Expansion is a novel mutation operator for Genetic Programming (GP). It uses Monte Carlo simulation to repeatedly expand and evaluate programs using unit instructions, which extends the search beyond the immediate - often misleading - horizon of offspring programs. To evaluate expansion, a standard Koza-style tree-based representation is used and a comparison is carried out between expansion and sub-tree crossover as well as point mutation. Using a diverse set of benchmark symbolic regression problems, we prove that expansion provides for better fitness performance than point mutation, when included with crossover. Expansion also provides a significant boost to fitness when compared to GP using crossover only, with similar or lower levels of program bloat. Despite expansion’s success in improving evolutionary performance, it does not eliminate the problem of program bloat. In response, an analogous genetic operator, reduction, is proposed and tested for its ability to keep a check on program size. We conclude that the best fitness can be achieved by including these three operators in GP: crossover, point mutation and expansion.

扩展是一种用于基因编程（GP）的新型变异算子。它使用蒙特卡洛模拟法使用单元指令反复扩展和评估程序，从而将搜索范围扩展到了后代程序（通常是误导性）的眼界。为了评估扩展，使用了标准的Koza风格的基于树的表示形式，并在扩展和子树交叉以及点突变之间进行了比较。通过使用各种基准符号回归问题，我们证明了扩展包含在分频器中时，比点突变具有更好的适应性。与仅使用交叉，程序膨胀程度相似或较低的GP相比，扩展还显着提高了适应性。尽管扩展成功地改善了进化绩效，它不能消除程序膨胀的问题。作为回应，提出了一个类似的遗传算子reduce，并对其保持程序大小的能力进行了测试。我们得出结论，可以通过在GP中包括以下三个运算符来实现最佳适应性：交叉，点突变和扩展。