# EvoDevo: Bioinspired Generative Design via Evolutionary Graph-Based Development
## 3 Proposed Method
### Normalising Inputs
For instance, if a member stores a lot of strain energy \((5\,se>v)\), the term is positive, and the cross-section grows, whereas if the member carries little energy relative to its volume \((5\,se<v)\), it becomes negative, and the member is thinned. The factors \(se^{2}\) and \((5\,se^{2}-se\,v-v)^{2}\) set how big the area change should be. They make the change large when a member is highly stressed and thin and small when the member already has a good balance between strain energy and volume. Figure 10: _Cont._

### Node-Only Results

Figure 11 shows the structure that achieved the highest reward across the runs for both the GNN and CGP controllers. As shown, both the GNN and CGP controllers followed almost the same trajectories. The total volume increased as a result of the node's relocation, which resulted in the extension of some edges. Conversely, strain energy exhibited a distinct trend and decreased throughout the developmental steps. The results indicate that the controller incorporated a minimal amount of material while achieving greater stiffness, demonstrating an effective trade-off. The CGP controller update rule for each node (\(x\) and \(y\) position) is

\[ \begin{array}{l}\Delta x=x\left(2x-y(2x+y)+y\right)\left(3x-y(2x+y)+y\right) \\ \\ \Delta y=\left(y^{2}-x^{2}\right)\left(y+1\right)\end{array}  \tag{14}\]

The controller preserves truss symmetry, as shown by the variable \(x\) in the \(\Delta x\) equation, resulting in zero horizontal displacement for any node on the vertical axis (\(x=0\)). However, on the vertical axis, because \(y+1>0\) is positive for all vertices, the sign of the update is controlled by \(y^{2}-x^{2}\). Nodes with \(y^{2}>x^{2}\) (located near the centre, where \(x\) is small) move upward, whereas nodes with \(y^{2}<x^{2}\) (near the supports, where \(x\) is large) move downward. Consequently, the initially flat top chord arches after 10 development steps (Figure 11), with the centre nodes elevated and the outer nodes dropped. Figure 11: _Cont._

Figure 10: Metrics related to the highest reward structures obtained by the edge-only method after 10 development steps. **(Left)**: GNN controller. **(Right)**: CGP controller. **(Top row)**: best performing structure. **(Second row)**: change in strain energy \(E\) through devo. **(Third row)**: change in volume \(V\) through devo. **(Fourth row)**: change in cost \(C=E+V\) through devo. ### Node-Edge Results

Figure 12 illustrates the way in which the node-edge controllers modify the truss structure. The CGP implements a considerable first adjustment, reducing both the strain energy and volume; however, it subsequently shows minimal improvements. The GNN controller, by comparison, decreases the energy and volume more gradually while maintaining this trend across all development steps, ultimately resulting in a lower overall cost. Therefore, Figure 12 demonstrates a potential trade-off: CGP is beneficial when only a limited number of development steps is feasible, whereas the GNN provides superior performance with long runs (development steps). In addition, based on Equation (15), the coupled CGP controllers applied one rule to each edge (regarding one output) and two rules to each node in each development step, as in the following equation:

\[ \begin{split}\Delta A&=2\,\mathrm{se}^{2}\big{(}3\, \mathrm{se}-v\big{)}\\ \Delta x&=x\,y\qquad\Delta y=y^{2}-x^{2}\end{split}  \tag{15}\]

Regarding the edge update \(\Delta A\), the term \(2\,se^{2}\) enhances the updates for highly stressed members, while the linear term \(3\,se-v\) determines the sign (positive or negative). The edges whose strain energy is higher than one-third of their volume become thicker, while the rest become thinner. This is the same \"energy-to-volume balance\" logic that was seen in the edge-only rule (Equation (13)), where \(5\,se-v\) played the same role with a different coefficient.