Linear genetic programming (LGP) is a genetic programming paradigm based on a linear sequence of instructions being executed. An LGP individual can be decoded into a directed acyclic graph. The graph intuitively reflects the primitives and their connection. However, existing studies on LGP miss an important aspect when seeing LGP individuals as graphs, that is, the reverse transformation from graph to LGP genotype. Such reverse transformation is an essential step if one wants to use other graph-based techniques and applications with LGP. Transforming graphs into LGP genotypes is nontrivial since graph information normally does not convey register information, a crucial element in LGP individuals. Here we investigate the effectiveness of four possible transformation methods based on different graph information including frequency of graph primitives, adjacency matrices, adjacency lists, and LGP instructions for sub-graphs. For each transformation method, we design a corresponding graph-based genetic operator to explicitly transform LGP parent’s instructions to graph information, then to the instructions of offspring resulting from breeding on graphs. We hypothesize that the effectiveness of the graph-based operators in evolution reflects the effectiveness of different graph-to-LGP genotype transformations. We conduct the investigation by a case study that applies LGP to design heuristics for dynamic scheduling problems. The results show that highlighting graph information improves LGP average performance for solving dynamic scheduling problems. This shows that reversely transforming graphs into LGP instructions based on adjacency lists is an effective way to maintain both primitive frequency and topological structures of graphs.

线性遗传编程（LGP）是基于正在执行的线性指令序列的遗传编程范例。LGP个体可以被解码为有向无环图。该图直观地反映了原语及其联系。然而，现有的LGP研究在将LGP个体视为图时忽略了一个重要方面，即从图到LGP基因型的逆转换。如果想要将其他基于图的技术和应用程序与 LGP 结合使用，这种反向转换是必不可少的步骤。将图转换为 LGP 基因型并非易事，因为图信息通常不传达寄存器信息，而寄存器信息是 LGP 个体的关键要素。在这里，我们研究了基于不同图信息的四种可能的变换方法的有效性，包括图元的频率、邻接矩阵、邻接列表和子图的 LGP 指令。对于每种转换方法，我们设计了相应的基于图的遗传算子，以将 LGP 父代的指令显式转换为图形信息，然后转换为在图上繁殖产生的后代的指令。我们假设进化中基于图的算子的有效性反映了不同图到 LGP 基因型转换的有效性。我们通过一个案例研究进行了调查，该案例应用 LGP 来设计动态调度问题的启发式方法。结果表明，突出显示图信息可以提高 LGP 解决动态调度问题的平均性能。这表明基于邻接表将图逆向变换为LGP指令是保持图的基元频率和拓扑结构的有效方法。