A fog-cloud system facilitates the integration of end devices with computational resources, including fog nodes and cloud services, within the Internet of Things (IoT) systems. The efficiency of these systems is affected by various factors, such as computational power, storage delays, energy usage, and associated expenses, due to their inherent heterogeneity and diversity of components. This study aims to tackle the challenge of task scheduling in fog-cloud settings by formulating a detailed model that incorporates multiple constraints. Metaheuristic methods were employed to optimize the scheduling of data processing tasks and address the issue as a multi-objective optimization challenge. The proposed fog-cloud model is validated through simulated experiments for its practical applicability. The findings also demonstrated that metaheuristic approaches significantly outperformed conventional scheduling methods like the Round-Robin strategy in effectively addressing task scheduling problems.