An effective discrete monarch butterfly optimization algorithm for distributed blocking flow shop scheduling with an assembly machine

Distributed scheduling with assembly machines has been an attractive research field in sustainable supply chains and multi-factory manufacturing systems. This paper investigates a distributed blocking flow shop scheduling problem with an assembly machine (DABFSP) with the total assembly completion time criterion, and proposes an effective discrete monarch butterfly optimization algorithm (EDMBO). First, a constructive heuristic combining the largest processing time rule and the earliest start assembly rule is provided to find a promising sequence. On this basis, an efficient initialization method is introduced to generate an initial population with high quality and diversity. Afterward, a global search procedure is presented, which integrates four kinds of improved operators and expands the solution space in a good direction. Then, according to different problem-specific characteristics, we present four targeted and flexible variable neighborhood search methods based on the critical job and critical factory to exploit the solution space. Finally, statistically significant numerical experiments are carried out with state-of-the-art optimization methods based on 1710 benchmark instances. The experimental results and detailed analysis demonstrate that the EDMBO is superior to preferred algorithms for addressing the DABFSP.