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R HIGHS Interface

Florian Schwendinger
Updated: 2023-01-21

CRAN status Licence

This repository contains an R interface to the HiGHS solver. The HiGHS solver, is a high-performance open-source solver for solving linear programming (LP), mixed-integer programming (MIP) and quadratic programming (QP) optimization problems.

1 Installation

The package can be installed from CRAN

install.packages("highs")

or GitLab.

remotes::install_gitlab("roigrp/solver/highs")

1.0.1 Using a preinstalled HiGHS library

It is possible to use a precompile HiGHS library by providing the system variable R_HIGHS_LIB_DIR. For example I used

mkdir build
cd build
cmake .. -DCMAKE_INSTALL_PREFIX=/Z/bin/highslib -DCMAKE_POSITION_INDEPENDENT_CODE:bool=ON -DSHARED:bool=OFF -DBUILD_TESTING:bool=OFF
make install

to install the HiGHS library to /Z/bin/highslib

Sys.setenv(R_HIGHS_LIB_DIR = "/Z/bin/highslib")
install.packages("highs")
# or 
# remotes::install_gitlab("roigrp/solver/highs")

2 Basic usage

library("highs")

args(highs_solve)
#> function (Q = NULL, L, lower, upper, A, lhs, rhs, types, maximum = FALSE, 
#>     offset = 0, control = list(), dry_run = FALSE) 
#> NULL

2.1 LP

# Minimize
#  x_0 +  x_1 + 3
# Subject to
#                 x_1 <= 7
#  5 <=   x_0 + 2 x_1 <= 15
#  6 <= 3 x_0 + 2 x_1
#  0 <=   x_0         <= 4
#  1 <=           x_1
A <- rbind(c(0, 1), c(1, 2), c(3, 2))
s <- highs_solve(L = c(1.0, 1), lower = c(0, 1), upper = c(4, Inf),
                 A = A, lhs = c(-Inf, 5, 6), rhs = c(7, 15, Inf),
                 offset = 3)
str(s)
#> List of 6
#>  $ primal_solution: num [1:2] 0.5 2.25
#>  $ objective_value: num 5.75
#>  $ status         : int 7
#>  $ status_message : chr "Optimal"
#>  $ solver_msg     :List of 6
#>   ..$ value_valid: logi TRUE
#>   ..$ dual_valid : logi TRUE
#>   ..$ col_value  : num [1:2] 0.5 2.25
#>   ..$ col_dual   : num [1:2] 0 0
#>   ..$ row_value  : num [1:3] 2.25 5 6
#>   ..$ row_dual   : num [1:3] 0 0.25 0.25
#>  $ info           :List of 18
#>   ..$ valid                     : logi TRUE
#>   ..$ mip_node_count            : num -1
#>   ..$ simplex_iteration_count   : int 2
#>   ..$ ipm_iteration_count       : int 0
#>   ..$ qp_iteration_count        : int 0
#>   ..$ crossover_iteration_count : int 0
#>   ..$ primal_solution_status    : chr "Feasible"
#>   ..$ dual_solution_status      : chr "Feasible"
#>   ..$ basis_validity            : int 1
#>   ..$ objective_function_value  : num 5.75
#>   ..$ mip_dual_bound            : num 0
#>   ..$ mip_gap                   : num Inf
#>   ..$ num_primal_infeasibilities: int 0
#>   ..$ max_primal_infeasibility  : num 0
#>   ..$ sum_primal_infeasibilities: num 0
#>   ..$ num_dual_infeasibilities  : int 0
#>   ..$ max_dual_infeasibility    : num 0
#>   ..$ sum_dual_infeasibilities  : num 0

