22:46
abbas omidiabbas omidi
67114 bronze badges
67114 bronze badges
2
$begingroup$
Out of curiosity, can you explain why/how these two types of constraints are related?
$endgroup$
– David M.
Aug 3 at 2:57
1
$begingroup$
@DavidM., some days ago, I saw a comment on the forum of one of the optimization solvers that, I can use logical constraints to deal with chance constraints.
$endgroup$
– abbas omidi
Aug 3 at 4:24
$begingroup$
Can you provide a link to or extract from the comment?
$endgroup$
– Mark L. Stone
Aug 3 at 11:50
add a comment |
2
$begingroup$
Out of curiosity, can you explain why/how these two types of constraints are related?
$endgroup$
– David M.
Aug 3 at 2:57
1
$begingroup$
@DavidM., some days ago, I saw a comment on the forum of one of the optimization solvers that, I can use logical constraints to deal with chance constraints.
$endgroup$
– abbas omidi
Aug 3 at 4:24
$begingroup$
Can you provide a link to or extract from the comment?
$endgroup$
– Mark L. Stone
Aug 3 at 11:50
2
2
$begingroup$
Out of curiosity, can you explain why/how these two types of constraints are related?
$endgroup$
– David M.
Aug 3 at 2:57
$begingroup$
Out of curiosity, can you explain why/how these two types of constraints are related?
$endgroup$
– David M.
Aug 3 at 2:57
1
1
$begingroup$
@DavidM., some days ago, I saw a comment on the forum of one of the optimization solvers that, I can use logical constraints to deal with chance constraints.
$endgroup$
– abbas omidi
Aug 3 at 4:24
$begingroup$
@DavidM., some days ago, I saw a comment on the forum of one of the optimization solvers that, I can use logical constraints to deal with chance constraints.
$endgroup$
– abbas omidi
Aug 3 at 4:24
$begingroup$
Can you provide a link to or extract from the comment?
$endgroup$
– Mark L. Stone
Aug 3 at 11:50
$begingroup$
Can you provide a link to or extract from the comment?
$endgroup$
– Mark L. Stone
Aug 3 at 11:50
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Logical constraints do not involve probability, except perhaps for the implicit probability of one or zero.
Chance constraints specify conditions (constraints) which must hold with a(t least) specified probability, which generally would not be one or zero.
Chance constraints could include logical conditions, and potentially even be specified in terms of holding with specified conditional probability, conditional on specified conditions.
Also note that neither logical constraints nor chance constraints need be linear.
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
$endgroup$
1
$begingroup$
you are so fast... it took 20 minutes for me to find some useful links.
$endgroup$
– Oguz Toragay
Aug 2 at 23:44
add a comment |
$begingroup$
These two types of constraint are totally different in terms of their applications in modeling. In fact, the way of using these constraint types (based on your modeling approach) end up in two totally distinct problems each of which can be solved different solution approaches. In the following, I will try to explain where we need to implement each of the constraint types:
The most direct way to treat stochastic data uncertainty in the context of uncertain Linear Optimization is offered by an old concept (going back to 50s) of chance constraints [source]. So you can use the chance constraint to deal with uncertainty in the problem and some of the possible approaches to solving this kind of problems are, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).
Logical constraints, on the other hand, do not enclose uncertainty. Most of the time logical statements in the problem can be explained and modeled by using constraints that shadow forth the logical situations in the problem.Here is a good explanation of how to use binary variables to model the logical situations in the form of logical constraints. To solve the problems with logical constraints most of the solvers can be easily used. This link, includes the details and examples of modeling logical situation in the constraints in one of the commercial modeling languages.
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
$endgroup$
1
$begingroup$
@Mark L. Stone and Oguz Toragay, thanks so much for your comments.
$endgroup$
– abbas omidi
Aug 3 at 4:25
add a comment |
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2 Answers
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2 Answers
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active
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$begingroup$
Logical constraints do not involve probability, except perhaps for the implicit probability of one or zero.
Chance constraints specify conditions (constraints) which must hold with a(t least) specified probability, which generally would not be one or zero.
