## 5 Illustrative Example
### Solution Improvement by Incrementing the SCV Algorithm  
For the second iteration, the combination of GIVs given by the SCV algorithm is: \(1_{1}\{p_{2}\}\), \(2_{1}\{p_{4}\}\), \(3_{1}\{p_{2}\}\), \(4_{1}\{p_{1}\}\), \(5_{1}\{p_{1}\}\); \(1_{2}\{p_{2}\}\), \(2_{2}\{p_{3}\}\), \(3_{2}\{p_{2}\}\), \(4_{2}\{p_{2}\}\), \(5_{2}\{p_{1}\}\); \(1_{3}\{p_{2}\}\), \(2_{3}\{p_{2}\}\), \(3_{3}\{p_{2}\}\), \(4_{3}\{p_{2}\}\), \(5_{3}\{p_{1}\}\). These results are obtained by applying the formalism from Equations (8) and (9). Table 2 shows the associated GIVs for the symbols \(p_{1}\), \(p_{2}\), \(p_{3}\), \(p_{4}\) above. For particle 1, the proposed variant is shown in Figure 6. In this case granularity is \(g_{r}\)= 83% (\(n_{f}\) = 5, \(n_{m}\) = 6), and the reconfiguration time is \(t_{r}\) = 24 min (\(t_{m}\) = 20 min, \(m_{i}\) = 1, \(m_{a}\) = 0). The utility function in this case is \(T_{1}\) = 1, thus variant 4 in Figure 6 might be considered one of the reliable solutions for the machine tool. For particle 2, at iteration 2, the solution is shown in Figure 7. For variant 5 the following results are obtained: granularity \(g_{r}\)= 83% (\(n_{f}\) = 5, \(n_{m}\) = 6), and the reconfiguration time is \(t_{r}\) = 24 min (\(t_{m}\) = 20 min, \(m_{i}\) = 1, \(m_{a}\) = 0). The utility function in this case is \(T_{2}\) = 1, thus variant 5 in Figure 8 may be considered another reliable soluti  
Figure 6: Particle 1 at iteration 2: variant 4. For particle 3, the solution from Figure 8 is proposed after the second iteration. In this case, granularity is \(g_{r}\)= 71% (\(n_{f}\) = 5, \(n_{m}\) = 7), and the reconfiguration time is \(t_{r}\) = 24 min (\(t_{m}\) = 20 min, \(m_{i}\) = 1, \(m_{a}\) = 0). The utility function in this case is \(T_{3}\) = 0.99. One can conclude that after the second iteration of the SCV algorithm, at least two reliable solutions were identified (variant 4 and variant 5, both reaching the target of the utility function and leading to a convergence index equal to 0). The best position in the swarm after the first and second iterations is reached by particle 1 (variant 4:1\(\{p_{2}\}\), 2\(\{p_{4}\}\), 3\(\{p_{2}\}\), 4\(\{p_{1}\}\), 5\(\{p_{1}\}\)). In principle, the SCV algorithm could be stopped after the second iteration. However, continuation with one or two more increments may be useful to see if there is some more potential for innovation (e.g., in this case, particle 3 still has further potential to explore the space of solutions). If the new iterations lead to distancing from the targets for the utility function and the convergence index, algorithm incrementing should be stopped. Thus, the third iteration of the SCV algorithm leads to the following combination of GIVs: \(1_{1}\{p_{1}\}\), \(2_{1}\{p_{3}\}\), \(3_{1}\{p_{1}\}\), \(4_{1}\{p_{1}\}\), \(5_{1}\{p_{1}\}\); \(1_{2}\{p_{1}\}\), \(2_{2}\{p_{2}\}\), \(3_{2}\{p_{1}\}\), \(4_{2}\{p_{1}\}\), \(5_{2}\{p_{1}\}\); \(1_{3}\{p_{1}\}\), \(2_{3}\{p_{1}\}\), \(3_{3}\{p_{1}\}\), \(4_{3}\{p_{1}\}\), \(5_{3}\{p_{1}\}\). Vectors' significance is given in Table 2, with further details in Table 1. The new positions of particles in the swarm are identical with the positions from iteration 1, excepting the fact that particle 1 takes the place of particle 3 and vice versa. Therefore, at the third iterations, particles move away from the maximum position in the searching space. Thus, a new iteration is considered. At the fourth iteration, the space for solution search is given by the following combination of GIVs: \(1_{1}\{p_{1}\}\), \(2_{1}\{p_{3}\}\), \(3_{1}\{p_{3}\}\), \(4_{1}\{p_{3}\}\), \(5_{1}\{p_{1}\}\); \(1_{2}\{p_{1}\}\), \(2_{2}\{p_{4}\}\), \(3_{2}\{p_{3}\}\), \(4_{2}\{p_{3}\}\), \(5_{2}\{p_{1}\}\); \(1_{3}\{p_{1}\}\),  
Figure 8: Particle 3 at iteration 2: variant 6. Figure 7: Particle 2 at iteration 2: variant 5. \(2_{3}\{p_{1}\}\), \(3_{3}\{p_{3}\}\), \(4_{3}\{p_{3}\}\), \(5_{3}\{p_{1}\}\).