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This study addresses a distributed assembly permutation flowshop scheduling problem, which is of great significance in practical manufacturing systems. We aim to sequence products and jobs, and assign jobs to the appropriate factory to minimize the total flowtime of products. First, a mathematical model is developed to describe the concerned problems. Then, four meta-heuristics, e.g., artificial bee colony, particle swarm optimization, genetic algorithm, and Jaya algorithm, and their variants are proposed. Three initialization strategies are developed to generate high-quality initial solutions. Four local search operators are designed to improve the performance of the algorithms. Q-learning is embedded to select the premium local search strategy during iterations. Based on 81 large-scale benchmark instances, comprehensive numerical experiments are carried out to evaluate the effectiveness of the proposed algorithms. The experimental results show that the proposed Jaya with Q-learning-based local search has strong competitiveness, and it updates optimal solutions for 51 out of 81 benchmark instances. [ABSTRACT FROM AUTHOR]