A Quantum‐Inspired Entropy‐Preserving Hybrid Metaheuristic for Efficient Workflow Scheduling in Heterogeneous Cloud–Fog Systems

ABSTRACT Cloud–fog computing has emerged as a promising paradigm for supporting latency‐sensitive and large‐scale scientific workflows by integrating edge‐level fog nodes with centralized cloud resources. However, efficient workflow scheduling in heterogeneous cloud–fog environments remains a challenging multiobjective optimization problem because of conflicting objectives, such as execution time, operational cost, and energy consumption, along with high‐dimensional scheduling search spaces. To address these challenges, this paper proposes a Multiobjective Quantum‐Inspired Hybrid Optimization algorithm (MOQIHO) for multiobjective workflow scheduling. The proposed model integrates amplitude‐based probabilistic encoding with a hybrid particle swarm optimization–whale optimization algorithm (PSO–WOA) to improve exploration–exploitation balance during scheduling. Unlike deterministic hybrid metaheuristics, the MOQIHA performs optimization in probabilistic amplitude space, enabling enhanced population diversity and preventing premature convergence. An information‐theoretic entropy analysis is further introduced to explain how the probabilistic representation preserves search diversity and improves convergence stability. The proposed model is evaluated using widely adopted scientific workflows, including Montage, Cybershake, Epigenomics, Sipht, and Inspiral, across multiple workflow scales in a heterogeneous cloud–fog simulation environment. The experimental results demonstrate significant improvements over conventional scheduling approaches, including RR, ACO, PSO, the WOA, and the hybrid PSO–WOA (HPWOA). In particular, the proposed model achieves substantial reductions in workflow makespan, execution cost, and energy consumption while maintaining stable performance across varying workflow sizes. The results confirm that integrating quantum‐inspired probabilistic representation with hybrid metaheuristic optimization provides an effective and scalable solution for intelligent workflow orchestration in next‐generation distributed cloud–fog infrastructures. The proposed method follows the principles of quantum‐inspired evolutionary algorithms and does not require quantum hardware.