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Zenodo
2026
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| Онлайн доступ: | https://doi.org/10.5281/zenodo.20131139 |
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| _version_ | 1866902100087144448 |
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| author | Sun, Hechun |
| author_facet | Sun, Hechun |
| contents | <p>传统自适应优化算法在高维非凸问题中易陷入局部最优。本研究受《易经》卦象变换规则启发,提出GuaXiang-Optimizer算法。将六十四卦编码为6维二进制矩阵,定义错卦(逐位取反)与综卦(逆序排列)变换规则,结合动态权重调度策略调节搜索方向。理论分析表明特定条件下算法可收敛,在CEC2013标准函数集测试中,低维问题收敛速度提升12.3%(p<0.01),高维问题性能与SLSQP相当,为传统文化符号工程化应用提供可复现数学模型。</p> <p> </p> <p>Traditional adaptive optimization algorithms tend to fall into local optima in high-dimensional non-convex problems. Inspired by the hexagram transformation rules in I Ching, this study proposes the GuaXiang-Optimizer. 64 hexagrams are encoded as 6-dimensional binary matrices. Two transformation rules are defined: reversed hexagram (bitwise NOT) and inverted hexagram (reverse order). A dynamic weight scheduling strategy is used to adjust the search direction. Theoretical analysis shows convergence under certain conditions. Experiments on the CEC2013 benchmark set show that the convergence speed is improved by 12.3% (p<0.01) for low-dimensional problems, and performance is comparable to SLSQP for high-dimensional problems. This work provides a reproducible mathematical model for the engineering application of traditional cultural symbols.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20131139 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | 基于卦象变换启发的自适应优化算法研究 Research on Adaptive Optimization Algorithm Inspired by Hexagram Transformation Sun, Hechun <p>传统自适应优化算法在高维非凸问题中易陷入局部最优。本研究受《易经》卦象变换规则启发,提出GuaXiang-Optimizer算法。将六十四卦编码为6维二进制矩阵,定义错卦(逐位取反)与综卦(逆序排列)变换规则,结合动态权重调度策略调节搜索方向。理论分析表明特定条件下算法可收敛,在CEC2013标准函数集测试中,低维问题收敛速度提升12.3%(p<0.01),高维问题性能与SLSQP相当,为传统文化符号工程化应用提供可复现数学模型。</p> <p> </p> <p>Traditional adaptive optimization algorithms tend to fall into local optima in high-dimensional non-convex problems. Inspired by the hexagram transformation rules in I Ching, this study proposes the GuaXiang-Optimizer. 64 hexagrams are encoded as 6-dimensional binary matrices. Two transformation rules are defined: reversed hexagram (bitwise NOT) and inverted hexagram (reverse order). A dynamic weight scheduling strategy is used to adjust the search direction. Theoretical analysis shows convergence under certain conditions. Experiments on the CEC2013 benchmark set show that the convergence speed is improved by 12.3% (p<0.01) for low-dimensional problems, and performance is comparable to SLSQP for high-dimensional problems. This work provides a reproducible mathematical model for the engineering application of traditional cultural symbols.</p> |
| title | 基于卦象变换启发的自适应优化算法研究 Research on Adaptive Optimization Algorithm Inspired by Hexagram Transformation |
| url | https://doi.org/10.5281/zenodo.20131139 |