Chance constraints could include logical conditions, and potentially even be specified in terms of holding with specified conditional probability, conditional on specified conditions.
Also note that neither logical constraints nor chance constraints need be linear.
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
$endgroup$
1
$begingroup$
you are so fast... it took 20 minutes for me to find some useful links.
$endgroup$
– Oguz Toragay
Aug 2 at 23:44
add a comment |
$begingroup$
Logical constraints do not involve probability, except perhaps for the implicit probability of one or zero.
Chance constraints specify conditions (constraints) which must hold with a(t least) specified probability, which generally would not be one or zero.
Chance constraints could include logical conditions, and potentially even be specified in terms of holding with specified conditional probability, conditional on specified conditions.
Also note that neither logical constraints nor chance constraints need be linear.
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
$endgroup$
1
$begingroup$
you are so fast... it took 20 minutes for me to find some useful links.
$endgroup$
– Oguz Toragay
Aug 2 at 23:44
add a comment |
$begingroup$
Logical constraints do not involve probability, except perhaps for the implicit probability of one or zero.
Chance constraints specify conditions (constraints) which must hold with a(t least) specified probability, which generally would not be one or zero.
Chance constraints could include logical conditions, and potentially even be specified in terms of holding with specified conditional probability, conditional on specified conditions.
Also note that neither logical constraints nor chance constraints need be linear.
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
$endgroup$
Logical constraints do not involve probability, except perhaps for the implicit probability of one or zero.
Chance constraints specify conditions (constraints) which must hold with a(t least) specified probability, which generally would not be one or zero.
Chance constraints could include logical conditions, and potentially even be specified in terms of holding with specified conditional probability, conditional on specified conditions.
Also note that neither logical constraints nor chance constraints need be linear.
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
answered Aug 2 at 23:19
Mark L. StoneMark L. Stone
3,2277 silver badges27 bronze badges
3,2277 silver badges27 bronze badges
1
$begingroup$
you are so fast... it took 20 minutes for me to find some useful links.
$endgroup$
– Oguz Toragay
Aug 2 at 23:44
add a comment |
1
$begingroup$
you are so fast... it took 20 minutes for me to find some useful links.
$endgroup$
– Oguz Toragay
Aug 2 at 23:44
1
1
$begingroup$
you are so fast... it took 20 minutes for me to find some useful links.
$endgroup$
– Oguz Toragay
Aug 2 at 23:44
$begingroup$
you are so fast... it took 20 minutes for me to find some useful links.
$endgroup$
– Oguz Toragay
Aug 2 at 23:44
add a comment |
$begingroup$
These two types of constraint are totally different in terms of their applications in modeling. In fact, the way of using these constraint types (based on your modeling approach) end up in two totally distinct problems each of which can be solved different solution approaches. In the following, I will try to explain where we need to implement each of the constraint types:
The most direct way to treat stochastic data uncertainty in the context of uncertain Linear Optimization is offered by an old concept (going back to 50s) of chance constraints [source]. So you can use the chance constraint to deal with uncertainty in the problem and some of the possible approaches to solving this kind of problems are, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).
Logical constraints, on the other hand, do not enclose uncertainty. Most of the time logical statements in the problem can be explained and modeled by using constraints that shadow forth the logical situations in the problem.Here is a good explanation of how to use binary variables to model the logical situations in the form of logical constraints. To solve the problems with logical constraints most of the solvers can be easily used. This link, includes the details and examples of modeling logical situation in the constraints in one of the commercial modeling languages.
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
$endgroup$
1
$begingroup$
@Mark L. Stone and Oguz Toragay, thanks so much for your comments.
$endgroup$
– abbas omidi
Aug 3 at 4:25
add a comment |
$begingroup$
These two types of constraint are totally different in terms of their applications in modeling. In fact, the way of using these constraint types (based on your modeling approach) end up in two totally distinct problems each of which can be solved different solution approaches. In the following, I will try to explain where we need to implement each of the constraint types:
The most direct way to treat stochastic data uncertainty in the context of uncertain Linear Optimization is offered by an old concept (going back to 50s) of chance constraints [source]. So you can use the chance constraint to deal with uncertainty in the problem and some of the possible approaches to solving this kind of problems are, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).
