GPU/CUDA-Accelerated gradient growth optimizer for efficient complex numerical global optimization

Abstract

Efficiently solving high-dimensional and complex numerical optimization problems remains a critical challenge in high-performance computing. This paper presents the GPU/CUDA-Accelerated Gradient Growth Optimizer (GGO)—a novel parallel metaheuristic algorithm that combines gradient-guided local search with GPU-enabled large-scale parallelism. Building upon the Growth Optimizer (GO), GGO incorporates a dimension-wise gradient-guiding strategy based on central difference approximations, which improves solution precision without requiring differentiable objective functions. To address the computational bottlenecks of high-dimensional problems, a hybrid CUDA-based framework is developed, integrating both fine-grained and coarse-grained parallel strategies to fully exploit GPU resources and minimize memory access latency. Extensive experiments on the CEC2017 and CEC2022 benchmark suites demonstrate the superior performance of GGO in terms of both convergence accuracy and computational speed. Compared to 49 state-of-the-art optimization algorithms, GGO achieves top-ranked results in 67% of test cases and delivers up to 7.8× speedup over its CPU-based counterpart. Statistical analyses using the Wilcoxon signed-rank test further confirm its robustness across 28 out of 29 functions in high-dimensional scenarios. Additionally, in-depth analysis reveals that GGO maintains high scalability and performance even as the problem dimension and population size increase, providing a generalizable solution for high-dimensional global optimization that is well-suited for parallel computing applications in scientific and engineering domains.