naginterfaces.library.mip.ilp_​info

naginterfaces.library.mip.ilp_info(n, m, comm)

ilp_info extracts more information associated with the solution of an integer programming problem computed by ilp_dense().

Deprecated since version 29.3.0.0: ilp_info is deprecated. Please use handle_solve_milp() instead. See also the Replacement Calls document.

For full information please refer to the NAG Library document for h02bz

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/h/h02bzf.html

Parameters

nint

This must be the same argument $n$ as supplied to ilp_dense().

mint

This must be the same argument $m$ as supplied to ilp_dense().

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to ilp_dense().

Returns

blfloat, ndarray, shape $(n+m)$

If ilp_dense() exits with the function exits successfully or $errno$ = 7 or 9, the values in the array $bl$ contain the lower bounds imposed on the integer solution for all the constraints. The first $n$ elements contain the lower bounds on the variables, and the next $m$ elements contain the lower bounds for the general linear constraints (if any).

bufloat, ndarray, shape $(n+m)$

If ilp_dense() exits with the function exits successfully or $errno$ = 7 or 9, the values in the array $bu$ contain the upper bounds imposed on the integer solution for all the constraints. The first $n$ elements contain the upper bounds on the variables, and the next $m$ elements contain the upper bounds for the general linear constraints (if any).

clamdafloat, ndarray, shape $(n+m)$

If ilp_dense() exits with the function exits successfully or $errno$ = 7 or 9, the values in the array $clamda$ contain the values of the Lagrange-multipliers for each constraint with respect to the current working set. The first $n$ elements contain the multipliers (reduced costs) for the bound constraints on the variables, and the next $m$ elements contain the multipliers (shadow costs) for the general linear constraints (if any).

istateint, ndarray, shape $(n+m)$

If ilp_dense() exits with the function exits successfully or $errno$ = 7 or 9, the values in the array $istate$ indicate the status of the constraints in the working set at an integer solution. Otherwise, $istate$ indicates the composition of the working set at the final iterate. The significance of each possible value of $istate\left[j\right]$ is as follows.

$istate\left[j\right]$	Meaning
$-2$	The constraint violates its lower bound by more than $\text{tolfes}$ (the feasibility tolerance, see ilp_dense()).
$-1$	The constraint violates its upper bound by more than $\text{tolfes}$.
$0$	The constraint is satisfied to within $\text{tolfes}$, but is not in the working set.
$1$	This inequality constraint is included in the working set at its lower bound.
$2$	This inequality constraint is included in the working set at its upper bound.
$3$	This constraint is included in the working set as an equality. This value of $istate$ can occur only when $bl\left[j\right]=bu\left[j\right]$.
$4$	This corresponds to an integer solution being declared with $x_j$ being temporarily fixed at its current value. This value of $istate$ can occur only when the function exits successfully or $errno$ = 7 or 9 on exit from ilp_dense().

Raises

NagValueError

(errno $1$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 0$.

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n>0$.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

ilp_info extracts the following information associated with the solution of an integer programming problem computed by ilp_dense(). The upper and lower bounds used for the solution, the Lagrange-multipliers (costs), and the status of the variables at the solution.

In the branch and bound method employed by ilp_dense(), the arrays $bl$ and $bu$ are used to impose restrictions on the values of the integer variables in each sub-problem. That is, if the variable $x_j$ is restricted to take value $v_j$ in a particular sub-problem, then $bl\left[j\right]=bu\left[j\right]=v_j$ is set in the sub-problem. Thus, on exit from this function, some of the elements of $bl$ and $bu$ which correspond to integer variables may contain these imposed values, rather than those originally supplied to ilp_dense().