2.2 QP

# Minimize
#  0.5 x^2 - 2 x + y
# Subject to
#  x <= 3
zero <- .Machine$double.eps * 100
Q <- rbind(c(1, 0), c(0, zero))
L <- c(-2, 1)
A <- t(c(1, 0))

cntrl <- list(log_dev_level = 0L)
s <- highs_solve(Q = Q, L = L, A = A, lhs = 0, rhs = 3, control = cntrl)
str(s)
#> List of 6
#>  $ primal_solution: num [1:2] 2e+00 -1e+07
#>  $ objective_value: num -1e+07
#>  $ status         : int 7
#>  $ status_message : chr "Optimal"
#>  $ solver_msg     :List of 6
#>   ..$ value_valid: logi TRUE
#>   ..$ dual_valid : logi TRUE
#>   ..$ col_value  : num [1:2] 2e+00 -1e+07
#>   ..$ col_dual   : num [1:2] 0 0
#>   ..$ row_value  : num 2
#>   ..$ row_dual   : num 0
#>  $ info           :List of 18
#>   ..$ valid                     : logi TRUE
#>   ..$ mip_node_count            : num -1
#>   ..$ simplex_iteration_count   : int 0
#>   ..$ ipm_iteration_count       : int 0
#>   ..$ qp_iteration_count        : int 5
#>   ..$ crossover_iteration_count : int 0
#>   ..$ primal_solution_status    : chr "Feasible"
#>   ..$ dual_solution_status      : chr "Feasible"
#>   ..$ basis_validity            : int 0
#>   ..$ objective_function_value  : num -1e+07
#>   ..$ mip_dual_bound            : num 0
#>   ..$ mip_gap                   : num Inf
#>   ..$ num_primal_infeasibilities: int 0
#>   ..$ max_primal_infeasibility  : num 0
#>   ..$ sum_primal_infeasibilities: num 0
#>   ..$ num_dual_infeasibilities  : int 0
#>   ..$ max_dual_infeasibility    : num 0
#>   ..$ sum_dual_infeasibilities  : num 0

3 Additional information

3.1 Sparse matrices

The HiGHs C++ library internally supports the matrix formats csc (compressed sparse column matrix) and csr (compressed Sparse Row array). The highs package currently supports the following matrix classes:

  1. "matrix" dense matrices,
  2. "dgCMatrix" compressed sparse column matrix from the Matrix package,
  3. "dgRMatrix" compressed sparse row matrix from the Matrix package,
  4. "matrix.csc" compressed sparse column matrix from the SparseM package,
  5. "matrix.csr" compressed sparse row matrix from the SparseM package,
  6. "simple_triplet_matrix" coordinate format from the slam package.

If the constraint matrix A is provided as dgCMatrix, dgRMatrix, matrix.csc or matrix.csr the underlying data is directly passed to HiGHs otherwise it is first transformed into the csc format an afterwards passed to HiGHs

library("Matrix")

A <- rbind(c(0, 1), c(1, 2), c(3, 2))
csc <- as(A, "CsparseMatrix")  # dgCMatrix
s0 <- highs_solve(L = c(1.0, 1), lower = c(0, 1), upper = c(4, Inf),
                  A = csc, lhs = c(-Inf, 5, 6), rhs = c(7, 15, Inf),
                  offset = 3)

csr <- as(A, "RsparseMatrix")  # dgRMatrix
s1 <- highs_solve(L = c(1.0, 1), lower = c(0, 1), upper = c(4, Inf),
                  A = csr, lhs = c(-Inf, 5, 6), rhs = c(7, 15, Inf),
                  offset = 3)

library("SparseM")

csc <- as.matrix.csc(A)
s2 <- highs_solve(L = c(1.0, 1), lower = c(0, 1), upper = c(4, Inf),
                  A = csc, lhs = c(-Inf, 5, 6), rhs = c(7, 15, Inf),
                  offset = 3)

csr <- as.matrix.csr(A)
s3 <- highs_solve(L = c(1.0, 1), lower = c(0, 1), upper = c(4, Inf),
                  A = csr, lhs = c(-Inf, 5, 6), rhs = c(7, 15, Inf),
                  offset = 3)

library("slam")
stm <- as.simple_triplet_matrix(A)
s4 <- highs_solve(L = c(1.0, 1), lower = c(0, 1), upper = c(4, Inf),
                  A = stm, lhs = c(-Inf, 5, 6), rhs = c(7, 15, Inf),
                  offset = 3)

