The proper management of diversity is essential to the success of Evolutionary Algorithms. Specifically, methods that explicitly relate the amount of diversity maintained in the population to the stopping criterion and elapsed period of execution, with the aim of attaining a gradual shift from exploration to exploitation, have been particularly successful. However, in the area of Genetic Programming, the performance of this design principle has not been studied. In this paper, a novel Genetic Programming method, Genetic Programming with Dynamic Management of Diversity (GP-DMD), is presented. GP-DMD applies this design principle through a replacement strategy that combines penalties based on distance-like functions with a multi-objective Pareto selection based on accuracy and simplicity. The proposed general method was adapted to the well-established Symbolic Regression benchmark problem using tree-based Genetic Programming. Several state-of-the-art diversity management approaches were considered for the experimental validation, and the results obtained showcase the improvements both in terms of mean square error and size. The effects of GP-DMD on the dynamics of the population are also analyzed, revealing the reasons for its superiority. As in other fields of Evolutionary Computation, this design principle contributes significantly to the area of Genetic Programming.

对多样性的适当管理对于进化算法的成功至关重要。具体而言，将种群中保持的多样性数量与停止标准和执行时间明确联系起来的方法特别成功，目的是实现从探索到开发的逐渐转变。然而，在遗传编程领域，这种设计原理的性能还没有被研究过。在本文中，提出了一种新颖的遗传规划方法，即具有多样性动态管理的遗传规划（GP-DMD）。GP-DMD 通过一种替换策略应用了这一设计原则，该策略将基于类距离函数的惩罚与基于准确性和简单性的多目标 Pareto 选择相结合。所提出的通用方法适用于使用基于树的遗传编程的成熟的符号回归基准问题。几种最先进的多样性管理方法被考虑用于实验验证，获得的结果展示了均方误差和大小方面的改进。还分析了 GP-DMD 对种群动态的影响，揭示了其优越性的原因。与进化计算的其他领域一样，这种设计原则对遗传编程领域做出了重大贡献。获得的结果展示了均方误差和大小方面的改进。还分析了 GP-DMD 对种群动态的影响，揭示了其优越性的原因。与进化计算的其他领域一样，这种设计原则对遗传编程领域做出了重大贡献。获得的结果展示了均方误差和大小方面的改进。还分析了 GP-DMD 对种群动态的影响，揭示了其优越性的原因。与进化计算的其他领域一样，这种设计原则对遗传编程领域做出了重大贡献。