An artificial immune differential evolution algorithm for scheduling a distributed heterogeneous flexible flowshop

This paper studies a distributed heterogeneous flexible flowshop problem (DHFFP) with sequence-dependent setup and transport times, where each job has a release time and each production stage has multiple unrelated parallel machines. An integer linear programming (ILP) model and a new artificial immune differential evolution (AIDE) algorithm are proposed aiming to minimize the makespan and total tardiness simultaneously. Firstly, the AIDE employs a two-dimensional vector encoding scheme including the information of job permutation and factory allocation for solution representation. In addition, a dynamic decoding scheme is designed to construct a feasible schedule. Secondly, three distributed Nawaz–Enscore–Ham (NEH) based constructive heuristics are presented to provide the initial antibody population. Thirdly, a discrete differential evolution algorithm is introduced to mutate the cloned antibodies. Further, clonal suppression is applied by eliminating the antibodies with lower stimulation values. Simulated annealing (SA) based local search is incorporated with four problem-specific neighborhood structures to enhance the algorithm. Finally, the optimal values of the algorithmic parameters are determined by the orthogonal test. Some numerical experiments of the ILP model on small-scale instances are conducted to show the effectiveness of the proposed AIDE algorithm. The AIDE algorithm is also compared with several existing algorithms for different scale instances. The results demonstrate that the AIDE algorithm generates average relative percentage deviation of 12.51% and 7.99% respectively for small & medium-scale instances and large-scale instances, which is the best-performing among all algorithms.