DAFSP with limited assembly buffers: A deadlock-free coding-decoding paradigm and hybrid cooperative co-evolutionary approach

Most prior studies on the Distributed Assembly Flowshop Scheduling Problem (DAFSP) presume infinite buffer capacity for assembly machines. However, in practical DAFSP, assembly buffers are often limited, potentially leading to a deadlock where buffers are full of jobs yet none of them can be assembled into a product. Since the deadlock in DAFSP is caused by incorrect jobs’ sequences in assembly buffers, we formulate a Petri net to model this entry process for the first time. Based on this Petri net model and improved Banker algorithm (IBA), we develop a polynomial-complexity algorithm IDAM to ensure the deadlock-free decoding of a DAFSP solution, which is coded by job and factory permutations. The makespan of such a solution is calculated backward to maintain its deadlock-free property. Furthermore, according to the proposed coding-decoding paradigm for deadlock-free solutions, we propose a hybrid cooperative co-evolution (HCCE) algorithm for DAFSP to minimize the makespan. Notably, our HCCE algorithm incorporates an elite archive (EAR) and two subpopulations. It employs problem-specific operators for heuristic initialization and global-search procedures, and four local-search operators are successively applied to every individual in the EAR. Finally, comprehensive experiments demonstrate the effectiveness and superiority of the proposed HCCE algorithm.