Analyzing Fitness Aggregation Strategies for Symbolic Regression Problem-Solving

Genetic Programming (GP) remains one of the most prominent methods for Symbolic RegressionSymbolic Regressiondue to its flexibility in evolving symbolic models. Traditionally, GP has relied on error-based fitness functions, such as mean squared error (MSE), to guide its search for promising solutions. However, such error based functions can hinder the discovery of correct structural forms by over-emphasizing the offset between the true and predicted values. Using the coefficient of determination ( \(R^2\) ) as the fitness function relieves GP from evolving the scale and translation factors and allows GP to focus on identifying the correct shape/functional form of the target function. While \(R^2\) demonstrates promising generalization capabilities and eliminates the need for per-individual linear scalinglinear scaling, it remains limited to detecting linear relationships, it is sensitive to noise, and can be zero even when two variables are statistically dependent. In this chapter, we extend the explorationexplorationof correlation-based fitness assessment beyond \(R^2\) by evaluating alternative measures of statistical dependence (such as Spearman’s Rank Correlation Coefficient and Distance Correlation), and similarity (such as Cosine Similarity). Furthermore, we explore combining these functions through multi-objectivemulti-objectivePareto optimization. Our experimental results on both synthetic and real-world datasets demonstrate that these alternatives can improve generalization ability of the SR models by capturing meaningful, non-linear structural similarities overlooked by \(R^2\) alone.