Nature-Inspired Adaptive Evolutionary Swarm Optimization for Energy-Efficient Computational Mathematics in High-Performance Computing Systems

High-Performance Computing (HPC) systems play a critical role in enabling complex simulations, large-scale data analysis, and scientific research. However, the significant energy demands of these systems raise concerns around operational sustainability and long-term cost-efficiency. Existing natureinspired algorithms—such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO)-have shown promise in task scheduling but often fall short due to issues like high computational overhead, premature convergence, and limited responsiveness to real-time energy dynamics. In response to these limitations, this study presents the Adaptive Evolutionary Swarm Optimization (AESO) algorithm, which integrates adaptive mutation control with swarm-based task clustering to improve energy-aware scheduling in HPC environments. Unlike conventional methods, AESO dynamically adjusts its behavior based on current workload and energy trends, aiming to strike a balance between energy consumption, execution speed, and computational accuracy. Evaluation using the Google Cloud Workload dataset indicates that AESO reduces execution time by 16.9% (118s vs. 142s in GA) and energy consumption by 31.4% (1680 J vs. 2450 J in GA), while achieving a scheduling efficiency of 94% and maintaining a high accuracy of 99.85%. These outcomes suggest that the pursuit of energy efficiency need not come at the cost of performance. Looking ahead, future work will explore integrating AI-driven predictive models and reinforcement learning to further enhance AESO's adaptability within evolving, cloud-based, and distributed HPC systems.