An offline-online collaborative optimization framework for the energy-efficient distributed hybrid flow shop scheduling problem with blocking constraints in electric anode carbon rod manufacturing system

The scheduling problem in the assembly workshop of carbon anodes for aluminum production is investigated within the distributed green manufacturing context. This scheduling problem is modeled as an Energy-Efficient Distributed Hybrid Flow Shop Scheduling Problem with Blocking Constraints (EEDHFSP-BC), with optimization objectives that include the minimization of both the makespan and the total energy consumption. To address this complex multi-objective optimization problem, an offline-online collaborative optimization framework (QLINSGA-II) integrating Q-Learning and an improved non-dominated sorting genetic algorithm (INSGA-II) is proposed. A two-phase offline-online scheduling strategy is adopted. First, a dedicated encoding scheme is designed according to the problem characteristics, and a hybrid initialization strategy is introduced during the offline learning phase. Meanwhile, three crossover and mutation operators integrating task assignment coordination and processing sequence allocation are developed to enhance global search capability. Second, a high-quality Pareto solution set is generated by INSGA-II, and Q-Learning is employed to learn from this solution set in the offline phase, thereby achieving intelligent guidance of the population evolution direction. Finally, trained agents are utilized in the online phase to dynamically adjust scheduling for newly arriving jobs. After the search process, a state evaluation mechanism is incorporated to dynamically guide the search by assessing the proportion of non-dominated solutions in the population, effectively improving the distribution and convergence of the Pareto solution set. Experimental results demonstrate that QLINSGA-II outperforms existing mainstream multi-objective optimization algorithms in terms of diversity, convergence speed, and solution coverage rate, providing an efficient and reliable solution for green workshop scheduling in the aluminum industry.