LOP {ConcordanceTest} | R Documentation |
This function computes the solution of the Linear Ordering Problem.
LOP(mat_LOP)
mat_LOP |
Preference matrix defining the Linear Ordering Problem. A numeric square matrix for which we want to obtain the permutation of rows/columns that maximizes the sum of the elements above the main diagonal. |
The function returns a list with the following elements:
obj_val
: Optimal value of the solution of the Linear Ordering Problem, i.e., the sum of the elements above the main diagonal under the permutation rows/cols solution.
permutation
: Solution of the Linear Ordering Problem, i.e., the rows/cols permutation.
permutation_matrix
: Optimal permutation matrix of the Linear Ordering Problem.
MartÃ, R. and Reinelt, G. The Linear Ordering Problem: Exact and Heuristic Methods in Combinatorial Optimization. Springer, first edition 2011.
## Square matrix ## ## | 1 2 2 | ## | 2 3 3 | ## | 3 2 2 | ## ## The optimal permutation of rows/cols is (2,3,1), ## and the solution of the Linear Ordering Problem is 8. ## Te permutation matrix of the solution is ## | 0 0 0 | ## | 1 0 1 | ## | 1 0 0 | mat_LOP <- matrix(c(1,2,3,2,3,2,2,3,2), nrow=3) LOP(mat_LOP)