论文标题
如何使用Hajós构造具有适应性等级遗传算法的hajós构造的长度5的对称周期
How to construct the symmetric cycle of length 5 using Hajós construction with an adapted Rank Genetic Algorithm
论文作者
论文摘要
2020年，Bang-Jensen等。 al。概括了两个图与Digraphs类别的Hajós连接，并概括了Digraphs中顶点着色的几个结果。虽然，由于这些结果，可以通过Hajós构造（定向Hajós加入并识别非贴剂的顶点）获得Digraph，但确定Hajós构造以获得Digraph是一个复杂的问题。特别是Bang-Jensen等。提出了确定朝霍斯操作的问题，即仅使用hajós构造从订单3的完整对称挖掘中构建对称的5循环。我们成功地调整了一种基于等级的遗传算法来通过从图理论中引入创新的重组和突变算子来解决此问题。 Hajós加入成为重组操作员，而独立顶点的识别成为突变操作员。通过这种方式，我们能够获得仅16个Hajós操作的序列来构建阶5的对称周期。
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.
