# EvoDevo: Bioinspired Generative Design via Evolutionary Graph-Based Development
## 3 Proposed Method
### Normalising Inputs
In addition, the gap between the trained and untrained GNNs is smaller than that between the CGPs, showing that the untrained GNN works better. In Environment #2, the larger \(17\times 30\) truss with a single mid-span load, the outputs of the trained and untrained controllers are more similar. Although the untrained GNN outperforms the untrained CGP, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Num\_Runs** & **Mean** & **Std** & **Min** & **Max** \\ \hline gnn\_edge & 15 & 0.103 & 0.002 & 0.095 & 0.104 \\ gnn\_node & 15 & 0.291 & 0.001 & 0.289 & 0.292 \\ gnn\_node\_edge & 15 & 0.425 & 0.075 & 0.291 & 0.500 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._

Figure 13: Distribution of the best reward obtained by each algorithm over 15 independent runs. The box shows the inter-quartile range, the horizontal line is the median, and the individual circles represent single runs. The circle’s colour varies for each method. Figure 16: CGP behaviour in Environment #1 (three loads and \(9\times 15\) truss). (**Left**): trained controller; (**right**): untrained controller. (**Top plots**) show the final geometry after ten devo steps with strain energy \(E\), volume \(V\) and cost. (**Lower plots**) trace \(E\), \(V\) and cost over the ten devo steps. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Seedling** & **GRN** & **Criteria** & **Trained Controller** & **Untrained Controller** \\ \hline \multirow{4}{*}{Environment \#1} & \multirow{2}{*}{GNN} & Energy & 0.590 & 0.6358 \\  & & Volume & 235.704 & 307.848 \\  & & Cost & 1.310 & 1.556 \\ \cline{2-4}  & \multirow{2}{*}{CGP} & Energy & 0.476 & 3.631 \\  & & Volume & 268.678 & 94.577 \\  & & Cost & 1.267 & 4.449 \\ \hline \multirow{4}{*}{Environment \#2} & \multirow{2}{*}{GNN} & Energy & 1.381 & 1.732 \\  & & Volume & 529.189 & 642.085 \\ \cline{1-1}  & & Cost & 1.469 & 1.816 \\ \cline{1-1} \cline{2-4}  & \multirow{2}{*}{CGP} & Energy & 1.201 & 1.459 \\ \cline{1-1}  & & Volume & 585.465 & 518.154 \\ \cline{1-1}  & & Cost & 1.440 & 1.500 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance of GNN and CGP controllers on the two new seedling benchmarks for the generalisation test. Figure 17: _Cont._

### Comparison with Other Topology Optimisation Methods

To benchmark the GNN-based truss against established continuum methods, the topology optimisation study in [54] is referred to. This work utilises SolidWorks, ANSYS Mechan

Figure 17: GNN behaviour in Environment #2 (one load and \(17\times 30\) truss). (**Left**): trained controller; (**right**): untrained controller. (**Top plots**) show the final geometry after ten devo steps with strain energy \(E\), volume \(V\) and cost. (**Lower plots**) trace \(E\), \(V\) and cost over the ten devo steps. Figure 18: CGP behaviour in Environment #2 (one load and \(17\times 30\) truss). (**Left**): trained controller; (**right**): untrained controller. (**Top plots**) show the final geometry after ten devo steps with strain energy \(E\), volume \(V\) and cost. (**Lower plots**) trace \(E\), \(V\) and cost over the ten devo steps. ical and ABAQUS software ([https://www.3 ds.com/products/simulia/abaqus](https://www.3 ds.com/products/simulia/abaqus) (accessed on 11 June 2025)) to optimise three structures, including a small bridge with dimensions of \(2555\times 500\times 600\) mm that carries a 800 kN distributed bottom load. The weight of the GNN-based truss is estimated and compared to the weight results derived by Solidworks, ANSYS and ABAQUS using the seedling parameters in Table 8 extracted from [54]. Table 9 shows the weights of the small bridge after optimisation compared to those of the GNN-based truss. For the GNN-based truss, the initial cross-sectional area of 75 mm is used. The resulting weight of the GNN-based truss is marginally comparable to the weights of the three methods reported in [54]. As shown in Figure 19, after ten development steps, the GNN-based truss has a total volume of \(V=538,357.169\) mm\({}^{3}\).