Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making them interesting for various practical applications. The usage of metaheuristics to construct rotation symmetric Boolean functions is a direction that has been explored for almost twenty years. Despite that, there are very few results considering evolutionary computation methods. This paper uses several evolutionary algorithms to evolve rotation symmetric Boolean functions with different properties. Despite using generic metaheuristics, we obtain results that are competitive with prior work relying on customized heuristics. Surprisingly, we find that bitstring and floating point encodings work better than the tree encoding. Moreover, evolving highly nonlinear general Boolean functions is easier than rotation symmetric ones.

翻译：旋转对称布尔函数是一类有趣的布尔函数，因为与一般布尔函数相比，它们相对稀有。同时，此类函数可以具有优异特性，使其在各种实际应用中具有价值。利用元启发式方法构造旋转对称布尔函数是一个已探索近二十年的研究方向。尽管如此，有关进化计算方法的研究成果仍然凤毛麟角。本文采用多种进化算法，以演化具有不同特性的旋转对称布尔函数。尽管使用了通用元启发式方法，我们仍获得了可与先前依赖定制启发式方法的研究相媲美的结果。令人惊讶的是，我们发现位串编码和浮点数编码的效果优于树编码。此外，演化高度非线性的通用布尔函数比演化旋转对称布尔函数更为容易。