# GRBModel.FeasRelax()

###

GRBModel.FeasRelax()

Modifies the `GRBModel`

object to create a feasibility relaxation.
Note that you need to call
Optimize
on the result to compute the actual relaxed solution.

The feasibility relaxation is a model that, when solved, minimizes the amount by which the solution violates the bounds and linear constraints of the original model. This method provides a number of options for specifying the relaxation.

If you specify `relaxobjtype=0`

, the objective of the
feasibility relaxation is to minimize the sum of the weighted
magnitudes of the bound and constraint violations. The `lbpen`

,
`ubpen`

, and `rhspen`

arguments specify the cost per unit
violation in the lower bounds, upper bounds, and linear constraints,
respectively.

If you specify `relaxobjtype=1`

, the objective of the
feasibility relaxation is to minimize the
weighted sum of the squares of the bound and constraint violations.
The `lbpen`

, `ubpen`

, and `rhspen`

arguments specify
the coefficients on the squares of the lower bound, upper bound, and
linear constraint violations, respectively.

If you specify `relaxobjtype=2`

, the objective of the
feasibility relaxation is to minimize the
weighted count of bound and constraint violations. The `lbpen`

,
`ubpen`

, and `rhspen`

arguments specify the cost of
violating a lower bound, upper bound, and linear constraint, respectively.

To give an example, if a constraint with `rhspen`

value
`p`

is violated by 2.0, it would contribute `2*p`

to the
feasibility relaxation objective for `relaxobjtype=0`

,
it would contribute `2*2*p`

for `relaxobjtype=1`

,
it would contribute `p`

for `relaxobjtype=2`

.

The `minrelax`

argument is a boolean that controls the type of
feasibility relaxation that is created. If `minrelax=false`

, optimizing
the returned model gives a solution that minimizes the cost of the
violation. If `minrelax=true`

, optimizing the returned model finds
a solution that minimizes the original objective, but only from among
those solutions that minimize the cost of the violation.
Note that `FeasRelax`

must solve an optimization problem to
find the minimum possible relaxation when `minrelax=true`

, which can
be quite expensive.

There are two signatures for this method. The more complex one takes
a list of variables and constraints, as well as penalties associated
with relaxing the corresponding lower bounds, upper bounds, and
constraints. If a variable or constraint is not included in one of
these lists, the associated bounds or constraints may not be violated.
The simpler signature takes a pair of boolean arguments,
`vrelax`

and `crelax`

, that indicate whether variable bounds
and/or constraints can be violated. If `vrelax`

/`crelax`

is `true`

, then every bound/constraint is allowed to be violated,
respectively, and the associated cost is 1.0.

Note that this is a destructive method: it modifies the model on which it is invoked. If you don't want to modify your original model, use the GRBModel constructor to create a copy before invoking this method.

double | FeasRelax ( | int | relaxobjtype, |

boolean | minrelax, | ||

GRBVar[] | vars, | ||

double[] | lbpen, | ||

double[] | ubpen, | ||

GRBConstr[] | constrs, | ||

double[] | rhspen ) |

Create a feasibility relaxation model.

Arguments:

relaxobjtype: The cost function used when finding the minimum cost relaxation.

minrelax: The type of feasibility relaxation to perform.

vars: Variables whose bounds are allowed to be violated.

lbpen: Penalty for violating a variable lower bound. One entry for each variable in argument vars.

ubpen: Penalty for violating a variable upper bound. One entry for each variable in argument vars.

constrs: Linear constraints that are allowed to be violated.

rhspen: Penalty for violating a linear constraint. One entry for each constraint in argument constrs.

Arguments:

Return value:

Zero if minrelax is false. If minrelax is true, the return value is the objective value for the relaxation performed. If the value is less than 0, it indicates that the method failed to create the feasibility relaxation.

double | FeasRelax ( | int | relaxobjtype, |

boolean | minrelax, | ||

boolean | vrelax, | ||

boolean | crelax ) |

Simplified method for creating a feasibility relaxation model.

Arguments:

relaxobjtype: The cost function used when finding the minimum cost relaxation.

minrelax: The type of feasibility relaxation to perform.

vrelax: Indicates whether variable bounds can be relaxed (with a cost of 1.0 for any violations.

crelax: Indicates whether linear constraints can be relaxed (with a cost of 1.0 for any violations.

Return value:

Zero if minrelax is false. If minrelax is true, the return value is the objective value for the relaxation performed. If the value is less than 0, it indicates that the method failed to create the feasibility relaxation.