# Using Optimization Techniques in Grammatical Evolution
## 3 Results
### Experimental Results
Significantly, it achieves a markedly lower median regression error than its predecessor, NNC, as indicated by the blue dots and supported by the three asterisks (***). This pattern of results underscores the broader applicability of the NNC-S method's local optimization enhancements, not only in classification accuracy but also in reducing regression errors. Additionally, the effectiveness and the robustness of the proposed method was evaluated by performing additional experiments with different values for the critical parameter \(g\) of the suggested Simulated Annealing variant. This parameter is used to control the number of random changes performed on any given chromosome. The experimental results in the classification datasets are shown in Table 4. Clearly, no significant variation in the performance of the proposed technique occurs when this critical parameter is varied. Figure 4: Scatter plot illustrating the variability and median classification error rates for six machine learning algorithms, with statistical significance denoted by asterisks. The asterisk-based notation above the clusters denotes statistical significance levels. The NNC-S method demonstrates notably lower error rates, as evidenced by the high statistical significance relative to other methods, which may indicate its superior performance in classification tasks. Continuing from the previous analysis, Figure 6 presents the classification error rates for variations of the NNC-S algorithm with differing values of the parameter \(g\). The plot aims to evaluate whether changes in the parameter \(g\) led to statistically significant differences in the algorithm's classification performance. The horizontal bars on the plot indicate the median classification error for each variation of the NNC-S method, providing a clear comparison across the different parameter values. The statistical annotations (\"ns\" for not significant, \"**\" for \(p<0.01\), and \"***\" for \(p<0.001\)) are used to denote the statistical significance of the differences between the groups. It appears that some variations, particularly between NNC-S (\(g=2\)) and NNC-S (\(g=5\)), as well as between NNC-S (\(g=10\)) and NNC-S (\(g=20\)), do not show significant differences in performance (denoted by \"ns\"). In contrast, other comparisons do reveal significant differences, suggesting that certain values of \(g\) can indeed impact the classification error rates of the NNC-S algorithm. In addition, in the graph of Figure 7, a comparison is made for the average execution time of each experiment for the classification datasets. The comparison was made between the initial method (denoted as NNC in the graph) as well as the various cases of the proposed technique by changing the parameter \(g\) to 5, 10, and 20. As expected, adding the local minimization technique to the Grammatical Evolution method significantly increases the execution time of the method; however, this increase remains almost constant for different values of the critical parameter \(g\). Moreover, by using parallel techniques that appear in the relevant literature this increase in execution time could be reduced. Figure 5: Scatter plot of regression error rates for various regression methods, demonstrating the distribution, median error rates, and statistical significance of differences in performance. The asterisk-based notation above the clusters denotes statistical significance levels The NNC-S method, shows statistically significant improvements in accuracy over the NNC method, underlining the efficacy of local optimization enhancements in regression tasks. The y-axis is presented on a logarithmic scale to clearly visualize the range of error magnitudes across methods. Figure 6: This figure examines the impact of varying the parameter g on the NNC-S algorithm’s classification errors, revealing that while some parameter adjustments do not significantly affect performance, others result in noticeable differences, as indicated by the statistical significance annotations.