# EvoDevo: Bioinspired Generative Design via Evolutionary Graph-Based Development
## 3 Proposed Method
### Normalising Inputs
Regarding the vertex rules, they were the same as in the node-only experiment, with \(\Delta y=y^{2}-x^{2}\) raising the centre nodes and lowering the outer ones, making an arch shape. Figure 11: Metrics related to the highest reward structures obtained by the node-only method after 10 development steps. (**Left**): GNN controller. (**Right**): CGP controller. Rows as described in Figure 10.

### Comparison Between GNN and CGP

Table 6 and Figure 13 depict the best reward obtained from 15 independent runs for each CGP and GNN controller. A clear trend is evident: expanding the control space from the edge method to the node method and ultimately to the combined node-edge method consistently increases the mean reward for both the CGP (0.10 \(\rightarrow\) 0.39) and GNN (0.10 \(\rightarrow\) 0.43) controllers. The GNN-based node-edge method has the highest reward score (0.50), but it also has the widest variance, revealing irregular stagnation in the local minimum. In contrast, the GNN-based node-edge variations and all three CGP methods have less variance, producing highly reproducible results. Overall, it is shown that a trade-off exists between performance (reward) and consistency in the GNN and CGP controllers. Furthermore, the CGP-based approaches are integrated as a white box, allowing the expert to interpret modifications based on the acquired equations. The full development trajectories from the 15 runs of the best CGP and GNN controllers (for each method) are presented in Appendix A and Appendix B, respectively. These figures illustrate the evolution of the truss during all 10 developmental stages for the edge-only, node-only and combined node-edge methodologies, demonstrating how each strategy incrementally transforms the truss structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Num\_Runs** & **Mean** & **Std** & **Min** & **Max** \\ \hline cgp\_edge & 15 & 0.098 & 0.003 & 0.094 & 0.102 \\ cgp\_node & 15 & 0.282 & 0.005 & 0.277 & 0.291 \\ cgp\_node\_edge & 15 & 0.389 & 0.021 & 0.364 & 0.447 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary statistics of best rewards achieved over 15 runs per method. Figure 12: Metrics related to the highest reward structures obtained by the node–edge method after 10 development steps. **(Left)**: GNN controller. **(Right)**: CGP controller. Rows as described in Figure 10.

### Generalisation to a New Environment

One of the most important aspects of an indirect representation for generative design systems is the ability of the development rules to generalize to new problems that differ from the one on which they were evolved. To investigate this capability, two additional \"seedling\" truss benchmarks are created (Figure 14). All the load cases are applied simultaneously to the structure. The first environment is a multi-load, \(9\times 15\) truss (Figure 14a) in which three point loads of 10 kN, 17 kN and 17 kN are applied to the original 9-vertex, 15-edge Warren seedling introduced in Section 4. The second environment is a single-load \(17\times 30\) truss (Figure 14b) in which a single 17 kN point load is applied in the middle of the 17-vertex, 30-edge Warren seedling. For each of the two new seedling environments, both GRN controllers (GNN and CGP) are trained and compared with the best node-edge controllers previously evolved on the original single-load \(9\times 15\) truss. The controller structures and all Evo/Devo parameters are set as described in Section 4 wherever possible. Table 7 shows the differences in the performance of the trained and frozen (untrained) GNN/CGP controllers on the two new seedling benchmarks. In Environment #1, the \(9\times 15\) truss with three point loads, both the trained GNN and CGP controllers perform better than the untrained controllers. The trained GNN lowers the cost mainly by decreasing the volume, while the trained CGP achieves the best cost by largely reducing the strain energy.