Parallel GPU-Acceleration of Metaphorless Optimization Algorithms: Application for Solving Large-Scale Nonlinear Equation Systems

Abstract

Traditional population-based metaheuristic algorithms are effective in solving complex real-world problems but require careful strategy selection and parameter tuning. Metaphorless population-based optimization algorithms have gained importance due to their simplicity and efficiency. However, research on their applicability for solving large systems of nonlinear equations is still incipient. This paper presents a review and detailed description of the main metaphorless optimization algorithms, including the Jaya and enhanced Jaya (EJAYA) algorithms, the three Rao algorithms, the best-worst-play (BWP) algorithm, and the new max–min greedy interaction (MaGI) algorithm. This article presents improved GPU-based massively parallel versions of these algorithms using a more efficient parallelization strategy. In particular, a novel GPU-accelerated implementation of the MaGI algorithm is proposed. The GPU-accelerated versions of the metaphorless algorithms developed were implemented using the Julia programming language. Both high-end professional-grade GPUs and a powerful consumer-oriented GPU were used for testing, along with a set of hard, large-scale nonlinear equation system problems to gauge the speedup gains from the parallelizations. The computational experiments produced substantial speedup gains, ranging from 33.9× to 561.8×, depending on the test parameters and the GPU used for testing. This highlights the efficiency of the proposed GPU-accelerated versions of the metaphorless algorithms considered.