HiGHS - Linear optimization software

HiGHS is a high performance serial and parallel solver for large scale sparse linear optimization problems of the form

Minimize (1/2) x^TQx + c^Tx subject to L <= Ax <= U; l <= x <= u

where Q must be positive semi-definite and, if Q is zero, there may be a requirement that some of the variables take integer values. Thus HiGHS can solve linear programming (LP) problems, convex quadratic programming (QP) problems, and mixed integer programming (MIP) problems. It is mainly written in C++, but also has some C. It has been developed and tested on various Linux, MacOS and Windows installations using both the GNU (g++) and Intel (icc) C++ compilers. Note that HiGHS requires (at least) version 4.9 of the GNU compiler. It has no third-party dependencies.

HiGHS has primal and dual revised simplex solvers, originally written by Qi Huangfu and further developed by Julian Hall. It also has an interior point solver for LP written by Lukas Schork, an active set solver for QP written by Michael Feldmeier, and a MIP solver written by Leona Gottwald. Other features have been added by Julian Hall and Ivet Galabova, who manages the software engineering of HiGHS and interfaces to C, C#, FORTRAN, Julia and Python.

Although HiGHS is freely available under the MIT license, we would be pleased to learn about users' experience and give advice via email sent to highsopt@gmail.com.

Reference

If you use HiGHS in an academic context, please acknowledge this and cite the following article. P arallelizing the dual revised simplex method Q. Huangfu and J. A. J. Hall Mathematical Programming Computation, 10 (1), 119-142, 2018. DOI: 10.1007/s12532-017-0130-5

http://www.maths.ed.ac.uk/hall/HuHa13/

Documentation

The rest of this file gives brief documentation for HiGHS. Comprehensive documentation is available via https://www.highs.dev.

Download

Precompiled static executables are available for a variety of platforms at: https://github.com/JuliaBinaryWrappers/HiGHSstatic_jll.jl/releases

These binaries are provided by the Julia community and are not officially supported by the HiGHS development team. If you have trouble using these libraries, please open a GitHub issue and tag @odow in your question.

Installation instructions

To install, download the appropriate file and extract the executable located at /bin/highs.

For Windows users: if in doubt, choose the file ending in x86_64-w64-mingw32.tar.gz
For M1 macOS users: choose the file ending in aarch64-apple-darwin.tar.gz
For Intel macOS users: choose the file ending in x86_64-apple-darwin.tar.gz

Shared libaries

For advanced users, precompiled executables using shared libraries are available for a variety of platforms at: https://github.com/JuliaBinaryWrappers/HiGHS_jll.jl/releases.

Similar download instructions apply.

These files link against libstdc++. If you do not have one installed, download the platform-specific libraries from: https://github.com/JuliaBinaryWrappers/CompilerSupportLibraries_jll.jl/releases/tag/CompilerSupportLibraries-v0.5.1%2B0 and copy all the libraries into the same folder as the highs executable.
Unless using the FORTRAN interface, any of versions libgfortran3-libgfortran5 should work. If in doubt, Windows users should choose the x86_64-w64-mingw32-libgfortran5.tar.gz.

Compilation

HiGHS uses CMake as build system. First setup a build folder and call CMake as follows

mkdir build
cd build
cmake ..

Then compile the code using

make

This installs the executable bin/highs. The minimum CMake version required is 3.15.

Testing

To perform a quick test whether the compilation was successful, run

ctest

Run-time options

In the following discussion, the name of the executable file generated is assumed to be highs.

HiGHS can read plain text MPS files and LP files and the following command solves the model in ml.mps

highs ml.mps

HiGHS options

Usage: highs [OPTION...] [file]

  --model_file arg        File of model to solve.
  --presolve arg          Presolve: "choose" by default - "on"/"off" are alternatives.
  --solver arg            Solver: "choose" by default - "simplex"/"ipm" are alternatives.
  --parallel arg          Parallel solve: "choose" by default - "on"/"off" are alternatives.
  --time_limit arg        Run time limit (seconds - double).
  --options_file arg      File containing HiGHS options.
  --solution_file arg     File for writing out model solution.
  --write_model_file arg  File for writing out model.
  --random_seed arg       Seed to initialize random number generation.
  --ranging arg           Compute cost, bound, RHS and basic solution ranging.

-h, --help Print help.

