Rglpk_solve_LP: 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(), ...)

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.
solution_dual: variable reduced cost, if available (NA otherwise).
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, NA otherwise).

Arguments

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 "<", "<=", ">", ">=", or "==". Note, however, that the GLPK API only allows for non-strict inequalities. Strict inequalities are handled the same way as non-strict inequalities.
rhs: a numeric vector representing 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. See *Details*.
...: a list of control parameters (overruling those specified in control).

Author

Stefan Theussl and Kurt Hornik

Details

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:

verbose:: turn GLPK terminal output on (TRUE) or off (FALSE, the default).
presolve:: turn presolver on (TRUE) or off (FALSE, the default).
tm_limit:: time limit in milliseconds of call to optimizer. Can be any nonnegative integer. Default: 0 (use GLPK default).
canonicalize_status:: a logical indicating whether to canonicalize GLPK status codes (on success Rglpk_solve_LP() returns code 0) or not (1). Default: TRUE.

References

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

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

Examples

Run this code

## 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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