## 6 Experiments and Results
### Experiments and Results Using Tournament Selection  
In the first set of experiments, using TS as the parent selection method, the initial experiment was conducted with a population size of 1000 over 30 generations. The system took 59 min and 36 s to successfully evolve only two solutions across thirty runs, as reported in Table 2. Somewhat arbitrarily, we set a target of 25/30 successful runs; if a setup produces fewer than that, we consider the setup inadequate. In Table 2, blue text indicates the training and test success rate on unsuccessful runs, while green text indicates the training and test success rate greater than 25. No further experiments were run once we managed a success rate greater or equal to 25. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline No. of Runs & 30 \\ \hline Population Size & 1000 \\ \hline No. of Genes. & 30 \\ \hline Initialisation & Sensible \\ \hline Mutation Prob. & 0.01 \\ \hline Crossover Prob. & 0.9 \\ \hline Elitism & Yes \\ \hline Training Cases & 64 \\ \hline Test Cases & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Hyperparameters used for experiments. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Parameter**} & \multicolumn{2}{c}{**Training and Test**} & \multicolumn{2}{c}{**Training and Test**} \\ \multicolumn{2}{c}{**Values**} & \multicolumn{2}{c}{**Results Using LS**} & \multicolumn{2}{c}{**Results Using TS**} \\ \hline \multirow{2}{*}{
\begin{tabular}{c} **Population** \\ **Size** \\ \end{tabular} } & **Number of** & **Success** & **Execution** & **Success** & **Execution** \\  & **Generations** & **Rate** & **Time** & **Rate** & **Time** \\ \hline \multirow{4}{*}{1000} & 30 & 09/30 & 57 min 42 s & 02/30 & 59 min 36 s \\ \cline{2-6}  & 100 & 17/30 & 178 min 41 s & 06/30 & 177 min 42 s \\ \cline{2-6}  & 500 & 29/30 & 867 min 56 s & 20/30 & 870 min 23 s \\ \cline{2-6}  & 1000 & NN & NN & 23/30 & 1732 min 53 s \\ \hline \multirow{2}{*}{5000} & 100 & NN & NN & 20/30 & 872 min 45 s \\ \cline{2-6}  & 500 & NN & NN & 30/30 & 4348 min 15 s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Success rate and execution time of evolved SDs according to the LS and TS method with respective population size and number of generations. (NN stands for ”Not Needed” and is used where a success rate of 25/30 or more is achieved and needs no more experiments. These success rates mark the successful runs and are highlighted in green. Unsuccessful runs are shown in blue). For this first experiment, the mean of the maximum fitness graph (all graphs for these experiments are provided in the SM, showing the mean maximum fitness scores of evolved circuits over 30 runs across the maximum number of generations) revealed consistently increasing error bars over the generations (as seen in the subsequent experiment shown in Figure 5(a)). Noting the significant variability in solutions indicated by the large error bars, the number of generations increased to 100, achieving a success rate of 6/30 and taking the execution time of 177 min and 42 s, almost three times the previous experiment. The resulting graph continued to show large error bars, as illustrated in Figure 5(a). The number of generations was then further increased to 500, taking an execution time of 870 min and 23 s and resulting in a success rate of 20/30. Although the results did not improve fivefold with the increased number of generations, the error bars remained substantial. The number of generations was further increased to 1000, resulting in a success rate of 23/30, taking execution time of 1732 min and 53 s. The error bars on the graph were significantly reduced. We experimented with swapping these values to explore whether a larger population size with fewer generations might yield better results. The population size was set to 5000, and the number of generations was reduced to 100 (thus keeping the total number of individuals the same).