# Calibration of an Adaptive Genetic Algorithm for Modeling Opinion Diffusion
## 3 Results
### Parameter Recovery  
Figure 3 shows parameter recovery RMSE by number of generations without improvement before the control parameters are modified and the elite chromosome reintroduced, the only set of hyperparameters that produces a notable difference in parameter recovery. This plot includes only the subset of the data where a perfect solution was identified within the first 1000 generations to illustrate our next point, but the features seen in this plot hold for the full dataset. Clearly, using 200 generations without improvement results in the best parameter recovery. Nothing that the populations of chromosomes requiring either 1000 or 5000 generations without improvement could not possibly have begun the exploitation phase within 1000 generations, this initially seems intuitive since we would expect solutions resulting from the exploitation phase to be better. Unfortunately, this does not explain the results since all the solutions presented here are perfect in terms of the value of the objective function. Instead, we must explain why perfect solutions identified during the exploration phase have worse recovery that perfect solutions identified during the exploitation phase. To do so, we revisit the intended purpose of the exploration process. During early iterations of the algorithm, we use control parameter values that result in drastic changes to the chro  
Figure 3: Boxplots and violin plots for root-mean-square-error for recovery by number of generations without improvement for runs that identified a solution with 1000 generations. mosomes and force--to varying degrees depending on the ProbSigma hyperparameters--the exploration of edge cases. As noted in our description of the procedures, our process for generating the true parameters is biased against edge cases. Consequently, populations forced to search the boundaries of the parameter space will identify solutions with poor recovery. Figure 4 supports this assertion by showing parameter recovery for 200, 1000, or 5000 generations without improvement by level of ProbSigma and number of time steps. For the purpose of transparency, this plot uses the full dataset. We use the number of time steps as a proxy for the prevalence of perfect solutions in the parameter space and include ProbSigma as it governs the extent to which early generations are forced to explore edge cases (The precision of the ordinal scale is also indicative of the ease of finding a perfect solution and demonstrates the same phenomenon seen in Figure 4. We selected number of time steps because the fewer levels of that factor improve readability of the plot). Comparing across number of time steps, we see the difference in parameter recovery between different numbers of generations without improvement decreases as the number of time steps increases (decreasing the number of potential perfect solutions). This supports our assertion that the poor parameter recovery is the result of forcing the algorithm to search the boundaries, where any solutions identified will inherently result in poor recovery. When an increased number of time steps makes it more difficult to identify an edge-case solution, the threshold for number of generations without improvement can then be reached, starting the transition away from the exploration phase and pulling the chromosomes away from the boundary. As expected, high values for the hyperparameters in the ProbSigma group--corresponding to the _high_ level--appear to exacerbate this difference since larger values of the control parameter \(\sigma\) apply stronger pressure to search the boundaries. It is much more difficult to assess any differences between the _low_ and _medium_ levels, but the level of ProbSigma also controls the values of \(p_{b}\), \(p_{c}\), and \(p_{m}\), any of which could have a moderating effect on the value of \(\sigma\).