## 6 Simulation Results and Discussion
### Numerical Results  
All numerical results attained in the experiments are listed in this section. Tables 3-5 list the averages and standard deviations of the obtained number of temporary nondominated solutions (denoted by N\({}_{\text{n}}\)), the obtained number of nondominated solutions in the Pareto front (denoted by N\({}_{\text{p}}\)), the converge metric GD, and the diversity metric SP, the required run time, the energy consumption values, and the makespan values for three different-sized benchmark problems with N\({}_{\text{sol}}\) = 50, 100, and 150, respectively. In these tables, the best of all the algorithms is indicated in bold, and the proposed BSSO with its nine parameter settings are denoted as BSSO\({}_{0-8}\), respectively, in Tables 3-5. From Tables 3-5, we can make the following general observations:  
1. The lower the \(c_{r}\) value, the better the performance. In the small-size problem, the proposed tSSO\({}_{7}\) with \(c_{p}\) = 0.5 and \(c_{w}\) = 0.3 is the best among all 12 algorithms. However, the proposed tSSO\({}_{8}\) with \(c_{p}\) = 0.5 and \(c_{w}\) = 0.5 is the best one for the medium- and large-size problems. The reason for this is that the number of real nondominated solutions is infinite. Even though in the update mechanism of the proposed tSSO when \(c_{r}\) = 0 there is only an exchange of information between the current solution itself and one of selected temporary nondominated solutions, it is already able to update the current solution to a better solution without needing any random movement. 2. The larger the size of the problem, e.g., N\({}_{\text{job}}\), the fewer the number of obtained nondominated solutions, e.g., N\({}_{\text{n}}\) and N\({}_{\text{p}}\). There are two reasons why this is the case: (1) due to the characteristic of the NP-hard problems, i.e., the larger the size of the NP-hard problem, the more difficult it is to solve; (2) it is more difficult to find nondominated solutions for larger problems with the same deadline of 30 for all problems. 3. The larger the N\({}_{\text{sol}}\), the more likely it is to find more nondominated solutions, i.e., the larger N\({}_{\text{n}}\) and N\({}_{\text{p}}\) for the best algorithm among these algorithms no matter the size of the problem. Hence, it is an effective method to have a larger value of N\({}_{\text{sol}}\) if we intend to find more nondominated solutions. 4. The smaller the N\({}_{\text{job}}\), the fewer the number of obtained nondominated solutions, e.g., There are two reasons for the above: (1) due to the characteristic of the NP-hard problems, i.e., the larger the size of the NP-hard problem, the more difficult it is to solve; (2) it is more difficult to find nondominated solutions for larger problems with the same deadline, which is set 30 for all problems. 5. The smaller the value of N\({}_{\text{p}}\), the shorter the run time. The most time-consuming aspect of finding nondominated solutions is filtering out these nondominated solutions from current solutions. Hence, a new method, called the group comparison, is proposed in this study to find these nondominated solutions from current solutions. However, even the proposed group comparison is more efficient than the traditional pairwise comparison on average, but it still needs O(N\({}_{\text{p}}\)2) to achieve the goal. 6. There is no special pattern in solution qualities, e.g., the value of GD, SP, N\({}_{\text{n}}\), and N\({}_{\text{p}}\), from the final average values of the energy consumption and the makspan. 7. The one with the better number of obtained nondominated solutions also has better DP and SP values. 8. The MOPSO [13] and the original MOSSO [17] share one common factor: each solution must inherit and update based on its predecessor (parent) and its \(pBest\), and this is the main reason that it is less likely to find new nondominated solutions. The above observation is coincident to that observed in item 1. Hence, the proposed tSSO and the NSGA-II [19; 20] are much better than MOSSO [17] and MOPSO [13] in solution quality.