# Software Product Line Maintenance Using Multi-Objective Optimization Techniques
## 6 Results and Discussion
### Results Generated by Quality Indicators  
The evaluation process for the results of the MOEAs was carried out by using quality multi-objective indicators and a statistical analysis, as discussed in [54,55]. In this research work, two quality indicators were selected to evaluate the results: Hypervolume [56] and Spacing [57]. There is a possibility that the efficiency of the MOEAs may have had an effect on the four objectives, therefore, to measure the better performance of the MOEAs, these two quality indicators were utilized to determine the spread, convergence, and smaller space for the non-dominated solutions generated by the algorithms regarding the Pareto front [55,58]. Table 4 represents the hypervolume and spacing indicators with their average and standard deviation values, respectively, for the 30 \(\mathit{PF}_{\text{contribution}}\) sets generated by each algorithm. To establish a quantitative analysis of the results, the above-mentioned quality indicators were utilized. These quality metrics helped to generate good-quality values [56]. The first column of Table 4 represents the hypervolume and spacing indicators, while the other columns represent the feature models and different algorithms to calculate the average and standard deviation values using the mentioned indicators. The best values are represented in bold in Table 4.  
For hypervolume, higher values are considered the best, while minimum values are taken into account as the best for spacing. To analyze the hypervolume values for Counter-Strike _FM_, it is discovered from Table 4 that the MOEA/D and SPEA2 algorithms originated the best average and standard deviation values (0.7094 and 0.0129) and (0.7022 and 0.0165), respectively. Comparatively, the NSGAIII results are also considered as better (0.6498 and 0.0113). However, in the cases of IBEA (0.2826 and 0.1162) and NSGAII (0.6029 and 0.0234), the generated hypervolume and spacing values are considered to be less than the number of solutions. For the SPL SimulES, PnP _FM_, it can be deduced from Table 4 that the NSGAIII values are not desirable in terms of average and standard deviation (0.5413 and 0.0176), and the same behavior is displayed by IBEA and NSGAII, showing values of (0.2698 and 0.0954), and (0.4659 and 0.0314), respectively. MOEAD generated the best values (0.6524 and 0.0150) in contrast to the other MOEAs. The values of SPEA2 are sufficient for creating the optimal values of the average and standard deviation (0.6390 and 0.0155). Figure 5: Non-dominated solution values for different feature models. In the case of the Smart Homev2.2 _FM_, nearly the same average values with a minor difference in standard deviation (0.6885 and 0.0160) and (0.6843 and 0.0198) can be generated by both the MOEA/D and SPEA2. NSGAIII remained deliberate in terms of producing good result values (0.6052 and 0.0300) for the Smart Homev2.2 _FM_. Nonetheless, the performances of IBEA and NSGAII are observed to be unsatisfactory, as they generated (0.3460 and 0.1105) and (0.5742 and 0.0353) values, respectively. While considering the results of the Video Player _FM_, the SPEA2 and MOEA/D both produced almost the same average values with an insignificant difference in standard deviation, (0.6961 and 0.0155) and (0.6864 and 0.0193). NSGAIII stayed deliberate concerning producing desirable result values (0.6085 and 0.0262) for the Smart Homev2.2 _FM_. On the other hand, IBEA and NSGAII delivered unsatisfactory performances and generated (0.3659 and 0.0969) and (0.5795 and 0.0108) values for the average and standard deviation, respectively. After analyzing the results of the Model Transformation _FM_, the MOEA/D and SPEA2 both generated approximately the same average values but with a minor difference in standard deviation values, (0.6009 and 0.0146) and (0.6136 and 0.021). NSGAIII was found to originate better result values (0.5276 and 0.021) for the Smart Homev2.2 _FM_.