Performance Analysis of the Simplex Method on OpenCL Hardware Accelerators

This work proposes an energy-efficient hardware accelerated Linear Programming (LP) solver. The system is based on the Simplex Algorithm for solving LP problems and is operable on Field Programmable Gate Arrays (FPGAs), Graphic Processing Units (GPUs), and Multi-Core Computer Processors (CPUs). The system is targeted towards the dense problems in radiotherapy applications as they represent a challenge to modern solvers. Performance benchmarking reveals speed ups relative to a sequential implementation that approach 2 and 10 on a CPU and GPU for random, dense problems. The FPGA exhibits unity speed up but proved to be the most efficient in terms of Simplex iterations processed per unit energy with an efficiency 5 times greater than the CPU. This is a notable speed improvement and power saving in comparison with current technology for solving dense problems as the GPU code can solve problems with speeds up to 50 times faster than a sparse solver.