  The simplex algorithm has been successfully used for many years in solving
linear programming (LP) problems. Due to the intensive computations required
(especially for the solution of large LP problems), parallel approaches have
also extensively been studied. The computational power provided by the modern
GPUs as well as the rapid development of multicore CPU systems have led OpenMP
and CUDA programming models to the top preferences during the last years.
However, the desired efficient collaboration between CPU and GPU through the
combined use of the above programming models is still considered a hard
research problem. In the above context, we demonstrate here an excessively
efficient implementation of standard simplex, targeting to the best possible
exploitation of the concurrent use of all the computing resources, on a
multicore platform with multiple CUDA-enabled GPUs. More concretely, we present
a novel hybrid collaboration scheme which is based on the concurrent execution
of suitably spread CPU-assigned (via multithreading) and GPU-offloaded
computations. The experimental results extracted through the cooperative use of
OpenMP and CUDA over a notably powerful modern hybrid platform (consisting of
32 cores and two high-spec GPUs, Titan Rtx and Rtx 2080Ti) highlight that the
performance of the presented here hybrid GPU/CPU collaboration scheme is
clearly superior to the GPU-only implementation under almost all conditions.
The corresponding measurements validate the value of using all resources
concurrently, even in the case of a multi-GPU configuration platform.
Furthermore, the given implementations are completely comparable (and slightly
superior in most cases) to other related attempts in the bibliography, and
clearly superior to the native CPU-implementation with 32 cores.
