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幻方问题的演化算法*

, PP. 28-34

Keywords: 幻方,演化算法,分步构造猜想

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Abstract:

幻方问题是具有悠久历史的复杂排列组合问题.幻方问题的复杂性不仅在于解的多样性随阶数指数递增,而且在于解在可行排列空间中所占的比例随阶数指数递减.本文在提出半幻方通过行置换与列置换可实现对角线数字幻和满足的分步构造猜想的基础上,提出基于演化策略的分步自适应幻方演化算法.变异操作包括元素对置换、整行置换、整列置换;启发式局部调整操作包括行列局部调整与对角局部调整等.计算表明,分步构造猜想至少在所完成的幻方构造计算实例上是成立的,幻方分步演化算法具有较高的计算效率.

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