4 Options

The function highs_available_solver_options lists the available solver options

d <- highs_available_solver_options()
d[["option"]] <- sprintf("`%s`", d[["option"]])
knitr::kable(d, row.names = FALSE)
option type category
allow_unbounded_or_infeasible bool advanced
allowed_cost_scale_factor integer advanced
allowed_matrix_scale_factor integer advanced
cost_scale_factor integer advanced
dual_simplex_cost_perturbation_multiplier double advanced
dual_simplex_pivot_growth_tolerance double advanced
dual_steepest_edge_weight_error_tolerance double advanced
dual_steepest_edge_weight_log_error_threshold double advanced
factor_pivot_threshold double advanced
factor_pivot_tolerance double advanced
keep_n_rows integer advanced
less_infeasible_DSE_check bool advanced
less_infeasible_DSE_choose_row bool advanced
log_dev_level integer advanced
lp_presolve_requires_basis_postsolve bool advanced
max_dual_simplex_cleanup_level integer advanced
max_dual_simplex_phase1_cleanup_level integer advanced
mps_parser_type_free bool advanced
no_unnecessary_rebuild_refactor bool advanced
presolve_pivot_threshold double advanced
presolve_rule_logging bool advanced
presolve_rule_off integer advanced
presolve_substitution_maxfillin integer advanced
primal_simplex_bound_perturbation_multiplier double advanced
rebuild_refactor_solution_error_tolerance double advanced
run_crossover bool advanced
simplex_dualise_strategy integer advanced
simplex_initial_condition_check bool advanced
simplex_initial_condition_tolerance double advanced
simplex_permute_strategy integer advanced
simplex_price_strategy integer advanced
simplex_unscaled_solution_strategy integer advanced
start_crossover_tolerance double advanced
use_implied_bounds_from_presolve bool advanced
use_original_HFactor_logic bool advanced
dual_feasibility_tolerance double file
glpsol_cost_row_location integer file
highs_analysis_level integer file
highs_debug_level integer file
infinite_bound double file
infinite_cost double file
ipm_iteration_limit integer file
ipm_optimality_tolerance double file
large_matrix_value double file
log_file string file
objective_bound double file
objective_target double file
primal_feasibility_tolerance double file
random_seed integer file
simplex_crash_strategy integer file
simplex_dual_edge_weight_strategy integer file
simplex_iteration_limit integer file
simplex_max_concurrency integer file
simplex_min_concurrency integer file
simplex_primal_edge_weight_strategy integer file
simplex_scale_strategy integer file
simplex_strategy integer file
simplex_update_limit integer file
small_matrix_value double file
solution_file string file
threads integer file
write_model_file string file
write_model_to_file bool file
write_solution_style integer file
write_solution_to_file bool file
icrash bool icrash
icrash_approx_iter integer icrash
icrash_breakpoints bool icrash
icrash_dualize bool icrash
icrash_exact bool icrash
icrash_iterations integer icrash
icrash_starting_weight double icrash
icrash_strategy string icrash
log_to_console bool logging
output_flag bool logging
mip_abs_gap double mip
mip_detect_symmetry bool mip
mip_feasibility_tolerance double mip
mip_heuristic_effort double mip
mip_lp_age_limit integer mip
mip_max_improving_sols integer mip
mip_max_leaves integer mip
mip_max_nodes integer mip
mip_max_stall_nodes integer mip
mip_min_cliquetable_entries_for_parallelism integer mip
mip_pool_age_limit integer mip
mip_pool_soft_limit integer mip
mip_pscost_minreliable integer mip
mip_rel_gap double mip
mip_report_level integer mip
parallel string run-time
presolve string run-time
ranging string run-time
solver string run-time
time_limit double run-time

for additional information see the HiGHS homepage.

5 Status codes

HiGHS currently has the following status codes defined in HConst.h".

enumerator status message
kNotset 0 "Not Set"
kLoadError 1 "Load error"
kModelError 2 "Model error"
kPresolveError 3 "Presolve error"
kSolveError 4 "Solve error"
kPostsolveError 5 "Postsolve error"
kModelEmpty 6 "Empty"
kOptimal 7 "Optimal"
kInfeasible 8 "Infeasible"
kUnboundedOrInfeasible 9 "Primal infeasible or unbounded"
kUnbounded 10 "Unbounded"
kObjectiveBound 11 "Bound on objective reached"
kObjectiveTarget 12 "Target for objective reached"
kTimeLimit 13 "Time limit reached"
kIterationLimit 14 "Iteration limit reached"
kUnknown 15 "Unknown"
kMin 0 "Not Set"
kMax 15 "Unknown"

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.