Virtualized Fog-Cloud Computing (VFCC) has emerged as a promising computing model in both research and industry. Its inherent characteristics, such as real-time service provisioning, resource heterogeneity, flexibility, and scalable computational resources, present new opportunities and challenges in the scheduling of computational workflows. Efficient workflow scheduling is crucial in optimizing resource utilization and improving service delivery in VFCC environments. In this paper, we first present a bi-objective optimization model for the workflow scheduling problem in VFCC systems with the aim of minimizing both the system’s makespan and energy consumption. We then propose an efficient list-based method to solve the model. The proposed method consists of two distinct phases. In the first phase, we employ the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to determine task priorities, establishing the task execution sequence. To ensure both convergence speed and diversity, we implement an intelligent semi-greedy approach when generating the initial population. In the second phase, we introduce an energy and makespan-aware heuristic algorithm to efficiently allocate virtual machines to the prioritized tasks. To evaluate the effectiveness of our proposed method, we conduct extensive experiments using both synthetic and real datasets, including the Epigenomics, Montage, and LIGO graphs. We compare the proposed method with the Heterogeneous Earliest Finish Time (HEFT) and Green-HEFT algorithms in terms of makespan and energy consumption, respectively. Furthermore, we evaluate our proposed method by comparing it to two other algorithms, Multi-objective HEFT (MOHEFT) and Multi-objective ACO (MOACO), using various quality indicators such as generation distance (GD), inverse generation distance (IGD), goal programming approach (GPA), and Hyper volume (HV). The simulation results demonstrate that our method effectively reduces the makespan by 6.38% to 51.19% and energy consumption by 3.52% to 16.49%. Moreover, on average, our method outperforms the other algorithms with an improvement of 2.3%, 5.7%, 9.8%, and 9.34% for the GD, IGD, GPA, and HV metrics, respectively.
