GPU-Based Acceleration of Metaphor-less Algorithms and Their Application for Solving Large Systems of Nonlinear Equations

Abstract

Traditional population-based metaheuristic algorithms are effective in solving complex real-world problems but require careful strategy selection and parameter tuning. Parameter-less 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. In this paper, a systematic review and detailed description of metaphor-less optimization algorithms is made, including the Jaya algorithm, the main Jaya variants for continuous optimization problems, with a focus on the Enhanced Jaya (EJAYA) algorithm, the three Rao algorithms, the best-worst-play (BWP) algorithm, and the very recent max-min-greedy-interaction (MaGI) algorithm. This paper also discusses a few previous parallelizations of the Jaya optimization algorithm, as well as recent GPU-based massively parallel implementations of the Jaya, Enhanced Jaya (EJAYA), Rao, and BWP algorithms developed by the authors. In addition, a novel GPU-accelerated version of the MaGI algorithm is proposed. The GPU-accelerated versions of the metaphor-less algorithms developed by the authors were implemented using the Julia programming language and tested primarily on GeForce RTX 3090 and NVIDIA A100 GPUs, as well as on Tesla V100S and Tesla T4 GPUs, using a set of difficult, large-scale nonlinear equation system problems. The computational experiments carried out produced quite significant speedups, which highlights the efficiency of the GPU-based versions of the metaphor-less algorithms developed for solving large-scale systems of nonlinear equations.