The demand for task scheduling in Internet of Things (IoT)-based edge and cloud computing environments is experiencing exponential growth due to the need to address real-world issues, such as load instability, slow convergence rates, and under-utilization of virtual machine devices. In this paper, a hybrid enhanced optimization method called RFOAOA is designed to solve challenging task scheduling scenarios in edge-cloud computing-based IoT environments. The proposed method leverages the strengths of two powerful search operators, such as Red Fox Optimization (RFO) and Arithmetic Optimization Algorithm (AOA). To evaluate the effectiveness of the proposed method, we conducted experiments on real and synthetic workload traces of NASA Ames iPSC/860 and HPC2N. The comparative analysis demonstrates that the proposed algorithm achieves better performance in terms of Makespan time and energy consumption and outperforms the other state-of-the-art scheduling methods.