**5.3. Computational complexity**

Table 3 shows the execution times required to solve these problems. Bold figures show the CPU time normalized to the time required to solve problem 15 using the μGA.

It can be seen how the computational burden of the proposed method is about 20% lower than that of the standard GA by Ngo and Li (Ngo, 1998) (18% in problem 15, 23% in problem 12, and 20% in problems 10 and 16).

On the other hand, the SQ method shows larger execution times in order to obtain similar convergence figures (as noticed in previous sections). Only in problem No. 15 SQ requires less computational load than the MGA algorithm, although, even in this problem, the μGA obtained the results faster. Notice that this reduction in the computational load observed in


GA-based approaches is achieved maintaining a very similar −or even better− percentage of convergence (Table 2) and with the three approaches getting optimal conflict-free solutions.

**Table 3.** Execution times (in seconds) for benchmark problems 10, 12, 14, 15 and 16. CPU: AMD Athlon XP 2100+ 1.8 GHz. Bold figures show the CPU time normalized to the time required to solve problem 15 using the μGA

Comparing the values given in Table 3 for (Ngo, 1998) with the specific values reported in the original author's paper, a small difference can be observed. The reason is that the algorithm has been programmed and run in a different computer and language. In order to get the comparative figures shown in Table 3, both methods were similarly programmed and run in the same computer environment.
