Multi-knowledge driven distributed heterogeneous co-evolution for fuzzy distributed assembly flowshop deadlock-free scheduling

The traditional distributed assembly flowshop Scheduling Problem (DAFSP) typically assume unlimited buffer capacity at the assembly stage and deterministic processing times, which deviate from real-world manufacturing environments. In practice, limited assembly buffers may cause system deadlocks when buffers become saturated and no job can proceed, thereby severely disrupting production. Meanwhile, processing times are often subject to uncertainty due to various disturbances. To address these issues, this paper investigates a more realistic variant, namely the fuzzy distributed assembly flowshop deadlock-free scheduling problem (FDAFDSP) with limited buffers. A Petri net–based deadlock detection and recovery mechanism is incorporated to ensure deadlock-free scheduling. Furthermore, fuzzy processing times are modeled, and the existing backward calculation strategy is extended to fuzzy processing-time environments to evaluate fuzzy completion times while preserving feasibility. To efficiently solve the problem, a multi-knowledge driven distributed heterogeneous co-evolutionary algorithm (MK-DHCEA) is proposed by integrating three complementary types of knowledge . Specifically, problem-specific knowledge is embedded through Petri net-based feasibility control and fuzzy performance evaluation; learning-based knowledge is acquired from accumulated search experience through DQN-guided operator selection to guide adaptive local improvement; and population-level evolutionary knowledge is extracted from superior and inferior solutions and shared across subpopulations through an improved discrete Jaya-based global search. In the proposed MK-DHCEA, the population is adaptively divided into exploitation, exploration, and restart subpopulations, which are responsible for local improvement, global exploration, and diversity restoration, respectively. Extensive computational results demonstrate that the proposed algorithm achieves superior performance in both solution quality and robustness compared with existing methods.