Driven by the pressing needs in coordinating and synchronizing multi-plant facilities for efficient production and manufacturing, distributed assembly permutation flowshop scheduling problem (DAPFSP) has been becoming the focus of concern of evolutionary computing and operations research, which is a typical NP-hard combinatorial optimization problem. In this paper, we propose a generalized version of DAPFSP, labeled here as multi-distributed assembly permutation flowshop problem (M- DAPFSP). In the M-DAPFSP, multiple assembly factories exist rather than only one assembly factory in the conventional DAPFSP, meanwhile no-wait constraint exists in the processing stage. To solve the aforementioned M-DAPFSP, we propose hybrid iterated local search with simulated annealing (ILS-SA) for the M-DAPFSP. Finally, simulation results based on 27 large-scale benchmark problems show that our proposed ILS-SA can effectively solve M-DAPFSP problems.