Rglpk_solve_LP | R Documentation |
High level R interface to the GNU Linear Programming Kit (GLPK) for solving linear as well as mixed integer linear programming (MILP) problems.
Rglpk_solve_LP(obj, mat, dir, rhs, bounds = NULL, types = NULL, max = FALSE,
control = list(), ...)
obj |
a numeric vector representing the objective coefficients. |
mat |
a numeric vector or a (sparse) matrix of constraint coefficients. If the optimization problem is unconstrained then a matrix of dimension 0 times the number of objective variables is required. |
dir |
a character vector with the directions of the constraints.
For a nonzero number of constraints each element must be one of
|
rhs |
a numeric vector representing the right hand side of the constraints. |
bounds |
|
types |
a character vector indicating the types of the objective
variables. |
max |
a logical giving the direction of the optimization.
|
control |
a list of parameters to the solver. See *Details*. |
... |
a list of control parameters (overruling those specified in
|
GLPK is open source. The current version can be found at https://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. R interface packages which port all low level C routines of the GLPK API to R are also available. Consult the ‘See Also’ Section for references.
Matrix mat
and obj
may be sparse arrays or matrices
(simple_triplet_matrix
) as provided by the slam
package.
The control
argument can be used to set GLPK's many
parameters. See the respective method section of the GNU Linear
Programming Kit Reference Manual for further details. The following
parameters are supported:
turn GLPK terminal output on (TRUE
) or
off (FALSE
, the default).
turn presolver on (TRUE
) or
off (FALSE
, the default).
time limit in milliseconds of call to optimizer. Can be any nonnegative integer. Default: 0 (use GLPK default).
a logical indicating
whether to canonicalize GLPK status codes (on success Rglpk_solve_LP()
returns code 0) or
not (1). Default: TRUE
.
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. If the control parameter |
solution_dual |
variable reduced cost, if available ( |
auxiliary |
a list with two vectors each containing the values of the
auxiliary variable associated with the respective constraint at
solution, primal and dual (if available, |
Stefan Theussl and Kurt Hornik
GNU Linear Programming Kit (https://www.gnu.org/software/glpk/glpk.html).
GLPK Interface to R (https://cran.R-project.org/package=Rglpk).
glpk and glpkAPI for C API bindings;
lp
in package lpSolve;
ROI_solve
in package ROI;
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 + 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 = types, max = 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, bounds, types, max)
## Examples from the GLPK manual
## Solver output enabled
## 1.3.1
## maximize: 10 x_1 + 6 x_2 + 4 x_3
## subject to: x_1 + x_2 + x_3 <= 100
## 10 x_1 + 4 x_2 + 5 x_3 <= 600
## 2 x_1 + 2 x_2 + 6 x_3 <= 300
## x_1, x_2, x_3 are non-negative real numbers
obj <- c(10, 6, 4)
mat <- matrix(c(1, 10, 2, 1, 4, 2, 1, 5, 6), nrow = 3)
dir <- c("<=", "<=", "<=")
rhs <- c(100, 600, 300)
max <- TRUE
Rglpk_solve_LP(obj, mat, dir, rhs, max = max, control = list("verbose" =
TRUE, "canonicalize_status" = FALSE))
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