The procedure GMP::Instance::AddIntegerEliminationRows adds integer elimination rows to the generated mathematical program which will eliminate an integer solution.

GMP::Instance::AddIntegerEliminationRows(
GMP,          ! (input) a generated mathematical program
solution,     ! (input) a solution
refNo         ! (input) a scalar integer value
)


## Arguments¶

GMP

An element in AllGeneratedMathematicalPrograms.

solution

An integer scalar reference to a solution.

refNo

A positive integer scalar value representing a reference number.

## Return Value¶

The procedure returns 1 on success, or 0 otherwise.

Note

• Rows and columns added before for refNo will be deleted first.

• If the GMP contains only binary variables then only one row will be added; if the GMP contains general integer variables then several rows and columns will be added.

• The exact definitions of the rows and columns that are added are as follows. Let $$x_i$$ be an integer column whose level value $$lev_i$$ is between its lower bound $$lb_i$$ and upper bound $$ub_i$$, i.e., $$lb_i < lev_i < ub_i$$. Then columns $$l_i \geq 0$$ and $$u_i \geq 0$$ are added together with a binary column $$z_i$$. Also the following three constraints are added:

(1)$l_i + (lev_i - lb_i)z_i \leq (lev_i - lb_i)$

(2)$u_i + (lev_i - ub_i) z_i \leq 0$
(3)$x_i - u_i + l_i = lev_i$

Every call to GMP::Instance::AddIntegerEliminationRows also adds the following constraint:

(4)\begin{aligned} \sum_{i\in S_{lo}} x_i - \sum_{i\in S_{up}} x_i + \sum_{i\in S_{in}} (l_i + u_i) \geq 1 + \sum_{i\in S_{lo}} lev_i - \sum_{i\in S_{up}} lev_i \end{aligned}

where $$S_{lo}$$ defines the set of integer columns whose level values equal their lower bounds, $$S_{up}$$ the set of integer columns whose level values equal their upper bounds, and $$S_{in}$$ the set of integer columns whose level values are between their bounds.

• By using the suffixes .ExtendedConstraint and .ExtendedVariable it is possible to refer to the rows and columns respectively that are added by GMP::Instance::AddIntegerEliminationRows:

• Variables v.ExtendedVariable('EliminationLowerBoundk',i), v.ExtendedVariable('EliminationUpperBoundk',i) and v.ExtendedVariable('Eliminationk',i) are added for each integer variable v(i) with the level value between its bounds. (These variables correspond to $$l_i$$, $$u_i$$ and $$z_i$$ respectively.)

• Constraints v.ExtendedConstraint('EliminationLowerBoundk',i), v.ExtendedConstraint('EliminationUpperBoundk',i) and v.ExtendedConstraint('Eliminationk',i) are added for each integer variable v(i) with the level value between its bounds. (These constraints correspond to (1), (2) and (3) respectively.)

• Constraint mp.ExtendedConstraint('Eliminationk'), where mp denotes the symbolic mathematical program, is added for every call to GMP::Instance::AddIntegerEliminationRows. (This constraint corresponds to (4).)

Here $$k$$ denotes the value of the argument refNo.

## Example¶

The procedure GMP::Instance::AddIntegerEliminationRows can be used to find the five best integer solutions for some MIP model:

gmp_mip := GMP::Instance::Generate( MIP_Model );

cnt := 1;

while ( cnt <= 5 ) do
GMP::Instance::Solve( gmp_mip );

! Eliminate previous found integer solution.

cnt += 1;

! Copy solution at position 1 to solution at position cnt
! in solution repository.
GMP::Solution::Copy( gmp_mip, 1, cnt );
endwhile;


After executing this code, the five best integer solutions will be stored at positions 2 - 6 in the solution repository, with the best solution at position 2 and the 5th best at position 6.

The routines GMP::Instance::DeleteIntegerEliminationRows and GMP::Solution::IsInteger. See Modifying an Extended Math Program Instance of the Language Reference for more details on extended suffixes.