- Procedure GMP::Instance::AddIntegerEliminationRows(GMP, solution, elimNo)
GMP::Instance::AddIntegerEliminationRows
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
elimNo ! (input) an elimination number
)
Arguments
- GMP
An element in
AllGeneratedMathematicalPrograms
.- solution
An integer scalar reference to a solution.
- elimNo
An integer scalar reference to an elimination number.
Return Value
The procedure returns 1 on success, or 0 otherwise.
Note
If the GMP is not integer then this procedure will fail.
Rows and columns added before for elimNo 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:
(2)\[l_i + (lev_i - lb_i)z_i \leq (lev_i - lb_i)\](3)\[u_i + (lev_i - ub_i) z_i \leq 0\](4)\[x_i - u_i + l_i = lev_i\]Every call to
GMP::Instance::AddIntegerEliminationRows
also adds the following constraint:(5)\[\begin{aligned} \sum_{i\in S_{lo}} x_i - \sum_{i\in S_{up}} x_i + \sum_{i\in S_{in}} (l_i + u_i) \geq 1 + \sum_{i\in S_{lo}} lev_i - \sum_{i\in S_{up}} lev_i \end{aligned}\]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 byGMP::Instance::AddIntegerEliminationRows
:Variables
v.ExtendedVariable('EliminationLowerBound
k',i)
,v.ExtendedVariable('EliminationUpperBound
k',i)
andv.ExtendedVariable('Elimination
k',i)
are added for each integer variablev(i)
with the level value between its bounds. (These variables correspond to \(l_i\), \(u_i\) and \(z_i\) respectively.)Constraints
v.ExtendedConstraint('EliminationLowerBound
k',i)
,v.ExtendedConstraint('EliminationUpperBound
k',i)
andv.ExtendedConstraint('Elimination
k',i)
are added for each integer variablev(i)
with the level value between its bounds. (These constraints correspond to ((2), ((3) and ((4) respectively.)Constraint
mp.ExtendedConstraint('Elimination
k')
, wheremp
denotes the symbolic mathematical program, is added for every call toGMP::Instance::AddIntegerEliminationRows
. (This constraint corresponds to ((5).)
Here \(k\) denotes the value of the argument elimNo.
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. GMP::Instance::AddIntegerEliminationRows(gmp_mip,1,cnt); 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.
See also
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.