In this paper, we analyze the population diversity of grammatical evolution (GE) on multiple levels of genetic information: chromosome diversity, expression diversity, and output diversity. Thereby, we use a tree-similarity metric from tree-based GP literature to determine similarity of expression trees generated in GE. The similarity of outputs is determined via their correlation. We track the pairwise similarities for all individuals within a generation on all three levels and track the distribution of similarity values over generations. We demonstrate the analysis method using four symbolic regression problem instances and find that the visualization highlights some issues that can occur when using GE such as: large groups of individuals with highly similar outputs, a high fraction of trees with constant outputs, or short and highly similar trees in the early stages of the GE run. Especially in the early phases of GE, we see that a large subset of the population represents equivalent expressions. In early stages, rather short expressions are produced leaving large parts of the chromosome unexpressed. More complex expressions can be derived only after GE has successfully evolved well-working beginnings of chromosomes.

在本文中，我们在遗传信息的多个级别上分析了语法进化（GE）的种群多样性：染色体多样性，表达多样性和输出多样性。因此，我们使用基于树的GP文献中的树相似度度量来确定GE中生成的表达树的相似度。输出的相似性通过它们的相关性来确定。我们在所有三个级别上跟踪一代中所有个体的成对相似性，并跟踪一代之间相似性值的分布。我们演示了使用四个符号回归问题实例的分析方法，并发现可视化突出显示了使用GE时可能发生的一些问题，例如：大量具有高度相似输出的个体，大量具有恒定输出的树木，或在GE早期运行的短而高度相似的树木。特别是在GE的早期阶段，我们看到人口的很大一部分代表了相同的表达。在早期阶段，会产生相当短的表达，而使大部分染色体未表达。只有在GE成功进化出染色体良好运转的起点之后，才能衍生出更复杂的表达。