A Hybrid Genetic Algorithm for the Distributed Permutation Flowshop Scheduling Problem with Sequence-Dependent Setup Times

The distributed permutation flowshop scheduling problem (DPFSP) has attracted many researchers' attention in recent years. In this paper, we extend the DPFSP by considering the sequence-dependent setup time (SDST). A new hybrid genetic algorithm (HGA) for the DPFSP with the SDST (SDST/DPFSP) is presented to minimize the maximum of the completion time. At first, a new population initialization is proposed. And then, the newly-designed operators are described in details, and we also introduce the mutation rate and the crossover rate to balance the mutation operator and the crossover operator. To further improve the obtained solution, a new local search method is developed. At last, the orthogonal experimental design is applied to adjust the parameters in the HGA, and a comprehensive computational campaign based on the 135 instances demonstrates the effectiveness of the proposed HGA for the SDST/DPFSP.