Multithreaded and GPU-Based Implementations of a Modified Particle Swarm Optimization Algorithm with Application to Solving Large-Scale Systems of Nonlinear Equations

This paper presents a novel Graphics Processing Unit (GPU) accelerated implementation of a modified Particle Swarm Optimization (PSO) algorithm specifically designed to solve large-scale Systems of Nonlinear Equations (SNEs). The proposed GPU-based parallel version of the PSO algorithm uses the inherent parallelism of modern hardware architectures. Its performance is compared against both sequential and multithreaded Central Processing Unit (CPU) implementations. The primary objective is to evaluate the efficiency and scalability of PSO across different hardware platforms with a focus on solving large-scale SNEs involving thousands of equations and variables. The GPU-parallelized and multithreaded versions of the algorithm were implemented in the Julia programming language. Performance analyses were conducted on an NVIDIA A100 GPU and an AMD EPYC 7643 CPU. The tests utilized a set of challenging, scalable SNEs with dimensions ranging from 1000 to 5000. Results demonstrate that the GPU accelerated modified PSO substantially outperforms its CPU counterparts, achieving substantial speedups and consistently surpassing the highly optimized multithreaded CPU implementation in terms of computation time and scalability as the problem size increases. Therefore, this work evaluates the trade-offs between different hardware platforms and underscores the potential of GPU-based parallelism for accelerating SNE solvers.