A collaborative iterated greedy algorithm with reinforcement learning for energy-aware distributed blocking flow-shop scheduling

Energy-aware scheduling has attracted increasing attention mainly due to economic benefits as well as reducing the carbon footprint at companies. In this paper, an energy-aware scheduling problem in a distributed blocking flow-shop with sequence-dependent setup times is investigated to minimize both makespan and total energy consumption. A mixed-integer linear programming model is constructed and a cooperative iterated greedy algorithm based on Q-learning (CIG) is proposed. In the CIG, a top-level Q-learning is focused on enhancing the utilization ratio of machines to minimize makespan by finding a scheduling policy from four sequence-related operations. A bottom-level Q-learning is centered on improving energy efficiency to reduce total energy consumption by learning the optimal speed governing policy from four speed-related operations. According to the structure characteristics of solutions, several properties are explored to design an energy-saving strategy and acceleration strategy. The experimental results and statistical analysis prove that the CIG is superior to the state-of-the-art competitors with improvement percentages of 20.16 % over 2880 instances from the well-known benchmark set in the literature.