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### Model.feasRelax()

feasRelax ( relaxobjtype, minrelax, vars, lbpen, ubpen, constrs, rhspen )

Modifies the Model object to create a feasibility relaxation. Note that you need to call optimize on the result to compute the actual relaxed solution. Note also that this is a more complex version of this method - use feasRelaxS for a simplified version.

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, and 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.

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 copy to create a copy before invoking this method.

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.

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.

Example usage:

  if model.status == GRB.INFEASIBLE:
vars = model.getVars()
ubpen = [1.0]*model.numVars
model.feasRelax(1, False, vars, None, ubpen, None, None)
model.optimize()