The Multifactorial Evolutionary Algorithm (MFEA) has emerged as an effective variant of the evolutionary algorithm. MFEA has been successfully applied to deal with various problems with many different types of solution encodings. Although clustered tree problems play an important role in real life, there haven’t been much research on exploiting the strengths of MFEA to solve these problems. One of the challenges in applying the MFEA is to build specific evolutionary operators of the MFEA algorithm. To exploit the advantages of the Cayley Codes in improving the MFEA’s performance, this paper introduces MFEA with representation scheme based on the Cayley Code to deal with the clustered tree problems. The new evolutionary operators in MFEA have two different levels. The purpose of the first level is to construct a spanning tree which connects to a vertex in each cluster, while the objective of the second one is to determine the spanning tree for each cluster. We focus on evaluating the efficiency of the new MFEA algorithm on known Cayley Codes when solving clustered tree problems. In the aspect of the execution time and the quality of the solutions found, each encoding type of the Cayley Codes is analyzed when performed on both single-task and multi-task to find the solutions of one or two different clustered tree problems respectively. In addition, we also evaluate the effect of those encodings on the convergence speed of the algorithms. Experimental results show the level of effectiveness for each encoding type and prove that the Dandelion Code outperforms the remaining encoding mechanisms when solving clustered tree problems.

中文翻译：

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解决聚类树问题的多元分解算法：Cayley码之间的竞争

多元进化算法（MFEA）已经成为进化算法的有效变体。MFEA已成功应用于许多不同类型的解决方案编码中，以解决各种问题。尽管簇生的树木问题在现实生活中起着重要的作用，但是关于利用MFEA的优势来解决这些问题的研究还很少。应用MFEA的挑战之一是建立MFEA算法的特定进化算子。为了利用Cayley代码在提高MFEA性能方面的优势，本文介绍了基于Cayley代码的MFEA表示方案，以解决聚类树的问题。MFEA中新的进化算子具有两个不同的层次。第一级的目的是构建连接到每个群集中的顶点的生成树，而第二级的目的是确定每个群集的生成树。在解决聚类树问题时，我们专注于在已知的Cayley码上评估新MFEA算法的效率。在执行时间和找到的解决方案的质量方面，在对单任务和多任务同时执行时，分析了Cayley码的每种编码类型，以分别找到一个或两个不同的聚类树问题的解决方案。此外，我们还评估了这些编码对算法收敛速度的影响。