The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a model-based EA framework that has been shown to perform well in several domains, including Genetic Programming (GP). Differently from traditional EAs where variation acts blindly, GOMEA learns a model of interdependencies within the genotype, that is, the linkage, to estimate what patterns to propagate. In this article, we study the role of Linkage Learning (LL) performed by GOMEA in Symbolic Regression (SR). We show that the non-uniformity in the distribution of the genotype in GP populations negatively biases LL, and propose a method to correct for this. We also propose approaches to improve LL when ephemeral random constants are used. Furthermore, we adapt a scheme of interleaving runs to alleviate the burden of tuning the population size, a crucial parameter for LL, to SR. We run experiments on 10 real-world datasets, enforcing a strict limitation on solution size, to enable interpretability. We find that the new LL method outperforms the standard one, and that GOMEA outperforms both traditional and semantic GP. We also find that the small solutions evolved by GOMEA are competitive with tuned decision trees, making GOMEA a promising new approach to SR.

中文翻译：

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改进基于模型的小表达式符号回归的遗传编程

基因池最优混合进化算法 (GOMEA) 是一种基于模型的 EA 框架，已被证明在多个领域表现良好，包括遗传编程 (GP)。与变异盲目行动的传统 EA 不同，GOMEA 学习基因型内的相互依赖性模型，即连锁，以估计要传播的模式。在本文中，我们研究了 GOMEA 在符号回归 (SR) 中执行的链接学习 (LL) 的作用。我们表明 GP 种群中基因型分布的不均匀性对 LL 产生了负面影响，并提出了一种纠正方法。我们还提出了在使用临时随机常数时改进 LL 的方法。此外，我们采用了一种交错运行方案，以减轻将种群大小（LL 的关键参数）调整为 SR 的负担。我们在 10 个真实世界的数据集上运行实验，对解决方案大小实施严格限制，以实现可解释性。我们发现新的 LL 方法优于标准方法，并且 GOMEA 优于传统和语义 GP。我们还发现 GOMEA 演化出的小型解决方案与调整后的决策树具有竞争力，使 GOMEA 成为一种很有前途的新 SR 方法。