###### Abstract
Parametric identification requires fewer data to identify a model; however, some a priori knowledge and engineering experience with respect to the analyzed system are required to choose a suitable model structure [29]. Moreover, there is no unique model structure corresponding to different crane applications under different operating conditions. In this case, non-parametric methods and machine learning techniques are alternative approaches that can be useful for determining a model structure for a specific process and data set. [PERSON] et al. [30] analyzed several multi-layer perceptron neural network (NN) structures and learning approaches (e.g., variable learning rate backpropagation, scaled conjugate gradients, recursive prediction error, and the Levenberg-Marquardt algorithm) to solve a time-series prediction problem in an MPC scheme for a quay crane. In [31], an overhead crane's dynamics were approximated by an adaptive neuro-fuzzy inference system (ANFIS) trained with operational data using a hairpin RNA genetic algorithm. [PERSON] et al. [32] used the NARX-NN data-driven model trained offline and online using extreme learning machines (ELMs) in the predictive control of a small-scale overhead crane with a prediction and control horizon of \(N_{p}=N_{c}=15\). The Koopman operator theory and deep learning are merged in [33] to identify a model of a gantry crane subsequently used to develop a linear quadratic controller tested on a laboratory stand. A data-driven active learning control scheme based on the Koopman operator was studied in simulations on a bridge crane model [34]. Different structures of artificial neural network (ANN) models of an overhead crane's inverse dynamics were trained and validated using the Levenberg-Marquardt algorithm, with data computed in simulations carried out using a model derived analytically in [35]. A hybrid PID and MPC scheme with Bayesian optimization for the data-driven identification of linear-model and controller parameter tuning was tested on a laboratory-scale overhead crane in [36]. An interesting alternative to model-based control is data-driven model-free control, which has recently proven its effectiveness for complex dynamical problems [37; 38]. Examples of such studies for underactuated crane systems are presented in [39; 40]. The selection of an appropriate model structure is a crucial point of identification that requires a tradeoff between model fitting and parsimony. Although the machine learning data-driven discovery of crane dynamics has been successfully explored in recent works, especially using an ANN framework, the problem of nonlinear model structure selection is rarely studied. To address this issue, a non-parametric data-driven identification of overhead crane dynamics using multi-gene genetic programming (MGGP) is proposed in [41]. However, symbolic regression can be prone to generating complex expressions and overfitting when aiming to decrease prediction error [42]. Thus, in [43], grammar-guided genetic programming (G3P) combined with \(l_{0}\) sparse regression is applied to find a compromise between model complexity and prediction accuracy. Following the work presented in [43] and in comparison to the linear parametric modeling-based MPC approach presented in [28], this paper develops an NMPC control strategy for an overhead crane based on a prediction model constructed using a regularized genetic programming (GP)-based approach. A polynomial NARX model structure is optimized using an evolutionary process and regularized least squares; the resulting prediction model is implemented in the NMPC scheme with a PSO algorithm used as the solver to find an optimal sequence of the control actions satisfying the multi-objective performance requirements and input constraints.