| Rglpk_solve_LP {Rglpk} | R Documentation |
High level R interface to the GNU Linear Programming Kit for solving linear as well as mixed integer linear programming problems (MILPs).
Rglpk_solve_LP(obj, mat, dir, rhs, types = NULL, max = FALSE,
bounds = NULL, verbose = FALSE)
obj |
a vector with the objective coefficients |
mat |
a vector or a matrix of the constraint coefficients |
dir |
a character vector with the directions of the constraints.
Each element must be one of "<", "<=", ">",
">=", or "==". |
rhs |
the right hand side of the constraints |
types |
a vector indicating the types of the objective
variables. types can be either "B" for binary,
"C" for continuous or "I" for integer. By default all
variables are of type "C". |
max |
a logical giving the direction of the optimization.
TRUE means that the objective is to maximize the objective
function, FALSE (default) means to minimize it. |
bounds |
NULL (default) or a list with elements
upper and lower containing the indices and
corresponding bounds of the objective variables. The default for
each variable is a bound between 0 and Inf. |
verbose |
a logical for turning on/off additional solver output:
Default: FALSE. |
The GNU Linear Programming Kit is open source. The current version can be found at http://www.gnu.org/software/glpk/glpk.html. Package Rglpk provides a high level solver function using the low level C interface of the GLPK solver. There also exists an R interface done by Lopaka Lee which ports all low level C Interface routines of the GLPK API to R (R package glpk).
A list containing the optimal solution, with the following components.
solution |
the vector of optimal coefficients |
objval |
the value of the objective function at the optimum |
status |
an integer with status information about the solution returned: 0 if the optimal solution was found, a non-zero value otherwise. |
Stefan Theussl and Kurt Hornik
GNU Linear Programming Kit (http://www.gnu.org/software/glpk/glpk.html).
GLPK Interface to R (http://cran.R-project.org/package=Rglpk).
lp in package lpSolve;
Rsymphony_solve_LP in package
Rsymphony.
## Simple linear program.
## maximize: 2 x_1 + 4 x_2 + 3 x_3
## subject to: 3 x_1 + 4 x_2 + 2 x_3 <= 60
## 2 x_1 + x_2 + x_3 <= 40
## x_1 + 3 x_2 + 2 x_3 <= 80
## x_1, x_2, x_3 are non-negative real numbers
obj <- c(2, 4, 3)
mat <- matrix(c(3, 2, 1, 4, 1, 3, 2, 2, 2), nrow = 3)
dir <- c("<=", "<=", "<=")
rhs <- c(60, 40, 80)
max <- TRUE
Rglpk_solve_LP(obj, mat, dir, rhs, max = max)
## Simple mixed integer linear program.
## maximize: 3 x_1 + 1 x_2 + 3 x_3
## subject to: -1 x_1 + 2 x_2 + x_3 <= 4
## 4 x_2 - 3 x_3 <= 2
## x_1 - 3 x_2 + 2 x_3 <= 3
## x_1, x_3 are non-negative integers
## x_2 is a non-negative real number
obj <- c(3, 1, 3)
mat <- matrix(c(-1, 0, 1, 2, 4, -3, 1, -3, 2), nrow = 3)
dir <- c("<=", "<=", "<=")
rhs <- c(4, 2, 3)
types <- c("I", "C", "I")
max <- TRUE
Rglpk_solve_LP(obj, mat, dir, rhs, types, max)
## Same as before but with bounds replaced by
## -Inf < x_1 <= 4
## 0 <= x_2 <= 100
## 2 <= x_3 < Inf
bounds <- list(lower = list(ind = c(1L, 3L), val = c(-Inf, 2)),
upper = list(ind = c(1L, 2L), val = c(4, 100)))
Rglpk_solve_LP(obj, mat, dir, rhs, types, max, bounds)