Parallelism

Generally

HiGHS currently has limited opportunities for exploiting parallel computing. When using a CPU, these are currently restricted to the dual simplex solver for LP, the factorisation-based interior point solver, and the MIP solver. Details of these and future plans are set out below. HiGHS has an implementation of a first order method (PDLP) for solving LPs that can exploit the availability of a GPU.

By default, when running in parallel, HiGHS will use half the available threads on a machine. This number can be modified by setting the value of the threads option.

Dual simplex

By default, the HiGHS dual simplex solver runs in serial. However, it has a variant allowing concurrent processing. This variant is used when the parallel option is set "on", by specifying --parallel when running the executable via the command line, or by setting it via a library call in an application.

The concurrency used will be the value of simplex_max_concurrency. If this is fewer than the number of threads available, parallel performance may be less than anticipated.

The speed-up achieved using the dual simplex solver is normally bounded by the number of memory channels in the architecture, and typically less than the values achieved by Huangfu and Hall. This is because enhancements to the serial dual simplex solver in recent years have not been propagated to the parallel solver.

Unless an LP has significantly more variables than constraints, the parallel dual simplex solver is unlikely to be worth using.

MIP

The only parallel computation currently implemented in the MIP solver occurs when performing symmetry detection on the model, when querying clique tables, and when the interior point solver is used to compute the analytic centre. This parallelism is always advantageous, so is performed regardless of the value of the parallel option.

IPM

The interior point solver HiPO uses multiple threads to process the elimination tree during the multifrontal factorisation (tree level) and to perform the dense factorisation of the frontal matrices (node level).

If the parallel option is set "on", the level of parallelism is determined by the hipo_parallel_type option, which can be "tree" for tree level only, "node" for node level only, or "both" for both levels.

If the parallel option is set "choose", the solver selects which level to use based on a heuristic. When the parallel option is set "choose" or "off", the value of the hipo_parallel_type option is ignored.

Future plans

The MIP solver has been written with parallel tree search in mind. Some work has started (Feb 2025), and it is hoped that a prototype solver will be available during 2025.

Multi-threading within HiPO will be extended to other phases of the solver, including the solve phase of the factorisation and the process of assemblying the matrices.

First-order solvers for LP are still very much in their infancy, and are not robust. Hence the availability of a PDLP solver for LP is unlikely to be used to enhance other solvers in HiGHS in the short or medium term.