Logical constraints, on the other hand, do not enclose uncertainty. Most of the time logical statements in the problem can be explained and modeled by using constraints that shadow forth the logical situations in the problem.Here is a good explanation of how to use binary variables to model the logical situations in the form of logical constraints. To solve the problems with logical constraints most of the solvers can be easily used. This link, includes the details and examples of modeling logical situation in the constraints in one of the commercial modeling languages.
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
$endgroup$
1
$begingroup$
@Mark L. Stone and Oguz Toragay, thanks so much for your comments.
$endgroup$
– abbas omidi
Aug 3 at 4:25
add a comment |
$begingroup$
These two types of constraint are totally different in terms of their applications in modeling. In fact, the way of using these constraint types (based on your modeling approach) end up in two totally distinct problems each of which can be solved different solution approaches. In the following, I will try to explain where we need to implement each of the constraint types:
The most direct way to treat stochastic data uncertainty in the context of uncertain Linear Optimization is offered by an old concept (going back to 50s) of chance constraints [source]. So you can use the chance constraint to deal with uncertainty in the problem and some of the possible approaches to solving this kind of problems are, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).
Logical constraints, on the other hand, do not enclose uncertainty. Most of the time logical statements in the problem can be explained and modeled by using constraints that shadow forth the logical situations in the problem.Here is a good explanation of how to use binary variables to model the logical situations in the form of logical constraints. To solve the problems with logical constraints most of the solvers can be easily used. This link, includes the details and examples of modeling logical situation in the constraints in one of the commercial modeling languages.
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
$endgroup$
These two types of constraint are totally different in terms of their applications in modeling. In fact, the way of using these constraint types (based on your modeling approach) end up in two totally distinct problems each of which can be solved different solution approaches. In the following, I will try to explain where we need to implement each of the constraint types:
The most direct way to treat stochastic data uncertainty in the context of uncertain Linear Optimization is offered by an old concept (going back to 50s) of chance constraints [source]. So you can use the chance constraint to deal with uncertainty in the problem and some of the possible approaches to solving this kind of problems are, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).
Logical constraints, on the other hand, do not enclose uncertainty. Most of the time logical statements in the problem can be explained and modeled by using constraints that shadow forth the logical situations in the problem.Here is a good explanation of how to use binary variables to model the logical situations in the form of logical constraints. To solve the problems with logical constraints most of the solvers can be easily used. This link, includes the details and examples of modeling logical situation in the constraints in one of the commercial modeling languages.
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
answered Aug 2 at 23:40
Oguz ToragayOguz Toragay
2,2102 silver badges25 bronze badges
2,2102 silver badges25 bronze badges
1
$begingroup$
@Mark L. Stone and Oguz Toragay, thanks so much for your comments.
$endgroup$
– abbas omidi
Aug 3 at 4:25
add a comment |
1
$begingroup$
@Mark L. Stone and Oguz Toragay, thanks so much for your comments.
$endgroup$
– abbas omidi
Aug 3 at 4:25
1
1
$begingroup$
@Mark L. Stone and Oguz Toragay, thanks so much for your comments.
$endgroup$
– abbas omidi
Aug 3 at 4:25
$begingroup$
@Mark L. Stone and Oguz Toragay, thanks so much for your comments.
$endgroup$
– abbas omidi
Aug 3 at 4:25
add a comment |
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$begingroup$
Out of curiosity, can you explain why/how these two types of constraints are related?
$endgroup$
– David M.
Aug 3 at 2:57
1
$begingroup$
@DavidM., some days ago, I saw a comment on the forum of one of the optimization solvers that, I can use logical constraints to deal with chance constraints.
$endgroup$
– abbas omidi
Aug 3 at 4:24
$begingroup$
Can you provide a link to or extract from the comment?
$endgroup$
– Mark L. Stone
Aug 3 at 11:50