An Efficient GPU Parallelization of the Jaya Optimization Algorithm and Its Application for Solving Large Systems of Nonlinear Equations

This paper presents a new GPU-accelerated parallel version of Jaya, a simple and efficient population-based optimization algorithm that has attracted increasing interest in different areas of science and engineering. Jaya has recently been demonstrated to be relatively effective at solving nonlinear equation systems, a class of complex, challenging problems that are hard to solve using conventional numerical methods, especially as the size of the systems increases. This class of problems was chosen to illustrate the application of the proposed GPU-based parallel Jaya algorithm and its efficiency in solving difficult large-scale problems. The GPU parallelization of Jaya was implemented and tested on a GeForce RTX 3090 GPU with 10 496 CUDA cores and 24 GB VRAM, using a set of scalable nonlinear equation system problems with dimensions ranging from 500 to 2000. When compared with the Jaya sequential algorithm, the parallel implementation provides significant acceleration, with average speedup factors between 70.4 and 182.9 in computing time for the set of problems considered. This result highlights the efficiency of the proposed GPU-based massively parallel version of Jaya.