This package provides an R interface to the high performance linear programming library Clp. Relevant source code of Clp is included in the R package for easy installation. A C++11 compiler is required if the package is built from source.
Below is an example problem taken from IBM Optimization Library Guide and Reference.
Minimize or maximize Z = x1 + 2x5 - x8
Subject to:
2.5 <= 3x1 + x2 - 2x4 - x5 - x8
2x2 + 1.1x3 <= 2.1
x3 + x6 == 4.0
1.8 <= 2.8x4 -1.2x7 <= 5.0
3.0 <= 5.6x1 + x5 + 1.9x8 <= 15.0
where:
2.5 <= x1
0 <= x2 <= 4.1
0 <= x3
0 <= x4
0.5 <= x5 <= 4.0
0 <= x6
0 <= x7
0 <= x8 <= 4.3
Using clplite, we can solve this problem by the following R code:
library(clplite)
obj = c(1, 0, 0, 0, 2, 0, 0, -1)
A = matrix(c(
3, 1, 0, -2, -1, 0, 0, -1,
0, 2, 1.1, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 1, 0, 0,
0, 0, 0, 2.8, 0, 0, -1.2, 0,
5.6, 0, 0, 0, 1, 0, 0, 1.9
), nrow = 5, byrow = TRUE)
constr_lb = c(2.5, -Inf, 4, 1.8, 3)
constr_ub = c(Inf, 2.1, 4, 5, 15)
var_lb = c(2.5, 0, 0, 0, 0.5, 0, 0, 0)
var_ub = c(Inf, 4.1, Inf, Inf, 4, Inf, Inf, 4.3)
clp_solve(obj, A, constr_lb, constr_ub, var_lb, var_ub, max = TRUE)$solution
[1] 2.5000000 0.0000000 0.0000000 0.6428571 1.0000000 4.0000000 0.0000000 0.0000000
$objval
[1] 4.5
$status
[1] 0
clp_solve(obj, A, constr_lb, constr_ub, var_lb, var_ub, max = FALSE)$solution
[1] 2.5000000 0.0000000 0.0000000 0.6428571 0.5000000 4.0000000 0.0000000 0.2631579
$objval
[1] 3.236842
$status
[1] 0
A significant feature of Clp and clplite is the ability to handle
sparse constraint matrices, which is critical in handling large-scale
optimization problems. Currently clplite supports matrices of types
matrix, dgTMatrix, dgCMatrix, dgRMatrix, and types that can be
coerced to them via the as() function.
library(Matrix)
As = as(A, "sparseMatrix")
clp_solve(obj, As, constr_lb, constr_ub, var_lb, var_ub, max = TRUE)
clp_solve(obj, As, constr_lb, constr_ub, var_lb, var_ub, max = FALSE)