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The Internet of Things (IoT) is constantly evolving. The variety of IoT applications has caused new demands to emerge on users' part and competition between computing service providers. On the one hand, an IoT application may exhibit several important criteria, such as deadline and runtime simultaneously, and it is confronted with resource limitations and high energy consumption on the other hand. This has turned to adopting a computing environment and scheduling as a fundamental challenge. To resolve the issue, IoT applications are considered in this paper as a workflow composed of a series of interdependent tasks. The tasks in the same workflow (at the same level) are subject to priorities and deadlines for execution, making the problem far more complex and closer to the real world. In this paper, a hybrid Particle Swarm Optimization and Simulated Annealing algorithm (PSO–SA) is used for prioritizing tasks and improving fitness function. Our proposed method managed the task allocation and optimized energy consumption and makespan at the fog-cloud environment nodes. The simulation results indicated that the PSO–SA enhanced energy and makespan by 5% and 9% respectively on average compared with the baseline algorithm (IKH-EFT). [ABSTRACT FROM AUTHOR]