Note:

If the file constrains some variables to take integer values (so the problem is a MIP) and "simplex" or "ipm" is selected for the solver option, then the integrality constraint will be ignored.
If the file defines a quadratic term in the objective (so the problem is a QP or MIQP) and "simplex" or "ipm" is selected for the solver option, then the quadratic term will be ignored.
If the file constrains some variables to take integer values and defines a quadratic term in the objective, then the problem is MIQP and cannot be solved by HiGHS

Language interfaces and further documentation

There are HiGHS interfaces for C, C#, FORTRAN, and Python in HiGHS/src/interfaces, with example driver files in HiGHS/examples. Documentation is availble via https://www.highs.dev/, and we are happy to give a reasonable level of support via email sent to highsopt@gmail.com.

Parallel code

Parallel computation within HiGHS is limited to the dual simplex solver and the MIP solver. However, performance gain is unlikely to be significant at present. For the simplex solver, at best, speed-up is limited to the number of memory channels, rather than the number of cores. For the MIP solver, the ability of HiGHS to exploit multicore architectures is expected to increase significantly.

HiGHS will identify the number of available threads at run time, and restrict their use to the value of the HiGHS option threads.

If run with threads=1, HiGHS is serial. The --parallel run-time option will cause the HiGHS parallel dual simplex solver to run in serial. Although this could lead to better performance on some problems, performance will typically be diminished.

If multiple threads are available, and run with threads>1, HiGHS will use multiple threads. Although the best value will be problem and architecture dependent, for the simplex solver threads=8 is typically a good choice. Although HiGHS is slower when run in parallel than in serial for some problems, it is typically faster in parallel.

HiGHS Library

HiGHS is compiled in a shared library. Running

make install

from the build folder installs the library in lib/, as well as all header files in include/. For a custom installation in install_folder run

cmake -DCMAKE_INSTALL_PREFIX=install_folder ..

and then

make install

To use the library from a CMake project use

find_package(HiGHS)

and add the correct path to HIGHS_DIR.

Compiling and linking without CMake

An executable defined in the file use_highs.cpp (for example) is linked with the HiGHS library as follows. After running the code above, compile and run with

g++ -o use_highs use_highs.cpp -I install_folder/include/ -L install_folder/lib/ -lhighs

LD_LIBRARY_PATH=install_folder/lib/ ./use_highs

Interfaces

Julia

A Julia interface is available at https://github.com/jump-dev/HiGHS.jl.

Rust

HiGHS can be used from rust through the highs crate. The rust linear programming modeler good_lp supports HiGHS.

Javascript

HiGHS can be used from javascript directly inside a web browser thanks to highs-js. See the demo and the npm package.

Python

In order to build the Python interface, build (and install?) the HiGHS library as described above, ensure the shared library is in the LD_LIBRARY_PATH environment variable, and then run

pip install ./

from the root HiGHS folder (there should be a setup.py file there).

You may also require

pip install pybind11
pip install pyomo

The Python interface can then be used:

python
>>> import highspy
>>> import numpy as np
>>> inf = highspy.kHighsInf
>>> h = highspy.Highs()
>>> h.addVars(2, np.array([-inf, -inf]), np.array([inf, inf]))
>>> h.changeColsCost(2, np.array([0, 1]), np.array([0, 1], dtype=np.double))
>>> num_cons = 2
>>> lower = np.array([2, 0], dtype=np.double)
>>> upper = np.array([inf, inf], dtype=np.double)
>>> num_new_nz = 4
>>> starts = np.array([0, 2])
>>> indices = np.array([0, 1, 0, 1])
>>> values = np.array([-1, 1, 1, 1], dtype=np.double)
>>> h.addRows(num_cons, lower, upper, num_new_nz, starts, indices, values)
>>> h.setOptionValue('log_to_console', True)
<HighsStatus.kOk: 0>
>>> h.run()

Presolving model
2 rows, 2 cols, 4 nonzeros
0 rows, 0 cols, 0 nonzeros
0 rows, 0 cols, 0 nonzeros
Presolve : Reductions: rows 0(-2); columns 0(-2); elements 0(-4) - Reduced to empty
Solving the original LP from the solution after postsolve
Model   status      : Optimal
Objective value     :  1.0000000000e+00
HiGHS run time      :          0.00
<HighsStatus.kOk: 0>
>>> sol = h.getSolution()
>>> print(sol.col_value)
[-1.0, 1.0]

xijunlee/HiGHS