# Software Product Line Maintenance Using Multi-Objective Optimization Techniques
## 6 Results and Discussion
### Discussion of Results and Answers to Research Questions  
It is considered that the solutions generated by every algorithm depended on the related fitness values. The solutions associated with the best results are analyzed to complete the SPL testing assessment, which is also the overall objective of the research. The ability to generate optimal values for four objectives is depicted by the findings revealed in the previous tables. The outcomes of the experiments have the potential to identify better solutions for all the objectives under consideration. Although some disparities may not be statistically meaningful, it can be seen that the approach is a settlement among the conflicting objectives. Hence, due to certain parameters, this is likely to compromise the four objectives. It is worth indicating that the aforementioned results are accomplished by the proposed approach over a reasonable number of generations (500 generations). Different parameters can have an effect on minimizing the number of products, which could be the answer to the first question. To find optimal solutions, the quality testers can gain insight through this direction as to why the testing optimization techniques were adopted. However, there are some considerable cases where the system reliability is higher than the justification for the test cases. This is the benefit of our proposed methodology, which can produce various solutions in terms of coverage as well. The choice would be in the hands of the tester in terms of adopting a better MOEA for a good performance. Single-objective algorithms produce one solution, which may not be an ideal selection in our case, where multiple objectives need to be optimized. The testers can define the priorities for selecting the values of different operators, such as the crossover rate and mutation rate, to affect the experiment results of different product lines. \begin{table}
\begin{tabular}{l l l} \hline \hline \multirow{2}{*}{**Feature Models**} & \multicolumn{2}{c}{**Quality Indicators**} \\ \cline{2-3}  & **Hyper Volume** & **Spacing** \\ \hline Counter Strike & MOEA/D, SPEA2, NSGAIII & MOEA/D, SPEA2, NSGAIII \\ \hline SPL SimulES, PnP & MOEA/D, SPEA2 & MOEA/D, SPEA2, NSGAIII \\ \hline Smart Home v2.2 & MOEA/D, SPEA2, NSGAIII & MOEA/D, SPEA2, NSGAIII \\ \hline Video Player & MOEA/D, SPEA2, NSGAIII & MOEA/D, SPEA2 \\ \hline Model Transformation & MOEA/D, SPEA2, NSGAIII & MOEA/D, SPEA2, NSGAIII \\ \hline Coche Ecologico & MOEA/D, SPEA2, NSGAIII & SPEA2, NSGAIII, \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Better MOEA algorithm concerning indicators (HV and spacing). The best solutions are identified to assess each feature model. The quality indicators from the optimization field, such as hypervolume and spacing, are also utilized. In consideration of Research Question 2, the results have a clear impact on the performance of the algorithms with the four objectives optimization, as discussed in detail in the different tables. In this section of four objectives, the versatility of the generated results is demonstrated. However, it is determined that, for all the SPL feature models, IBEA generated the worst results in terms of optimization. MOEAD, SPEA, and NSGAIII performed well in all cases of feature models with small, medium, and larger sizes. Table 4 presents an analysis of the percentage of non-dominated solutions generated by the different MOEAs. Again, SPEA2 surpassed and originated the maximum percentage of non-dominated solutions for all the _F_Ms. Similarly, MOEA/D and NSGAIII also produced a better percentage of solutions. However, the numbers of solution percentages in the cases of IBEA and NSGAII were not comparatively found to be good and generated a lower percentage of non-dominated solutions. According to Table 5, reasoning with the average and standard deviation results of the hypervolume and spacing quality indicators obliged in the proposed approach, SPEA2 also achieved the best results using the hypervolume and spacing quality indicators.