Genotype–phenotype mapping plays an essential role in the design of an evolutionary algorithm. Variation occurs at the genotypic level but fitness is evaluated at the phenotypic level, therefore, this mapping determines if and how variations are effectively translated into quality improvements. In evolutionary algorithms, this mapping has often been observed as highly redundant, i.e., multiple genotypes can map to the same phenotype, as well as heterogeneous, i.e., some phenotypes are represented by a large number of genotypes while some phenotypes only have few. We numerically study the redundant genotype–phenotype mapping of a simple Boolean linear genetic programming system and quantify the mutational connections among phenotypes using tools of complex network analysis. The analysis yields several interesting statistics of the phenotype network. We show the evidence and provide explanations for the observation that some phenotypes are much more difficult to find as the target of a search than others. Our study provides a quantitative analysis framework to better understand the genotype–phenotype map, and the results may be utilized to inspire algorithm design that allows the search of a difficult target to be more effective.

中文翻译：

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遗传编程中基因型-表型映射的网络视角

基因型-表型映射在进化算法的设计中起着至关重要的作用。变异发生在基因型水平，但适应度是在表型水平上评估的，因此，这种映射决定了变异是否以及如何有效地转化为质量改进。在进化算法中，这种映射经常被认为是高度冗余的，即多个基因型可以映射到相同的表型，以及异质性的，即一些表型由大量基因型代表而一些表型只有很少。我们数值研究了简单布尔线性遗传规划系统的冗余基因型-表型映射，并使用复杂网络分析工具量化表型之间的突变联系。该分析产生了表型网络的几个有趣的统计数据。我们展示了证据并解释了某些表型作为搜索目标比其他表型更难找到的观察结果。我们的研究提供了一个定量分析框架来更好地理解基因型-表型图，并且结果可用于启发算法设计，使搜索困难的目标更加有效。