GPU Acceleration of the GWO Optimization Algorithm: Application to the Solution of Large Nonlinear Equation Systems

Abstract

Large-scale optimization problems present formidable challenges in various scientific and engineering domains. To address these challenges, population-based computational intelligence algorithms have emerged as potent tools capable of being parallelized. Among these algorithms, the gray wolf optimizer (GWO) stands out for its ability to simulate the hierarchical structure and hunting behaviors of gray wolves in the wild and has been used successfully to solve several hard optimization problems. However, the study of its applicability for solving nonlinear equation systems (NESs), which is arguably one of the most difficult classes of numerical problems, poses significant challenges in terms of computational efficiency and scalability. To address this gap, this article introduces a novel GPU-based parallel implementation of the GWO algorithm aimed at addressing the particular challenges of optimizing large-scale NESs by employing the substantial parallel processing capabilities of GPUs. The GPU-based version of GWO was developed using the Julia programming language, and its performance was evaluated with two GPUs of professional grade: the NVIDIA Tesla V100 SXM2 with 32 GB VRAM and the NVIDIA A100 PCIe with 80 GB VRAM. The testing involved a series of complex, scalable NESs with dimensions ranging from 500 to 4000. The results obtained demonstrate average speedups ranging from 154.9$\times$ to 250.2$\times$ for the V100 GPU and 204.0$\times$ to 923.9$\times$ for the A100. These results highlight the effectiveness of the proposed GPU-based acceleration technique in reducing computation times.