Dual-self-learning co-evolutionary algorithm for energy-efficient flexible job shop scheduling problem with processing- transportation composite robots.

The processing-transportation composite robots, with their dual functions of processing and transportation, as well as comprehensive robot-machine interactions, have been widely and efficiently applied in the manufacturing industry, leading to a continuous increase in energy consumption. Hence, this work focuses on investigating robot-machine integrated energy-efficient scheduling in flexible job shop environments. To address the new problem, an innovative mixed-integer linear programming model and a novel dual-self-learning co-evolutionary algorithm are proposed, aimed at minimizing the total energy consumption and makespan. In the proposed algorithm, a three-dimensional vector is first used to comprehensively express the solution, and then a greedy decoding strategy is designed to reduce the idle time and energy consumption simultaneously. A hybrid initialization method with adaptive random selection and chaos mapping is developed to ensure the diversity and high quality of the initial solutions. A dual-self-learning mechanism, including a self-learning evolutionary mechanism and a self-learning cooperation mechanism, is designed to select suitable evolutionary operators and enhance interactions between populations, respectively. Finally, multiple sets of experiments are conducted to demonstrate the effectiveness of the proposed mathematical model, improved components and algorithm through numerical, statistical, and differential analyses.