An effective memetic algorithm for the distributed flowshop scheduling problem with an assemble machine

The distributed flowshop has been a hot topic in research in recent years. This paper considers a distributed permutation flowshop scheduling problem with an assemble machine, so-called the distributed assembly permutation flowshop scheduling problem (DAPFSP), with total tardiness criterion. We propose an effective memetic algorithm (EMA). Firstly, a constructive heuristic combining the well-known earliest due date rule and largest processing time rule is presented for producing a seed sequence. On this basis, an effective initialisation method is used to generate an initial population with a high level of quality and diversity. The EMA uses a new structure of a small iteration nested within a large iteration. Moreover, an improved crossover and mutation expand the solution space in a good direction. According to different operation situations and objects, we design four targeted and flexible local search methods. We evaluate the strategies of the EMA, compare and analyse it with seven efficient algorithms based on the 810 benchmark instances. The experimental results confirm the effectiveness and efficiency of the proposed EMA.