## 4 Results
### PSO Results  
The optimal HEV layouts resulting from the PSO algorithm for the four different design targets (i.e., TFO, MFO, MPO, TPO) are shown in Figure 8 as a Pareto frontier for average fuel economy and HEV production cost. As already stated in Section 3.1, the different HEV designs are oriented fully or mostly towards one of the two costs to be optimized, i.e., the production or the operative ones. This is performed by varying the value of \(w_{gasol}\) in the PSO objective function considering four discretized values ranging from 0.05 to 0.95 and repeating the entire HEV design workflow. Before presenting the final results obtained, it may be helpful to point out that about 24 days (i.e., approximately 570 h of computation) were dedicated to the design of the four different HEV layouts. To this end, the adoption of the PSO made possible an overall time reduction by guiding the sizing \"evolution\", still providing exhaustive outcomes. Figure 7: Example of the DP control results for a four-speed HEV driving the WLTP, equipped with a 99 kW ICE and a 29 kW EM. As seen in Figure 8, the two HEV layouts identified by PSO as TFO and TPO exhibit considerably different results in terms of production and fuel-related costs. This confirms the quality of PSO as design algorithm, which is able to intelligently optimize the different sizing parameters. The sizing parameters for the different optimal HEV powertrain layouts identified by the PSO are found in Table 5, along with additional information (i.e., HEV production cost, HEV fuel related cost, average fuel economy, and CO\({}_{2}\) penalty). In this table, the first layout corresponds to the totally production cost-oriented objective function (TPO), whereas the fourth is the totally fuel economy-oriented one (TFO). More in detail, the TPO HEV layout resulted in 10,875 \(\epsilon\) in production cost and 9854 \(\epsilon\) for the lifetime operative cost. On the opposite side, the TFO HEV layout obtained 11,736 \(\epsilon\) in cost due to the production (which corresponds to 860 \(\epsilon\) more than the previous design), yet the operative price dropped by about 500 \(\epsilon\), resulting in 9345 \(\epsilon\). Moreover, the two \"middle\" designs resulted in similar costs and their absolute differences are approximately 160 \(\epsilon\) regarding the production cost and about 90 \(\epsilon\) concerning the operative costs. No CO\({}_{2}\) penalties were added to any optimal layout as all resulted in an emission value below the threshold. It might be worth reasoning on the choice of the PSO to the outcome of a four-speed HEV for the totally fuel economy-oriented layout. In this scenario, it is crucial to remember  
Figure 8: HEV optimal layouts for the different objective functions implemented in the PSO algorithm expressed in a Pareto frontier. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **TPO** & **MPO** & **MFO** & **TFO** \\ \hline ICE size [kW] & 68 & 71 & 80 & 99 \\ EM size [kW] & 14 & 27 & 30 & 29 \\ Number of Gears & 2 & 3 & 3 & 4 \\ First Gear Ratio & 3.52 & 3.92 & 2.58 & 2.95 \\ Last Gear Ratio & 0.73 & 0.37 & 0.46 & 0.54 \\ Final Drive Ratio & 2.61 & 2.22 & 2.61 & 2.29 \\ ICE-Transm Ratio & 2.17 & 1.56 & 1.42 & 1.11 \\ Prod. Cost [\(\epsilon\)] & 10.875 & 11.210 & 11,371 & 11,736 \\ Fuel Cost. [\(\epsilon\)] & 9854 & 9556 & 9461 & 9345 \\ Avg. FE [L/100 km] & 3.39 & 3.29 & 3.26 & 3.22 \\ CO\({}_{2}\) penalty & / & / & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal HEV layouts’ parameters. that, even in the TFO HEV design case, a small percentage in the PSO objective function is assigned to the non-optimized cost (i.e., the production cost in this framework), the benefits in average fuel economy of having higher number of gears are shadowed by the substantial increase in production cost. As a general trend observed in Table 5, the more importance given to the lifetime operative cost, the larger the size of both ICE and EM and the higher the number of gears in the transmission.