The Energy-Efficient Hybrid Flow Shop Scheduling Problem poses a significant multi-objective optimization challenge, necessitating the simultaneous minimization of conflicting objectives: Total Tardiness, Total Energy Cost, and Carbon Trading Cost. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is a classic algorithm in the field of multi-objective optimization. However, this algorithm frequently lacks the adaptive capability required to navigate high-dimensional solution spaces, often trapping the search in local optima, particularly when constrained by practical energy states of heterogeneous machines. To address these complexities, this study proposes a hybrid algorithm, named QGN, integrating Q-learning, the Grey Wolf Optimizer (GWO), and the NSGA-II. Specifically, QGN algorithm integrates NSGA-II for robust diversity maintenance with GWO for high-precision intensification. Unlike static hybrid methods, QGN employs a Q-learning agent as an adaptive controller to dynamically balance global exploration and local refinement, providing a theoretically grounded response to the rugged search landscape created by machine heterogeneity. Comprehensive experimental validation across diverse production scenarios confirms that QGN significantly outperforms baselines, including NSGA-II, Jaya, and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), as well as the state-of-the-art Q-learning- and GVNS-driven NSGA-II (QVNS) algorithm, in terms of both convergence and diversity. The results indicate that the proposed algorithm yields superior solution dominance, generates a substantially larger set of non-dominated solutions, and maintains a more uniform distribution along the Pareto front.
Liu et al. (Fri,) studied this question.