Evolutionary feature construction has been successfully applied to various scenarios. In particular, multi-tree genetic programming-based feature construction methods have demonstrated promising results. However, existing crossover operators in multi-tree genetic programming mainly focus on exchanging genetic materials between two trees, neglecting the interaction between multi-trees within an individual. To increase search effectiveness, we take inspiration from the geometric semantic crossover operator used in single-tree genetic programming and propose a macro geometric semantic crossover operator for multi-tree genetic programming. This operator is designed for feature construction, with the goal of generating offspring containing informative and complementary features. Our experiments on 98 regression datasets show that the proposed geometric semantic macro-crossover operator significantly improves the predictive performance of the constructed features. Moreover, experiments conducted on a state-of-the-art regression benchmark demonstrate that multi-tree genetic programming with the geometric semantic macro-crossover operator can significantly outperform all 22 machine learning algorithms on the benchmark.

进化特征构建已成功应用于各种场景。特别是，基于多树遗传规划的特征构建方法已经显示出有希望的结果。然而，现有的多树遗传规划中的交叉算子主要集中在两棵树之间交换遗传物质，忽略了个体内多树之间的相互作用。为了提高搜索效率，我们从单树遗传规划中使用的几何语义交叉算子中汲取灵感，提出了一种用于多树遗传规划的宏观几何语义交叉算子。该算子是为特征构建而设计的，目的是生成包含信息和互补特征的后代。我们在 98 个回归数据集上的实验表明，所提出的几何语义宏交叉算子显着提高了构造特征的预测性能。此外，在最先进的回归基准上进行的实验表明，使用几何语义宏交叉算子的多树遗传编程可以显着优于基准上的所有 22 种机器学习算法。