Algorithm::Simplex - Simplex Algorithm Implementation using Tucker Tableaux
Given a linear program formulated as a Tucker tableau, a 2D matrix or ArrayRef[ArrayRef] in Perl, seek an optimal solution.
use Algorithm::Simplex::Rational;
my $matrix = [
[ 5, 2, 30],
[ 3, 4, 20],
[10, 8, 0],
];
my $tableau = Algorithm::Simplex::Rational->new( tableau => $matrix );
$tableau->solve;
my ($primal_solution, $dual_solution) = $tableau->current_solution;
Set the number of rows. This number represent the number of rows of the coefficient matrix. It is one less than the full tableau.
Set the number of columns given the tableau matrix. This number represent the number of columns of the coefficient matrix.
Set x variable names for the given tableau, x1, x2 ... xn These are the decision variables of the maximization problem. The maximization problem is read horizontally in a Tucker tableau.
Set y variable names for the given tableau. These are the slack variables of the maximization problem.
Set u variable names for the given tableau. These are the slack variables of the minimization problem.
Set v variable names for the given tableau: v1, v2 ... vm These are the decision variables for the minimization problem. The minimization problem is read horizontally in a Tucker tableau.
Given a column number (which represents a u variable) build the bland number from the generic variable name.
Find the pivot column using Bland ordering technique to prevent cycles.
Find the pivot row using Bland ordering technique to prevent cycles.
Determine the index of the element with minimal value. Used when finding bland pivots.
Exchange the variables when a pivot is done. The method pivot() does the algrebra while this method does the variable swapping, and thus tracking of what variables take on non-zero values. This is needed to accurately report an optimal solution.
Get the dimensions of the tableau.
Higher level function that uses others to return the (bland) pivot point.
Mateu X. Hunter hunter@missoula.org
Strong design influence by George McRae at the University of Montana.
#moose for solid assistance in the refactor: particularly _build_* approach and PDL + Moose namespace management, 'inner'.
Copyright 2009, Mateu X. Hunter
You may distribute this code under the same terms as Perl itself.
Base class for the Simplex model using Tucker tableaus.
The implementation is currently limited to phase II, i.e. one must start with a feasible solution.
This class defines some of the methods concretely, and others such as:
are implemented in one of the three model types:
We have implicit variable names: x1, x2 ... , y1, y2, ... , u1, u2 ... , v1, v2 ...
Our variables are represented by:
x, y, u, and v
as found in Nering and Tuckers' book.
x and y are for the primal LP while u and v belong to the dual LP.
These variable names are set using the lazy feature of Moo.
The API is stabilizing, but still subject to change.
The algorithm requires that the initial tableau be a feasible solution.
