FPGA Implementation of Floating Point Linear Programming

Linear programming is often applied in real-life situations and computer science, particularly in various resource allocation problems, such as optimizing the production of machines that produce different-priced products within the same unit of time or integrated circuit (IC) layout optimization. The Simplex algorithm is the most commonly used core algorithm, known for its robustness and high scalability. However, since linear programming models usually store variables in floating-point format to maintain accuracy, processing them on an FPGA platform is difficult. This paper proposes a logic circuit design for the Simplex algorithm model that uses the IEEE-754 single-precision format. The proposed method significantly accelerates the solving time by taking advantage of the high-speed computation of FPGA. Since FPGA IP Cores are not used, these algorithms can be implemented on any FPGA platform.