A knowledge-driven memetic algorithm for distributed green flexible job shop scheduling considering the endurance of machines

Flexible job shop scheduling (FJSP) stands as one of the most pivotal scheduling problems, attracting considerable research efforts aimed at discovering improved solutions. The distributed variant of FJSP, which extends the problem's scope, has garnered substantial interest among scholars. Recognizing the inherent limitation in machine endurance and the inevitable degradation with accumulating workloads, the significance of preventive maintenance in enhancing machine reliability is emphasized and ensuring process control. This study endeavors to concurrently optimize three key metrics: makespan, total energy consumption, and maintenance cost. To this end, a knowledge-driven memetic algorithm is tailored specifically to the problem's characteristics. Our approach commences with a hybrid initialization incorporating eight strategic approaches, crafted to address the factory assignment, operation sequence, and machine selection subproblems, thereby yielding an initial population characterized by high quality and diversity. Subsequently, genetic operators are employed to generate offspring, wherein elite segments from exemplary solutions are selectively inherited during crossover. A two-stage mutation mechanism is introduced to foster the emergence of novel individuals. Finally, three tailored local search strategies are executed, striking a balance between exploration and exploitation.Comprehensive experimental findings emphasize the superior performance of the proposed algorithm in addressing the pertinent problem. The experimental results presented in this paper indicate increases of 20% and 141% in Hypervolume (HV) values and Metric for Diversity (DM) values, respectively, while the reduction in Inverted Generation Distance (IGD) values amounts to 85%, thereby demonstrating the effectiveness of our proposed methodology.