HiGHS - Linear optimization software

HiGHS is a high performance serial and parallel solver for large scale sparse linear programming (LP) problems of the form

Maximize c^Tx subject to L <= Ax <= U; l <= x <= u

It is written in C++ with OpenMP directives. It is based on the dual revised simplex method implemented in HSOL, exploiting parallelism using either "parallel minor iterations" (PAMI) or "single iteration parallelism" (SIP). A full technical reference to PAMI and SIP is

Parallelizing the dual revised simplex method Q. Huangfu and J. A. J. Hall Technical Report ERGO-14-011.

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

HSOL was originally written by Qi Huangfu, with features such as presolve, crash and advanced basis start added by Julian Hall and Ivet Galabova.

HSOL has been developed and tested on various linux installations using both the GNU (g++) and Intel (icc) C++ compilers.

Compilation

HiGHS uses CMake as build system. To compile the run you need to setup a build directory and define your build configuration:

mkdir build
cd build
cmake .. [add otional parameters here]

Afterwards you may compile the code wrt the set configuration using your defined build generator, e.g. make:

make

Useful options

Set custom options with -D <option>=<value> during the configuration step (cmake ..):

• OPENMP: turn OpenMP support on or off

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 only read plain text MPS files, and the following command solves the model in ml.mps

highs -f ml.mps

Usage

usage: highs [options] -f fName.mps 

Options:
    -p mode  : use presolve mode. Values:
             : Off On
    -c mode  : use crash mode to mode. Values:
             : Off LTSSF LTSSF1 LTSSF2 LTSSF3 LTSSF4 LTSSF5 LTSSF6 LTSSF7
    -e edWt  : set edge weight to edWt. Values:
             : Dan Dvx DSE DSE0 DSE1
    -s       : use option sip
    -m [cut] : use pami. Cutoff optional double value.
    -t fName : use pami with partition file fName
    -d       : debug mode on

Run-time options -p and -s direct HiGHS to use PAMI or SIP.

When compiled with the OpenMP directives invoked, the number of threads used at run time is the value of the environment variable OMP_NUM_THREADS. For example, to use HiGHS with PAMI and eight threads to solve ml.mps execute

export OMP_NUM_THREADS=8
highs -m -f ml.mps

If OMP_NUM_THREADS is not set, either because it has not been set or due to executing the command

unset OMP_NUM_THREADS

then all available threads will be used.

Observations

When compiled without the OpenMP directives, or if run with OMP_NUM_THREADS=1, HiGHS is serial. The -sip run-time option will not affect performance. The -pami run-time option will cause HiGHS to use serial minor iterations and, although this could lead to better performance on some problems, performance will typically be diminished.

When compiled with the OpenMP directives and OMP_NUM_THREADS>1 or unset, HiGHS will use multiple threads if the -pami or -sip run-time option is specified. If OMP_NUM_THREADS is unset, HiGHS will try to use all available threads so performance may be very slow. Although the best value will be problem and architecture dependent, OMP_NUM_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, with the -pami option usually faster than the -sip option.