R: Linear and Mixed Integer Programming Solver Using GLPK

Rglpk_solve_LP {Rglpk}

R Documentation

Linear and Mixed Integer Programming Solver Using GLPK

Description

High level R interface to the GNU Linear Programming Kit (GLPK) for solving linear as well as mixed integer linear programming (MILP) problems.

Usage

Rglpk_solve_LP(obj, mat, dir, rhs, bounds = NULL, types = NULL, max = FALSE,
               control = list(), ...)

Arguments

`obj`	a numeric vector representing the objective coefficients.
`mat`	a numeric vector or a matrix of 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.
`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`.
`types`	a character vector indicating the types of the objective variables. `types` can be either `"B"` for binary, `"C"` for continuous or `"I"` for integer. By default `NULL`, taken as all-continuous. Recycled as needed.
`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.
`control`	a list of parameters to the solver. Currently the only options are: `verbose`, a logical for turning on/off additional solver output; `canonicalize_status`, a logical indicating whether to canonicalize GLPK status codes or not. Defaults: `FALSE`; `TRUE`.
`...`	a list of control parameters (overruling those specified in `control`).

Details

GLPK 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. 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.

Value

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 `canonicalize_status` is set (the default) then it will return 0 for the optimal solution being found, and non-zero otherwise. If the control parameter is set to `FALSE` it will return the GLPK status codes.

Author(s)

Stefan Theussl and Kurt Hornik

References

GNU Linear Programming Kit (http://www.gnu.org/software/glpk/glpk.html).

GLPK Interface to R (http://cran.R-project.org/package=Rglpk).

Examples

## 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))

[Package Rglpk version 0.6-0 Index]