## 3 Experiments and Results
If for the GA population considered for computing the final posterior distribution sample, the lb = 100 \(\times\) (\(\gamma/2\))% and ub = 100 \(\times\) (1 \(-\gamma/2\))% quantiles represent lower and upper bounds for a given regression parameter, then the percentage improvement in parameter IW from the no-information IW can be computed using the following expression:  
\[Percentage IW Improvement(\%imp.)=\bigg{(}1-\frac{(ub-lb)}{2\times(1-\gamma)\times \lambda}\bigg{)}. \tag{15}\]  
Finally, in Section 2, it was mentioned that a posterior distribution sample from the final population at convergence is considered for the computing parameter confidence intervals. Since the mutation operation introduces some randomness, it is not always necessary to pick the last generation of the population to compute a parameter confidence interval. From a practical standpoint, a sample is extracted from generation \(g^{*}\) for population \(Q^{*}\), where \(g^{*}\) is determined using the following expression:  
\[g^{*}=\operatorname*{argmax}_{g\in\{0,\ldots,\theta\}}\left(\frac{\sum\limits_ {s=1}^{\Omega}f_{s}^{g}}{\Omega}\right) \tag{16}\]  
Equation (16) implies that a sample is extracted when the average population fitness value is highest. Generally, this extraction generation is closer to the final population generation \(\theta\), but it may or may not be the final population at generation \(\theta\). The objective of using a GA for learning regression parameters is like running a ridge regression to avoid overfitting the training dataset. As a heuristic procedure, in most cases, a GA-based regression model may not outperform OLS in terms of the RMS error. Still, it may provide better generalizability for unseen future cases, leading to improved predictability compared to the traditional OLS regression model. Given a small dataset, three regression parameters, and an initial seeded population, minor initial experiments were conducted to select GA parameters for the experiments. These parameters were \(\Omega\) = 100, \(\theta\) = 200, \(p_{c}\) = 30%, and \(p_{m}\) = 5%. The reader should note that the initial population in the procedure used in this research was always random for each run. This randomization was obtained using a random number that uses computer clock times as a seed for generating a random number. There are random number generators that allow users to define the seed for the random number generation procedure. When such a random number generator is used, the same initial population can be generated for each run by keeping the value of the seed constant. In such cases, the selection of parameters will be essential because then the parameters are the only criteria that will govern the quality of the final results. However, when the initial population for each run is randomly generated using computer clock times, the impact of parameters on the quality of solutions is hard to ascertain. In the case of computer clock time-seeded random numbers for the same set of parameters, slightly different results can be obtained owing to different starting populations. Extensive experiments on GA parameters in such a case are not necessary. Different runs with different initial populations can be conducted, and the percentage improvement criterion highlighted in Equation (15) can be used to separate high-quality results from low-quality results. Additionally, the average fitness of the GA population can be compared with the benchmark mentioned earlier (a value of 0.823) to monitor the gap between the average population fitness and its upper bound value, with a lower gap representing a better solution. The GA literature advises against using very high mutation rate values because high mutation rates introduce randomness [10]. Some randomness is necessary for searching for better solutions, but too much randomness can be detrimental to solution quality [10]. A general rule of thumb is that the crossover rate value should be less than 50%, and the mutation rate value should be less than the crossover rate value.