A reinforcement-learning-based multi-strategy Harris hawks optimization (RLMHHO) is developed to address the scheduling problem of distributed hybrid flow-shop, with the optimization objectives of minimizing the maximum completion time and delay time. The algorithm uses a grouping chaos initialization strategy to improve the randomness and diversity of the initial search. A four-group eagle management mechanism of exploration, development, balance, and elite is introduced to achieve synergy between global search and local development. A reinforcement learning coordinator based on deep Q-networks dynamically selects the optimal search strategy based on a 14-dimensional state space. Simulation experiments have verified that the proposed algorithm offers better solution quality and stronger search capability for solving this type of scheduling problem.