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<p>This paper introduces the Quantum Geometric Dynamics Optimizer (QGDO), a novel algorithmic framework designed to solve complex continuous nonlinear optimization problems. QGDO establishes a new framework by synergistically integrating principles from three distinct domains: it leverages information geometry to overcome the geometric myopia of traditional search operators, employs quantum-inspired tunneling to escape deep local optima, and uses adaptive topological dynamics to orchestrate the exploration–exploitation balance. This integrated design requires a substantial computational investment, a deliberate trade-off that yields demonstrably superior solution accuracy and positions QGDO as a heavyweight solver for the high-performance computing (HPC) era. Its efficacy is validated through extensive experiments on the IEEE CEC2017, CEC2019, and CEC2022 benchmarks, where it achieved statistically significant performance advantages over 14 competitors. QGDO’s practical utility is further confirmed through its success in solving complex, constrained engineering design problems and in optimizing Echo State Network hyperparameters. The comprehensive results, including a full ablation study and parameter sensitivity analysis, establish QGDO as a powerful and robust optimizer for challenging real-world problems where solution quality is paramount.</p>

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Quantum geometric dynamics optimizer: a novel metaheuristic integrating information geometry and quantum tunneling for global optimization

  • 期刊论文

  • 发表日期：

    2025年9月16日

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  • Fangzhou Zhao,
  • Hui Zhao,
  • Qingfang Meng,
  • Yuehui Chen,
  • Lixiang Li

摘要

This paper introduces the Quantum Geometric Dynamics Optimizer (QGDO), a novel algorithmic framework designed to solve complex continuous nonlinear optimization problems. QGDO establishes a new framework by synergistically integrating principles from three distinct domains: it leverages information geometry to overcome the geometric myopia of traditional search operators, employs quantum-inspired tunneling to escape deep local optima, and uses adaptive topological dynamics to orchestrate the exploration–exploitation balance. This integrated design requires a substantial computational investment, a deliberate trade-off that yields demonstrably superior solution accuracy and positions QGDO as a heavyweight solver for the high-performance computing (HPC) era. Its efficacy is validated through extensive experiments on the IEEE CEC2017, CEC2019, and CEC2022 benchmarks, where it achieved statistically significant performance advantages over 14 competitors. QGDO’s practical utility is further confirmed through its success in solving complex, constrained engineering design problems and in optimizing Echo State Network hyperparameters. The comprehensive results, including a full ablation study and parameter sensitivity analysis, establish QGDO as a powerful and robust optimizer for challenging real-world problems where solution quality is paramount.