Existing genetic programming (GP) methods are typically designed based on a certain representation, such as tree-based or linear representations. These representations show various pros and cons in different domains. However, due to the complicated relationships among representation and fitness landscapes of GP, it is hard to intuitively determine which GP representation is the most suitable for solving a certain problem. Evolving programs (or models) with multiple representations simultaneously can alternatively search on different fitness landscapes since representations are highly related to the search space that essentially defines the fitness landscape. Fully using the latent synergies among different GP individual representations might be helpful for GP to search for better solutions. However, existing GP literature rarely investigates the simultaneous effective use of evolving multiple representations. To fill this gap, this paper proposes a multi-representation GP algorithm based on tree-based and linear representations, which are two commonly used GP representations. In addition, we develop a new cross-representation crossover operator to harness the interplay between tree-based and linear representations. Empirical results show that navigating the learned knowledge between basic tree-based and linear representations successfully improves the effectiveness of GP with solely tree-based or linear representation in solving symbolic regression and dynamic job shop scheduling problems.

翻译：现有的遗传规划方法通常基于特定表示（如树形或线性表示）设计。这些表示在不同领域展现出各自的优势与局限。然而，由于遗传规划中表示方式与适应度地形之间存在复杂关联，难以直观判定何种遗传规划表示最适合解决特定问题。通过多表示并行演化程序（或模型），可在不同适应度地形上进行交替搜索，因为表示方式与本质上定义适应度地形的搜索空间高度相关。充分利用不同遗传规划个体表示间的潜在协同效应，可能有助于遗传规划搜索更优解。然而，现有遗传规划研究鲜少探讨多表示并行演化的有效运用。为填补这一空白，本文提出一种基于树形与线性表示的多表示遗传规划算法——这两种是遗传规划常用的表示形式。此外，我们开发了新型跨表示交叉算子，以利用树形与线性表示间的交互作用。实验结果表明，在符号回归和动态作业车间调度问题求解中，通过在基础树形与线性表示间传递习得知识，能有效提升单一树形或线性表示遗传规划的性能。