## 4 Composite Optimization
### Comparison of Optimization Criteria  
The selection of optimization criteria requires evidence-based validation. Specifically, employing mass as the sole criterion should be critically evaluated against alternative metrics to assess potential performance improvements and ancillary benefits. This study examined two criteria: total structural mass and the ratio of structural mass to torsional stiffness. As a direct comparison proved inconclusive, fitness was evaluated via finite element simulations, with results analyzed and presented schematically. The mass optimization procedure generates data that can be represented as two- or three-dimensional surfaces, elucidating the mechanical behavior of the structure under various compositional modifications. Due to the impossibility of visualizing data beyond the three-dimensional space, specific simplifications were implemented. This sub-study assumed that the sub-laminate layers of woven and unidirectional C.F.R.P. form a symmetric composite; thus, sub-laminates corresponding to variables (1), (3), (5), (7), (8), (10), (12), and (14) were set to have equal values, as were those corresponding to variables (2), (4), (6), (9), (11), and (13). Only variables (1), (2), and the torsional stiffness-to-mass ratio were plotted on the X, Y, and Z axes, respectively, since the remaining variables within each subcategory were assigned values equal to either (1) or (2), reflecting their shared characteristics. The results and plotted data for the composite laminations are presented in Figures 13-15. \begin{table}
\begin{tabular}{l l l l} \hline
**Initialization Parameters** & **Selection Parameters** & **Crossover Parameters** & **Mutation Parameters** \\ \hline Initial population size: 100 & Number of parents: 20 & Crossover probability: 60\% & Mutation probability: 10\% \\ Min. number of generations: 200 & Selection method: & & No adaptive mutation \\ Max. number of generations: 200 & Tournament & & \\ Termination criteria: & 50 generations of stagnation or reaching max number of generations (200) & \\ \(\quad\) & \(\quad\) & \(\quad\) & \\ \(\quad\) & \(\quad\) & \(\quad\) & \\ \(\quad\) & \(\quad\) & \(\quad\) & \\ \(\quad\) & \(\quad\) & \(\quad\) & \\ \(\quad\) & \(\quad\) & \(\quad\) & \\ \hline \end{tabular}
\end{table} 
Table 7: Setup parameters of the GA. \begin{table}
\begin{tabular}{l l l l} \hline
**Ranking:** & **Ranking No. 1** & **Ranking No. 3** & **Ranking No. 3** \\ \hline Fitness of designs: & 0.04861 & 0.04787 & 0.04713 \\ Selection probability: & 6.3658\% & 5.3585\% & 5.2764\% \\ \hline \end{tabular}
\end{table} 
Table 8: Selection probabilities for the three fittest results of G.A. The data in Figure 14 illustrates the torsional stiffness-to-mass ratio of the monocoque under torsion, obtained using methods consistent with those in the finite element optimization experiments. Analysis along the x-axis, representing the number of unidirectional laminae, reveals a slight decline in the torsional stiffness-to-mass ratio with up to three U.D. layers. Subsequently, the ratio plateaus before increasing nonlinearly as woven plies are added. The incorporation of both U.D. and woven plies substantially enhances the torsional stiffness-to-mass ratio, particularly beyond the seventh woven ply; however, this improvement coincides with an approximately linear mass increase, as shown in Figure 13. Although the stiffness gains outweigh the mass increase--suggesting the torsional stiffness-to-mass ratio as a suitable optimization criterion--it should be noted that the optimization targets that were set to prioritize minimizing the total mass due to its greater impact on  
Figure 14: Surface fitted to data of torsional rigidity from F.E. experiments. Figure 13: Surface fitted to data for estimates of mass from F.E. experiments. Figure 15: Surface fitted to data of torsional rigidity to mass ratio from F.E. experiments. vehicle performance.