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package Algorithm::Simplex::Float; |
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420555
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use Moo; |
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26526
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extends 'Algorithm::Simplex'; |
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with 'Algorithm::Simplex::Role::Solve'; |
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use namespace::clean; |
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my $one = 1; |
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my $neg_one = -1; |
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my $EMPTY_STRING = q(); |
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=head1 Name |
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Algorithm::Simplex::Float - Float model of the Simplex Algorithm |
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=head1 Methods |
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=head2 pivot |
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Do the algebra of a Tucker/Bland pivot. i.e. Traverse from one node to an |
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adjacent node along the Simplex of feasible solutions. |
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=cut |
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sub pivot { |
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my $self = shift; |
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my $pivot_row_number = shift; |
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my $pivot_column_number = shift; |
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# Do tucker algebra on pivot row |
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my $scale = |
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$one / ($self->tableau->[$pivot_row_number]->[$pivot_column_number]); |
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for my $j (0 .. $self->number_of_columns) { |
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$self->tableau->[$pivot_row_number]->[$j] = |
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$self->tableau->[$pivot_row_number]->[$j] * ($scale); |
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} |
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$self->tableau->[$pivot_row_number]->[$pivot_column_number] = $scale; |
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# Do tucker algebra elsewhere |
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for my $i (0 .. $self->number_of_rows) { |
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if ($i != $pivot_row_number) { |
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my $neg_a_ic = |
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$self->tableau->[$i]->[$pivot_column_number] * ($neg_one); |
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for my $j (0 .. $self->number_of_columns) { |
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$self->tableau->[$i]->[$j] = |
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$self->tableau->[$i]->[$j] + |
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($neg_a_ic * ($self->tableau->[$pivot_row_number]->[$j])); |
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} |
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$self->tableau->[$i]->[$pivot_column_number] = $neg_a_ic * ($scale); |
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} |
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} |
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return; |
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} |
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57
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# Count pivots made |
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after 'pivot' => sub { |
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my $self = shift; |
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# TODO: Confirm whether clear is needed or not. Appears not in testing. |
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# $self->clear_display_tableau; |
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$self->number_of_pivots_made($self->number_of_pivots_made + 1); |
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return; |
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}; |
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=head2 is_optimal |
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Check the basement row to see if any positive entries exist. Existence of |
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a positive entry means the solution is sub-optimal and optimal otherwise. |
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This is how we decide when to stop the algorithm. |
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Use EPSILON instead of zero because we're dealing with floats (imperfect numbers). |
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=cut |
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sub is_optimal { |
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my $self = shift; |
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for my $j (0 .. $self->number_of_columns - 1) { |
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if ($self->tableau->[ $self->number_of_rows ]->[$j] > $self->EPSILON) { |
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return 0; |
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} |
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} |
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return 1; |
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} |
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=head2 determine_simplex_pivot_columns |
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Find the columns that are candiates for pivoting in. This is based on |
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their basement row value being greater than zero. |
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=cut |
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sub determine_simplex_pivot_columns { |
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my $self = shift; |
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my @simplex_pivot_column_numbers; |
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# Assumes the existence of at least one pivot (use optimality check to insure this) |
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# According to Nering and Tucker (1993) page 26 |
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# "selected a column with a positive entry in the basement row." |
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# NOTE: My intuition indicates a pivot could still take place but no gains would be made |
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# when the cost is zero. This would not lead us to optimality, but if we were |
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# already in an optimal state if may (should) lead to another optimal state. |
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# This would only apply then in the optimal case, i.e. all entries non-positive. |
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for my $col_num (0 .. $self->number_of_columns - 1) { |
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if ($self->tableau->[ $self->number_of_rows ]->[$col_num] > |
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$self->EPSILON) |
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{ |
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push(@simplex_pivot_column_numbers, $col_num); |
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} |
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} |
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return (@simplex_pivot_column_numbers); |
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} |
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=head2 determine_positive_ratios |
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Once a a pivot column has been chosen then we choose a pivot row based on |
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the smallest postive ration. This function is a helper to achieve that. |
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=cut |
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sub determine_positive_ratios { |
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my $self = shift; |
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my $pivot_column_number = shift; |
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# Build Ratios and Choose row(s) that yields min for the bland simplex column as a candidate pivot point. |
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# To be a Simplex pivot we must not consider negative entries |
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my @positive_ratios; |
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my @positive_ratio_row_numbers; |
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#print "Column: $possible_pivot_column\n"; |
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for my $row_num (0 .. $self->number_of_rows - 1) { |
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if ($self->tableau->[$row_num]->[$pivot_column_number] > $self->EPSILON) |
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{ |
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push(@positive_ratios, |
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$self->tableau->[$row_num]->[ $self->number_of_columns ] / |
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$self->tableau->[$row_num]->[$pivot_column_number]); |
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# Track the rows that give ratios |
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push @positive_ratio_row_numbers, $row_num; |
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} |
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} |
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146
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return (\@positive_ratios, \@positive_ratio_row_numbers); |
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} |
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149
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=head2 current_solution |
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Return both the primal (max) and dual (min) solutions for the tableau. |
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153
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=cut |
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sub current_solution { |
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my $self = shift; |
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# Report the Current Solution as primal dependents and dual dependents. |
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my @y = @{ $self->y_variables }; |
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my @u = @{ $self->u_variables }; |
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161
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162
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# Dependent Primal Variables |
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my %primal_solution; |
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for my $i (0 .. $#y) { |
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$primal_solution{ $y[$i]->{generic} } = |
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$self->tableau->[$i]->[ $self->number_of_columns ]; |
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} |
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169
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# Dependent Dual Variables |
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my %dual_solution; |
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for my $j (0 .. $#u) { |
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$dual_solution{ $u[$j]->{generic} } = |
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$self->tableau->[ $self->number_of_rows ]->[$j] * -1; |
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} |
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return (\%primal_solution, \%dual_solution); |
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} |
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=head2 is_basic_feasible_solution |
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Check if we have any negative values in the right hand column. |
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183
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=cut |
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185
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sub is_basic_feasible_solution { |
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my $self = shift; |
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188
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for my $i (0 .. $self->number_of_rows - 1) { |
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3
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if ($self->tableau->[$i]->[ $self->number_of_columns ] < |
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-($self->EPSILON)) |
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{ |
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return 0; |
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} |
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} |
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return 1; |
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} |
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1; |