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<p>To enhance the convergence speed and solution precision of the firefly algorithm (FA), this paper proposes a multi-population quantum firefly algorithm with an Ergodic Correction Mechanism (MQFA-ecm). Unlike traditional quantum-inspired metaheuristics, MQFA-ecm integrates a self-adaptive multi-population strategy managed by a quantum revolving gate mechanism, which dynamically adjusts qubit probability amplitudes to finely regulate the exploration–exploitation trade-off. To mitigate premature convergence, an ergodic correction mechanism based on Holt’s linear exponential smoothing is introduced to forecast the trajectory of potential global optima, guiding the search toward under-explored regions during stagnation. Comprehensive evaluations on 20 benchmark functions and the IEEE CEC 2022 test suite demonstrate the algorithm’s robustness. Nonparametric statistical tests, including Wilcoxon signed-rank and Friedman tests, confirm that MQFA-ecm achieves statistically superior optimization accuracy and convergence speed compared to nine state-of-the-art algorithms. These results underscore the effectiveness of MQFA-ecm in solving complex, high-dimensional numerical optimization tasks.</p>

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Multi-population quantum firefly algorithm via ergodic correction mechanism for continuous optimization problems

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Yufan Wang,
  • Jinliang Li,
  • Jiaxin Li,
  • Xiaowei Fu

摘要

To enhance the convergence speed and solution precision of the firefly algorithm (FA), this paper proposes a multi-population quantum firefly algorithm with an Ergodic Correction Mechanism (MQFA-ecm). Unlike traditional quantum-inspired metaheuristics, MQFA-ecm integrates a self-adaptive multi-population strategy managed by a quantum revolving gate mechanism, which dynamically adjusts qubit probability amplitudes to finely regulate the exploration–exploitation trade-off. To mitigate premature convergence, an ergodic correction mechanism based on Holt’s linear exponential smoothing is introduced to forecast the trajectory of potential global optima, guiding the search toward under-explored regions during stagnation. Comprehensive evaluations on 20 benchmark functions and the IEEE CEC 2022 test suite demonstrate the algorithm’s robustness. Nonparametric statistical tests, including Wilcoxon signed-rank and Friedman tests, confirm that MQFA-ecm achieves statistically superior optimization accuracy and convergence speed compared to nine state-of-the-art algorithms. These results underscore the effectiveness of MQFA-ecm in solving complex, high-dimensional numerical optimization tasks.