The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

Getting Started with highs

The highs package provides an R interface to HiGHS, a high-performance solver for linear programming (LP), mixed-integer programming (MIP), and quadratic programming (QP) problems.

Linear Programming

Consider the LP:

\[ \max \; 2x_1 + 4x_2 + 3x_3 \] subject to \[ 3x_1 + 4x_2 + 2x_3 \le 60, \quad 2x_1 + x_2 + 2x_3 \le 40, \quad x_1 + 3x_2 + 2x_3 \le 80, \quad x_1, x_2, x_3 \ge 0. \]

library(highs)

L <- c(2, 4, 3)
A <- matrix(c(3, 4, 2,
              2, 1, 2,
              1, 3, 2), nrow = 3, byrow = TRUE)
rhs <- c(60, 40, 80)

sol <- highs_solve(L = L, lower = 0, A = A, rhs = rhs, maximum = TRUE)
sol$objective_value
#> [1] 76.66667
sol$primal_solution
#> [1]  0.000000  6.666667 16.666667

Mixed-Integer Programming

Adding integrality constraints makes this a MIP. Use the types argument with "I" for integer, "C" for continuous.

L <- c(3, 1, 3)
A <- rbind(c(-1,  2,  1),
           c( 0,  4, -3),
           c( 1, -3,  2))
rhs <- c(4, 2, 3)
lower <- c(-Inf, 0, 2)
upper <- c(4, 100, Inf)
types <- c("I", "C", "I")

sol <- highs_solve(L = L, lower = lower, upper = upper,
                   A = A, rhs = rhs, types = types, maximum = TRUE)
sol$objective_value
#> [1] 23.5
sol$primal_solution
#> [1] 4.0 2.5 3.0

Quadratic Programming

For QP problems, supply the Hessian matrix Q in the objective \(\frac{1}{2} x^T Q x + L^T x\):

Q <- matrix(c(8, 2, 2,
              2, 6, 0,
              2, 0, 4), nrow = 3)
L <- c(-14, -6, -12)

sol <- highs_solve(Q = Q, L = L, lower = 0)
sol$objective_value
#> [1] -23.69156
sol$primal_solution
#> [1] 1.0292208 0.4545455 2.4285714

Solver Options

Control solver behaviour with highs_control():

sol <- highs_solve(
  L = c(2, 4, 3), lower = 0,
  A = matrix(c(3, 4, 2, 2, 1, 2, 1, 3, 2), nrow = 3, byrow = TRUE),
  rhs = c(60, 40, 80), maximum = TRUE,
  control = highs_control(
    threads = 1L,
    time_limit = 60,
    log_to_console = FALSE
  )
)
sol$status_message
#> [1] "Optimal"

View all available options:

highs_available_solver_options()

Sparse Matrix Support

The A matrix can be any of the following formats:

library(Matrix)
A_sparse <- Matrix(c(3, 4, 2, 2, 1, 2, 1, 3, 2),
                   nrow = 3, byrow = TRUE, sparse = TRUE)
sol <- highs_solve(L = c(2, 4, 3), lower = 0,
                   A = A_sparse, rhs = c(60, 40, 80), maximum = TRUE)
sol$objective_value
#> [1] 76.66667

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.