Energy consumption has become a critical issue in modern distributed manufacturing systems due to increasing production complexity and sustainability requirements. This paper addresses the Distributed Flow Shop Scheduling Problem (DFSP) with the objective of minimizing Total Energy Consumption (TEC), which is known to be a challenging NP-hard combinatorial optimization problem.

To tackle this problem, several metaheuristic algorithms are considered, including the Genetic Algorithm (GA), Artificial Bee Colony (ABC), and Iterated Greedy (IG) algorithm, along with their hybrid versions integrating Q-Learning (QL). In the proposed approaches, Q-Learning is embedded within the optimization process to guide the search through the adaptive selection of neighborhood-based operators, such as insertion, swapping, and reconstruction moves. This reinforcement learning mechanism enables the algorithm to dynamically learn the most effective search strategies based on their impact on energy consumption, thus improving the balance between exploration and exploitation.

The performance of the proposed methods is evaluated through extensive computational experiments on different problem instances with varying sizes and configurations. The results demonstrate that integrating Q-Learning significantly enhances the performance of the metaheuristic algorithms, leading to improved solution quality in terms of energy consumption. In particular, the hybrid approaches consistently outperform classical methods, with the HMBOQL-VNS approach achieving the best performance and a dominance rate of 82.1%.

These results highlight the effectiveness of combining reinforcement learning with metaheuristic optimization for developing efficient and sustainable scheduling strategies in distributed manufacturing systems.