A GPU-Based Parallel Implementation of the GWO Algorithm: Application to the Solution of Large-Scale Nonlinear Equation Systems

Population-based computational intelligence algorithms are natural candidates for parallelization and have been utilized to solve a variety of difficult and complex real-world problems. The gray wolf optimizer (GWO) is one of these algorithms. It is a metaheuristic that simulates the leadership hierarchy and hunting mechanism of gray wolves in the wild and has been used successfully to solve several hard optimization problems. However, the study of its applicability to the solution of nonlinear equation systems, which is arguably the most difficult class of numerical problems, is still quite incipient and needs to be better accessed and verified, particularly in the case of large-scale systems of nonlinear equations, which have not been considered until now and whose resolution difficulty increases with the number of equations they contain. This paper presents a new and efficient GPU-based massively parallel implementation of the gray wolf optimizer algorithm for solving large-scale optimization problems. The proposed parallelization of the GWO algorithm is illustrated by its application to solving large systems of nonlinear equations, a class of problems that appear and have great importance in different fields of pure and applied sciences and engineering. The GPU-accelerated version of GWO was implemented in Julia and tested on a GeForce RTX 3090 GPU with 24 GB GDDR6X VRAM and 10 496 CUDA cores using a set of hard, scalable systems of nonlinear equations with dimensions ranging from 500 to 2000. The obtained results, with average speedups between 69.91× and 241.54× , show the efficiency of the proposed GPU-based acceleration of the GWO algorithm.