A two stage learning based knowledge driven evolutionary algorithm for energy efficient distributed hybrid flow shop scheduling problem with heterogeneous factories

With the advancement of industry-driven smart manufacturing, distributed manufacturing systems are evolving toward a high-efficiency, intelligent, and green direction. This transformation is reshaping sustainable production paradigms at the strategic intersection of Industry 4.0 and carbon neutrality initiatives. As global environmental concerns increasingly prioritize sustainable practices, optimizing the scheduling of distributed manufacturing systems has become a key challenge as global environmental issues increasingly emphasize sustainable manufacturing practices. This study deals with the energy-efficient distributed hybrid flow shop scheduling problem with heterogeneous factories (EEDHFSP-HF), a complex multi-objective optimization issue general in contemporary manufacturing settings. The main objectives are to minimize the makespan and the total electricity cost (TEC) while combining Time-of-Use (TOU) strategies to optimize energy consumption. In response to this challenge, we introduce a two stage learning based knowledge-driven evolutionary algorithm (TLKEA). TLKEA integrates Q-learning with evolutionary strategies to explore and exploit the solution space. TLKEA is designed with an adaptive search mechanism to navigate the complex, time-varying cost landscape defined by TOU tariffs, allowing it to learn and select suitable search actions, thereby enhancing scheduling efficiency. A key feature of our approach is its two-stage strategy, which effectively balances global exploration and local exploitation, ensuring a diverse and high-quality solution set. Comprehensive computational experiments confirm that TLKEA outperforms state-of-the-art algorithms in producing high-quality solutions, demonstrating its effectiveness in enhancing energy efficiency and scheduling optimization. This study significantly contributes to the field by offering a robust and adaptive framework for optimizing production schedules in distributed manufacturing systems while promoting sustainable energy practices and enhancing scheduling efficiency.