Abstract Energy efficiency in fog-cloud IoT task scheduling has become a pressing research challenge as the number of connected devices escalates toward 75 billion. Existing metaheuristic schedulers-including the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and the vanilla Grey Wolf Optimizer (GWO)-are single-objective or weakly multi-objective and fail to jointly optimize energy consumption, deadline satisfaction, and cost in heterogeneous fog-cloud networks. In this paper, we propose HGWO-DRL (Hybrid Grey Wolf Optimizer with Deep Reinforcement Learning), a novel energy-aware multi-objective task scheduling framework. The GWO component is enhanced with: (i) a nonlinear control parameter decay that sharpens the exploration-exploitation balance, and (ii) a Lévy flight perturbation that prevents stagnation in local optima. A lightweight tabular Deep RL (DRL) agent fine-tunes the top-ranked GWO
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