Fog-cloud computing has emerged as a transformative paradigm for managing the growing demands of Internet of Things (IoT) applications, where efficient task scheduling is crucial for optimizing system performance. However, existing task scheduling methods often struggle to balance makespan minimization and energy efficiency in dynamic and resource-constrained fog-cloud environments. Addressing this gap, this paper introduces a novel Task Scheduling algorithm based on a modified Grey Wolf Optimization approach (TS-GWO), tailored specifically for IoT requests in fog-cloud systems. The proposed TS-GWO incorporates innovative operators to enhance exploration and exploitation capabilities, enabling the identification of optimal scheduling solutions. Extensive evaluations using both synthetic and real-world datasets, such as NASA Ames iPSC and HPC2N workloads, demonstrate the superior performance of TS-GWO over established metaheuristic methods. Notably, TS-GWO achieves improvements in makespan by up to 46.15% and reductions in energy consumption by up to 28.57%. These results highlight the potential of TS-GWO to effectively address task scheduling challenges in fog-cloud environments, paving the way for its application in broader optimization tasks. [ABSTRACT FROM AUTHOR]

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