## 1 Introduction  
Time series forecasting predicts future data points based on observed data over a period known as the lead-time. The purpose of forecasting data points is to provide a basis for economic planning, production planning, production control and optimizing industrial processes. The major objective is to obtain the best forecast function, i.e., to ensure that the mean square of the deviation between the actual and the forecasted values is as small as possible for each lead-time [1; 2]. Much effort has been devoted over the past few decades to the development and improvement of time series forecasting models [3]. Traditional models for time series forecasting, such as the Box-Jenkins or autoregressive integrated moving average (ARIMA) model, assume that the studied time series are generated from linear processes. However, these models may be inappropriate if the underlying mechanism is nonlinear. In fact, real-world systems are often nonlinear [4; 5]. The multi-objective genetic algorithm (GA) is often compatible with nonlinear systems and uses a particular optimization from the principle of natural selection of the optimal solution on a wide range of forecasting populations [6; 7]. The proposed multi-objective GA optimizes a particular function based on the ARIMA model. The ARIMA model is a stochastic process modelling framework [1] that is defined by three parameters \((p,d,q)\). The parameter \(p\) stands for the order of the autoregressive \(AR(p)\) process, \(d\) for the order of integration (needed for the transformation into a stationary stochastic process), and \(q\) for the order of the moving average process, \(MA(q)\)[8]. A stationary stochastic process means a process where the data properties have the same variance and autocorrelation [9]. The weakness of the ARIMA model is the difficulty of estimating the parameters. To address this problem, a process for automated model selection needs to be implemented in the automated optimization to achieve an accurate forecasting [10]. The GA is a well-established method which helps in solving complex and nonlinear problems that often lead to cases where the search space shows a curvy landscape with numerous local minima. The multi-objective GA is designed to find the best forecasting solution through automated optimization of the ARIMA model and to select the best parameters \((p,d,q)\) to compute point forecasts based on time series data. The parameters of the ARIMA model are influenced by the selecting process of the GA. In addition, the multi-objective GA can evaluate the forecasting accuracy using multiple fitness functions based on statistics models. [PERSON] and [PERSON] [11] modified the ARIMA model based on the genetic algorithm and particle swarm optimization (PSO) to estimate and predict data of time. They found that the genetic algorithm could find a suitable ARIMA model and pointed to improvements through individual binary randomization for every parameter input of the ARIMA model. Their model shows the best set of coefficients obtained with PSO compared with the best set obtained with a classical ARIMA prediction. However, these authors present the ARIMA parameters in a binary setting with limited possibilities and they consider the forecasting based on an ARIMA evaluation only. [PERSON] & [PERSON] [12] proposed a combination of grey theory and the genetic algorithm to overcome industrial development constraints and establish a high-precision forecasting model. They used a genetic algorithm to optimize grey forecasting model parameters. They demonstrated a successful application of their model which provided an accurate forecasting with a low forecasting error rate. However, these authors proposed randomization in combination with grey theory without integrating grey theory functionality within the GA. They used only one forecasting error rate to judge the forecasting accuracy. [PERSON] et al.