<p>The fog-cloud computing environment represents an emerging paradigm that combines the computational capabilities of the cloud and fog layers to enhance the Internet of Things (IoT) application performance and scalability. In this environment, heterogeneous scheduling and offloading task workflow are crucial for improving the performance and resource management in terms of efficiently distributing workload within the cloud and fog layers. This paper aims to simultaneously minimize the key performance metrics, such as execution time, energy, and cost of the jobs/tasks on the computing machines. In this paper, we propose a hybrid algorithm that integrates Particle Swarm Optimization (PSO) with the JAYA Algorithm, especially to handle the scheduling challenges for such an environment. The workflow model is represented as a Directed Acyclic Graph (DAG), considering the spatial distribution of edge resources and the dynamic deployment of characteristics of serverless computing functions. The proposed hybrid PSOJAYA algorithm is extensively evaluated through simulations and compared with three well-known metaheuristic algorithms: JAYA, PSO, and ACO. The simulation results demonstrate&#xa0;that the PSOJAYA algorithm significantly improves workflow completion time, energy consumption, and cost while maintaining a balanced trade-off among objectives. These outcomes highlight its effectiveness in optimizing workflow execution within complex fog-cloud computing environments.</p>