Bridging directed acyclic graphs to linear representations in linear genetic programming: a case study of dynamic scheduling

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.