We propose to take advantage of symmetry that exists in some quadratic assignment instances when employing genetic or hybrid genetic algorithms to solve such instances. Such symmetry usually exists when the potential sites for the facilities are arranged in a rectangle. We designed a simple and effective approach to identify equivalent solutions if such symmetry exists. We propose three variants of this modification. Extensive computational experiments (performing 21,000 runs on instances with up to 150 facilities) show that the modified approach performed significantly better without increasing the running times.

中文翻译：

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在某些二次分配问题中利用对称性

我们建议在采用遗传或混合遗传算法求解此类实例时，利用某些二次分配实例中存在的对称性。当设施的潜在位置布置为矩形时，通常存在这种对称性。如果存在对称性，我们设计了一种简单有效的方法来识别等效解决方案。我们提出了此修改的三个变体。大量的计算实验（在具有多达150个设施的实例上执行21,000次运行）表明，改进的方法在不增加运行时间的情况下表现明显更好。