## 3 Results and Discussion
### Results of a Comparison of the Methods  
Tables 1 and 2 below show the deviation averages for the labour and material cost data for the three methods presented in this paper. The results presented in these tables confirm our judgement on the best method for forecasting cost data objects. Table 1 shows that, for the labour cost data, the lowest values for the deviation averages DV1 and DV2 were obtained with the multi-objective GA based on the ARIMA model. Table 2 shows that, for the material cost data, the lowest values for the deviation averages DV1 and DV2 were also obtained with the multi-objective GA based on the ARIMA model.  
The literature cited present different methodologies for forecasting compared with our methods. [PERSON] & [PERSON] [11], [PERSON] et al. [13] and [PERSON] & [PERSON] [6] used GAs with the ARIMA model to improve results compared with use of the ARIMA model alone. These authors used GAs to obtain a randomization of the ARIMA parameters, which is not always sufficient because ARIMA parameter estimation should be based on the data and research problem to achieve better forecasting. In addition, these authors used only one evaluation for the forecasting accuracy. Our method uses a GA to estimate the ARIMA parameters from the data and finds the best-fit model in forecasting. In addition, our method evaluates the forecasting accuracy using five different statistical fitness functions to achieve the optimal forecasting. The previously published studies have assumed that the data are accurate, while our study is based on clustered and improved data through imputing the missing data from other previous research [26].  
[PERSON] et al. [14] and [PERSON] et al. [15] proposed a combination approach involving the BPNN and improved this approach by adopting a hybrid intelligent approach named the ADE-BPNN for time series forecasting. These authors used GA operators to improve the forecasting accuracy. These approaches have shown a relatively high accuracy, but have not been used for long-term forecasts and to process samples consisting of big data. Our model has a different integration of the ARIMA model with the GA and different GA operators to make it more suitable for the problem addressed in our research study. In addition, our model shows better performance when processing variant data samples and is able to make long-term forecasts.  
Our model has been developed using Python as an open source programming language and the developed model can be used in different work environments with different systems. In the present study the model has been implemented on real cost data for a tunnel fan turbine system operated by Trafikverket. In addition, the model results show the achievement of optimal forecasting through GA variations and operations for short or long periods, in contrast to other methods. Trafikverket can use this model in forecasting different parameters with different data samples, systems or structures. The GA can adapt with the problem to achieve the purpose. To achieve the optimal solution, our model needs to be implemented on a server with the minimum specifications mentioned in Section 2.5.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **DV1** & **DV2** \\ \hline
**ARIMA model** & 0.2374 & 1.2169 \\
**Multi-objective GA based on the ARIMA model** & 0.1192 & 0.3869 \\
**Multi-objective GA based on the dynamic regression model** & 1.2630 & 6.2324 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The deviation averages for the labour cost object for every method.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **DV1** & **DV2** \\ \hline
**ARIMA model** & 0.4171 & 1.0438 \\
**Multi-objective GA based on the ARIMA model** & 0.3555 & 0.8477 \\
**Multi-objective GA based on the dynamic regression model** & 0.5615 & 3.9543 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The deviation averages for the material cost object for every method.