The advent of the so-called Big Data paradigm has motivated a flurry of research aimed at enhancing machine learning models by following very di- verse approaches. In this context this work focuses on the automatic con- struction of features in supervised learning problems, which differs from the conventional selection of features in that new characteristics with enhanced predictive power are inferred from the original dataset. In particular this manuscript proposes a new iterative feature construction approach based on a self-learning meta-heuristic algorithm (Harmony Search) and a solution encoding strategy (correspondingly, Cartesian Genetic Programming) suited to represent combinations of features by means of constant-length solution vectors. The proposed feature construction algorithm, coined as Adaptive Cartesian Harmony Search (ACHS), incorporates modifications that allow exploiting the estimated predictive importance of intermediate solutions and, ultimately, attaining better convergence rate in its iterative learning proce- dure. The performance of the proposed ACHS scheme is assessed and com- pared to that rendered by the state of the art in a toy example and three practical use cases from the literature. The excellent performance figures obtained in these problems shed light on the widespread applicability of the proposed scheme to supervised learning with legacy datasets composed by already refined characteristics.