## 1 Introduction
DynaGrow uses a multiobjective evolutionary algorithm (MOEA) that monitors and detects critical points at which the climate in a greenhouse integrates local climate data, electricity energy price forecasts, and outdoor weather forecasts. Dynagrow showed that it was feasible to grow different plants and improve the use of resources without affecting the quality of the produce [23]. A mathematical expression to control the temperature in greenhouses based on the fuzzy proportional, integral, and derivative (PID) and the greenhouse temperature model was designed. The graphs obtained through simulations indicated that the model had a short response time and could maintain a stable temperature inside the closed production plant system [24; 25; 26]. Also, neural networks have been used in CPPS to estimate indoor temperature and humidity [27], predict climatic conditions [28; 29] or forecast energy consumption [30]. Energy prediction models (EPM) to evaluate the energy requirements and performance of the system for the production of plants in closed spaces have been implemented. Similarly, a predictive control model (MPC) has been proposed for temperature regulation through ventilation and optimization of crop production [31; 32]. Another proposal was a MPC to increase the precision of actuator control and to minimize energy consumption [33]; the cost of energy, ventilation, and the price of managing CO\({}_{2}\) were the inputs. The aim was the optimization of the greenhouse process, as well as reducing the disturbance and inadaptability of the system [34]. According to the literature, there are different proposals to monitor, control and predict aspects such as weather conditions, energy consumption, humidity, temperature, and CO\({}_{2}\) levels, among others, in a CPPS. Implemented approaches include computer systems, fluid dynamics, multi-objective evolutionary algorithms (MOEA), Neural Networks, and the predictive control model. However, predictions of energy consumption in artificial lighting systems based on light recipes considering the light operation modes (pulsed and continuous) have not been reported. Hence, it is essential to assume that a challenge for CPPS is to apply strategies to improve energy consumption without affecting crop yield and quality. Aiming to generate new alternatives that may contribute to forecasting CPPS energy consumption, we propose two nonlinear models based on artificial intelligence that support modeling of the energy requirements of the LED lighting. The models include a vector with seven inputs and an output represented by the energy consumption of the CPPS. In the literature, no proposal has yet considered the components of light (red, blue, green, and white) and its mode of operation, i.e., continuous or pulsed (i.e., intensity, pulse frequency, and duty cycle). The first model uses genetic programming (GP), and the second feedforward neural networks (FNNs). We applied and compared these techniques in the generation of nonlinear models because they have been used for this propose [35; 36; 37; 38; 39; 40; 41]. This research applies 10-fold cross-validation to select the training complexity parameters because this approach almost eliminates the bias of the estimated error [42; 43; 44; 45; 46]. Ten-fold cross-validation is the most widely used in the literature because, even with random sampling, it reflects the behavior in the original dataset. Furthermore, it has been shown that any increase in the number of folds beyond 10 only increases computational effort, while slightly reducing the variance in the results owing to the number of folds does not impact the dataset distributions [42; 44; 46]. Additionally, we used test values outside the ranges established in the training stage to verify the generalization of the model. A Spearman's correlation was applied to generate the model only with representative inputs. Different light recipes extracted from the literature that are normally used for plant growth were configured in the artificial lighting system to generate the two datasets.