如何使用自适应排名遗传算法通过Hajós构造构建长度为5的对称环
How to construct the symmetric cycle of length 5 using Hajós construction with an adapted Rank Genetic Algorithm
AI总结：
本文改编排名遗传算法，以Hajós并和顶点识别为算子，解决了从3阶完全对称有向图构造对称5环的问题，得到16步构造序列。
摘要：
2020年，Bang-Jensen等人将两个图的Hajós并推广到有向图类，并推广了有向图中顶点着色的若干结果。尽管作为这些结果的推论，有向图可以通过Hajós构造（有向Hajós并和识别非相邻顶点）获得，但确定获得该有向图的Hajós构造是一个复杂问题。特别是，Bang-Jensen等人提出了仅使用Hajós构造从3阶完全对称有向图构造对称5环的Hajós操作确定问题。我们通过引入来自图论的新型重组和变异算子，成功改编了基于排名的遗传算法来解决此问题。Hajós并成为重组算子，独立顶点的识别成为变异算子。通过这种方式，我们能够获得仅16个Hajós操作的序列来构造5阶对称环。
英文摘要：
In 2020 Bang-Jensen et. al. generalized the Hajós join of two graphs to the class of digraphs and generalized several results for vertex colorings in digraphs. Although, as a consequence of these results, a digraph can be obtained by Hajós constructions (directed Hajós join and identifying non-adjacent vertices), determining the Hajós constructions to obtain the digraph is a complex problem. In particular, Bang-Jensen et al. posed the problem of determining the Hajós operations to construct the symmetric 5-cycle from the complete symmetric digraph of order 3 using only Hajós constructions. We successfully adapted a rank-based genetic algorithm to solve this problem by the introduction of innovative recombination and mutation operators from graph theory. The Hajós Join became the recombination operator and the identification of independent vertices became the mutation operator. In this way, we were able to obtain a sequence of only 16 Hajós operations to construct the symmetric cycle of order 5.
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