## 2 Parametric Design and Optimisation
### Optimisation Results  
The results are summarised in Table 1. Depending on which fitness value is defined and which parameters are released for optimisation, different truss configurations are generated.  
The early optimisation processes were calculated with deformation as the fitness value. For these calculations, the value was set to be as low as possible. The results were very stiff trusses, with deformations smaller than 5 mm, a value of less than one-sixth of the limit of 32 mm according to Eurocode 5 (EN1995-1-1:2019-06-01). The resulting material savings of 1.4% were not considered as relevant improvements. Ultimately the deformation was only improved from 7 to 5 mm.  
The next attempt was optimising the structure using the maximum absolute normal force (both compression and tensile forces) as the fitness value of the algorithm. The compression forces were considerably reduced (\(-22\%\)), while the tensile forces decreased only slightly (\(-6\%\)). The detailed values can be found in Table 1. The goal of achieving an optimal structure through the minimisation of the occurring normal forces in all struts and chord members of the truss resulted in a mass reduction of 6.7%.  
Figure 2: Reference model, 12 segments, alternating diagonals.  
The optimisation was most successful when the fitness value was set as the total mass of the construction, which is directly proportional to the wood consumption. This resulted in a significant reduction of 14.9% compared to the reference model.  
Only chosen variables were released within the optimisation for the truss configuration of the housing. The distance between the divisions was defined evenly in order to meet aesthetic requirements. Figure 3 shows a truss with uneven distribution of the subdivisions. In addition, the cross section of the chords and struts was set to 80 \(\times\) 80 mm\({}^{2}\) in regard to the envisaged node configuration.  
For the final implementation of the housing, shown in Figures 1 and 4, a truss with 7 segments, regular spacing between the subdivisions and free diagonal member arrangement was defined, requiring 129.4 kg of timber, 18.1 kg less than the reference model.  
If the entire truss structure is calculated on a pure theoretical basis, without the consideration of node configurations, the environmental impact can be reduced even further. By allowing the algorithm to change the cross-sectional dimensions of the chords and struts, a reduction of 60% in material consumption is possible. For this case, the truss would need more subdivisions, use smaller cross sections and have a total weight of 59.3 kg for the 8.20 m span. Figure 5 shows a comparison of a solution with cross section of 80 \(\times\) 80 mm\({}^{2}\) and 7 subdivisions and the result of the rather theoretical optimisation allowing for optimisation of the cross section, leading to 11 subdivisions and cross sections of 60 \(\times\) 60 mm\({}^{2}\) and 40 \(\times\) 40 mm\({}^{2}\) (inner struts).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fitness Value** & **Reference Model** & **Deformation** & **Normal Force** & **Mass** \\ \hline Subdivisions & 12 & 13 & 8 & 6 \\ (n) & 0.46 & 0.81 & 0.70 & 0.90 \\ Buckling (-) & 0.39 & 0.30 & 0.30 & 0.37 \\ Cross section (-) & 0.39 & 0.30 & 0.30 & 0.37 \\ Deformation & 7 & 5 & 8 & 7 \\ (mm) & 147.5 & 145.4 & 137.6 & 125.5 \\ Weight (kg) & - & \(-\)1.4 & \(-\)6.7 & \(-\)14.9 \\ Resource reduction (\%) & - & \(-\)1.4 & \(-\)6.7 & \(-\)14.9 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results with different fitness values (optimisation with constant cross section).  
Figure 3: Optimisation result with uneven distribution of subdivisions (reference model in grey).