## 3 Results and Discussion
### Optimization Process Proposed  
After the theoretical model had been validated by experimental data, an optimization algorithm was proposed. This was done to ensure that that transport of a load of given weight, dimensions, and CoG by road would be safe, taking into account such route conditions as camber, wind pressure, and slope. The objective of optimization is to minimize the number of axles that are necessary to carry the desired load. The optimization increases the maneuverability of the load and reduces the costs of assembly and transport. The optimization algorithm was developed in R language [37]. Its programming was based on the iterative and automatic testing of the proposed model in different locations on the trailer and with different hydraulic configurations. Accordingly, the load's weight and CoG, and the trailer's weight, number of axles, axle distance, and configuration were considered, in addition to highway conditions. The optimization process assumed that the tipping angle would be less than 7\({}^{\circ}\) and that the loads per axle would be less than 50% of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{6}{c}{**Pressures**} \\ \cline{2-6}  & **A** & **B** & **C** & **D** & **MAPE** \\  & **[bar]** & **[bar]** & **[bar]** & **[bar]** & **[\%]** \\ \hline
1-5 & 59.0 & 58.0 & 84.4 & 84.4 & 4.4 \\
6 & 28.0 & 89.3 & 84.4 & 84.4 & 8.8 \\
7 & 18.3 & 98.7 & 84.4 & 84.4 & 13.6 \\
8 & 69.8 & 68.9 & 62.6 & 62.6 & 7.4 \\
9 & 38.6 & 100.2 & 62.6 & 62.6 & 4.6 \\
10 & 29.2 & 109.6 & 62.6 & 62.6 & 7.6 \\
11 & 80.7 & 79.8 & 40.9 & 40.9 & 3.8 \\
12 & 49.4 & 111.1 & 40.9 & 40.9 & 6.2 \\
13 & 40.1 & 120.4 & 40.9 & 40.9 & 6.4 \\  & & Average: & & & 7.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Predicted values and errors. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Range** & **Mean [\(\mu\)]** & **SD [s]** \\ \hline Pressure A & 9 bar & 59.2 bar & 2.9 bar \\ Pressure B & 7 bar & 60.6 bar & 2.4 bar \\ Pressure C & 15 bar & 80.0 bar & 5.3 bar \\ Pressure D & 20 bar & 78.4 bar & 7.2 bar \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variability of the experiments 1 to 5.  
the limit that the manufacturer had established. This 50% axle load limit is a restriction that is usually imposed by most transport companies as a means to increase the trailer's useful lifers. The tipping angle restriction ensures the stability of the transport under any road condition. The optimization was carried out in two stages. The first stage involved determining the minimum number of axles that were necessary and establishing the trailer's hydraulic configuration and the load's probable location. In this first stage, the optimization algorithm randomly generated a number of transport designs with different axes, configurations, and location of the transport's CoG. These were obtained from a grid of 500 \(\times\) 500 mm nodes. This grid was constructed from the properties of the surfaces of the trailers that were available. They should cover the entire stability triangle. Each transport design was calculated by using the proposed theoretical model for the camber, slope, and wind pressure (route conditions) considered. The model determined the tipping angle and maximum load on the trailer's axles for each transport design. After these values had been obtained, the design that required the least number of axles and best complied with the tipping angle and load per axle optimization restrictions was selected. The second stage focused on the search for the load's optimal location on the trailer, without changing the number of axles and hydraulic configuration that were obtained in stage 1. The best node in stage 1 was assumed to be the CoG of a new 10 \(\times\) 10 mm node grid. The same iterative process that was used in the first stage was employed in the second stage with the 10 \(\times\) 10 mm node grid. Thus, the optimal location of the load on all of the modular trailers was located with a precision of 10 mm.