An improved memetic algorithm to solve the energy-efficient distributed flexible job shop scheduling problem with transportation and start-stop constraints.

In the current global cooperative production environment, modern industries are confronted with intricate production plans, demanding the adoption of contemporary production scheduling strategies. Within this context, distributed manufacturing has emerged as a prominent trend. Manufacturing enterprises, especially those engaged in activities like automotive mold production and welding, are facing a significant challenge in managing a significant amount of small-scale tasks characterized by short processing times. In this situation, it becomes imperative to consider the transportation time of jobs between machines. This paper simultaneously considers the transportation time of jobs between machines and the start-stop operation of the machines, which is the first time to our knowledge. An improved memetic algorithm (IMA) is proposed to solve the multi-objective distributed flexible job shop scheduling problem (MODFJSP) with the goal of minimizing maximum completion time and energy consumption. Then, a new multi-start simulated annealing algorithm is proposed and integrated into the IMA to improve the exploration ability and diversity of the algorithm. Furthermore, a new multiple-initialization rule is designed to enhance the quality of the initial population. Additionally, four improved variable neighborhood search strategies and two energy-saving strategies are designed to enhance the search ability and reduce energy consumption. To verify the effectiveness of the IMA, we conducted extensive testing and comprehensive evaluation on 20 instances. The results indicate that, when faced with the MODFJSP, the IMA can achieve better solutions in almost all instances, which is of great significance for the improvement of production scheduling in intelligent manufacturing.