Scheduling is an NP-hard problem, and metaheuristic algorithms are often used to find approximate solutions within a feasible time frame. Existing metaheuristic algorithms, such as ACO, PSO, and BOA address this problem either in cloud or fog environments. However, when these environments are combined into a hybrid cloud-fog environment, these algorithms become inefficient due to inadequate handling of local and global search strategies. This inefficiency leads to suboptimal scheduling across the cloud-fog environment because the algorithms fail to adapt effectively to the combined challenges of both environments. In our proposed Improved Butterfly Optimization Algorithm (IBOA), we enhance adaptability by dynamically updating the computation cost, communication cost, and total cost, effectively balancing both local and global search strategies. This dynamic adaptation allows the algorithm to select the best resources for executing tasks in both cloud and fog environments. We implemented our proposed approach in the CloudSim simulator and compared it with traditional algorithms such as ACO, PSO, and BOA. The results demonstrate that IBOA offers significant reductions in total cost, communication cost, and computation cost by 19.65%, 18.28%, and 25.41%, respectively, making it a promising solution for real-world cloud-fog computing (CFC) applications.

Cloud fog computing is a new paradigm that combines cloud computing and fog computing to boost resource efficiency and distributed system performance. Task scheduling is crucial in cloud fog computing because it decides the way computer resources are divided up across tasks. Our study suggests that the Shark Search Krill Herd Optimization (SSKHOA) method be incorporated into cloud fog computing's task scheduling. To enhance both the global and local search capabilities of the optimization process, the SSKHOA algorithm combines the shark search algorithm and the krill herd algorithm. It quickly explores the solution space and finds near-optimal work schedules by modelling the swarm intelligence of krill herds and the predator-prey behavior of sharks. In order to test the efficacy of the SSKHOA algorithm, we created a synthetic cloud fog environment and performed some tests. Traditional task scheduling techniques like LTRA, DRL, and DAPSO were used to evaluate the findings. The experimental results demonstrate that the SSKHOA outperformed the baseline algorithms in terms of task success rate increased 34%, reduced the execution time by 36%, and reduced makespan time by 54% respectively.