Cartesian Genetic Programming (CGP) is a variant of Genetic Programming (GP) with the individuals represented by a two-dimensional acyclic directed graph, which can flexibly encode many computing structures. In general, CGP only uses a point mutation operator and the genotype of an individual is of fixed size, which may lead to the lack of population diversity and then cause the premature convergence. To address this problem in CGP, we propose a Frameshift Mutation Cartesian Genetic Programming (FMCGP), which is inspired by the DNA mutation mechanism in biology and the frameshift mutation caused by insertion or deletion of nodes is introduced to CGP. The individual in FMCGP has variable-length genotype and the proposed frameshift mutation operator helps to generate more diverse offspring individuals by changing the compiling framework of genotype. FMCGP is evaluated on the symbolic regression problems and Even-parity problems. Experimental results show that FMCGP does not exhibit the bloat problem and the use of frameshift mutation improves the search performance of the standard CGP.

笛卡尔遗传编程（CGP）是遗传编程（GP）的一种变体，其个体由二维无环有向图表示，该图可以灵活地编码许多计算结构。通常，CGP仅使用点突变算子，并且个体的基因型大小固定，这可能导致缺乏种群多样性，从而导致过早收敛。为了解决CGP中的这个问题，我们提出了一种移码突变笛卡尔遗传程序设计（FMCGP），它受到生物学中DNA突变机制的启发，并将由于节点插入或缺失引起的移码突变引入到CGP中。FMCGP中的个体具有可变长度的基因型，拟议的移码突变算子通过改变基因型的编制框架，有助于产生更多不同的后代个体。FMCGP在符号回归问题和偶数奇偶问题上进行评估。实验结果表明，FMCGP不会出现膨胀问题，而使用移码突变可提高标准CGP的搜索性能。