Multi-subpopulation quantum particle swarm optimization with dual chaotic encoding for flexible job-shop scheduling problem

The flexible job-shop scheduling problem (FJSP) is a fundamental challenge in modern manufacturing and artificial intelligence (AI) due to its NP-hard complexity. Efficiently solving the FJSP requires balancing solution quality, computational efficiency, and convergence speed, but existing optimization algorithms often suffer from premature convergence, poor diversity preservation, and inefficient exploration. To address these limitations, this study proposes a multi-subpopulation quantum particle swarm optimization (MQPSO) algorithm with dual chaotic encoding for the FJSP. MQPSO incorporates a hierarchical population structure to enhance search diversity and quantum-inspired position updates for improved exploration. Furthermore, it integrates a random perturbation strategy to prevent search stagnation, a dynamic parameter adaptation mechanism to balance exploration and exploitation, along with elite competition and migration operations to maintain solution quality and prevent subpopulation isolation. Additionally, a novel dual chaotic encoding scheme is designed to dynamically select between two complementary chaotic maps, ensuring well-distributed population initialization, mitigating premature convergence, and improving overall search efficiency. Extensive experiments on Kacem and Brandimarte benchmark datasets, along with an industrial case study, validate the effectiveness of MQPSO. The results demonstrate that MQPSO consistently outperforms the competing algorithms, achieving higher solution quality, faster convergence, and greater computational efficiency. These findings establish MQPSO as a robust and scalable solution for the FJSP, with broad implications for intelligent manufacturing and AI-driven optimization applications.