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Interaction-transformation evolutionary algorithm with coefficients optimization

Symbolic Regression is the task of finding a mathematical expression to describe the relationship between one or more independent variables with a dependent variable. The search space can be vast and include any algebraic function; thus, finding optimal values for coefficients may not be a trivial task. The Interaction-Transformation representation alleviates this problem enforcing that the coefficients of the expression is part of a linear transformation, allowing the application of least squares. But this solution also limits the search space of the expressions. This paper proposes four different strategies to optimize the coefficients of the nonlinear part of the Interaction-Transformation representation. We benchmark the proposed strategies by applying the Interaction-Transformation Evolutionary Algorithm (ITEA) to six well-known data sets to evaluate four optimization heuristics combining linear and non-linear methods. The results show that optimizing the non-linear and linear coefficients separately was the best strategy to find better-performing expressions with a higher run-time and expression size. The non-linear optimization method alone was the worst-performing method.