Massively Parallel GPU Implementation of the TLBO Algorithm for Solving High-Dimensional Systems of Nonlinear Equations

This work outlines an efficient GPU-based parallel version of the teaching–learning-based optimization (TLBO) algorithm, a simple population-based metaheuristic that does not require adjustment of any algorithm-specific parameter. The proposed parallelization of the TLBO algorithm is illustrated by its application to solving large-scale nonlinear equation systems, a class of problems that is difficult to solve using traditional numerical techniques and is of significant importance in areas such as science, engineering, and economics. The GPU-accelerated TLBO algorithm was evaluated on a GeForce RTX 3090 GPU with 24 GB GDDR6X VRAM and 10 496 CUDA cores using a collection of hard and scalable nonlinear equation system problems ranging in dimension from 500 to 2000. The results obtained with the problems considered in this study showed accelerations between 43.53 \(\times \) and 144.48 \(\times \) , with an average acceleration of 86.53 \(\times \) , thus showing the efficiency of the proposed GPU parallelization of the TLBO algorithm.