## 4 Experimental Results
### SACT Statistic Review
(**c**) SACT, DMU08 (30 tests). (**d**) SACT, DMU09 (30 tests). (**e**) SACT, DMU10 (30 tests). of the bar plot the frequency is 1 and the quality results is 4036. At the far right of the bar plot the frequency is 4 and the quality results is 4096. For DMU48 (Figure 15c), 9 results out of 30 obtained, have a makespan value better or equal to the midpoint and are within the range 3878-3900. At the far left of the bar plot the frequency is 1 and the quality results is 3878. At the far right of the bar plot the frequency is 1 and the quality results is 3988. For DMU49 (Figure 15d), 12 results out of 30 obtained, have a makespan value better or equal to the midpoint and are within the range 3831-3849. At the far left of the bar plot the best frequency is 1 and the quality results is 3831. At the far right of the bar plot the frequency is 3 and the quality results is 3876. For DMU50 (Figure 15e), 15 results out of 30 obtained, have a makespan value better or equal to the midpoint and are within the range 3842-3868. At the far left of the bar plot the best frequency is 1 and the quality results is 3842. At far right of the bar plot the frequency is 6 and the quality results is 3907. Figure 15: Cont. Table 5 presents the MS results with SACT for medium benchmarks. For all the benchmarks, the optimum value is reached (RE = 0). For most benchmarks, a small value of standard deviation (\(\sigma<\) 7) is obtained. The exception is the LA38 problem with the highest standard deviation of 21; however, this value is less than half of the arithmetic mean (mean) and this represents little dispersion of the data, however the dispersion of the data found by SACT in a frequency distribution for medium-sized benchmarks, is greater than the dispersion found for small-sized benchmark data. LA29 finds the optimal solution in 54 s. LA40 finds in 37 min. TA07 finds the optimal solution in 99 s and TA07 finds in 85 min. More than half of the benchmarks of medium size have a mode equal to the optimal solution. For most benchmarks, the median obtained is not the optimal solution. The most difficult problems for obtaining the optimal solution according to the mode and median were the benchmark LA40, TA03, TA05 to TA08, and TA10. LA40 was the most complicated of these benchmarks, the optimal solution was obtained in only one of the 30 executions, where the median and mode were furthest from the optimal value. Table 5 shows, based on the standard deviation that the data distribution in each benchmark is completely homogeneous and the data are grouped very close to each other or with the same optimal value. LA38 presents the data a little more dispersed (\(\sigma\) = 20.6). Table 6 presents the MS results with SACT for large benchmarks. Most of the obtained values are close to the upper bound (UB), four of the benchmarks achieve this value. TA28 finds the greatest relative error (RE = 0.87%). TA22, TA30, YN3, and YN4 find the lowest RE = 0. The DMU benchmarks (46-50) are an exception because DMU49 finds the largest RE = 3.06 and DMU47 finds the lowest RE = 2.08. The largest standard deviation was 41.8 for the problem DMU08, and the lowest standard deviation was 4.9 for the problem YN1; however, this value is less than half of the arithmetic mean (mean) and this represents little dispersion of the data, however the dispersion of the data found by SACT in a frequency distribution for large-sized benchmarks, is greater than the dispersion found for small-sized benchmark data and medium-sized benchmark data. The mean is greater than the median and mode for DMU06 to DMU08 and DMU10, but with very close values, indicating very little skewed frequency distributions (see Figure 14). With DMU09 the mean is between the median and the mode indicating that the frequency distribution is close to a symmetrical distribution (see Figure 14). The mean is less than the median and mode for DMU46 to DMU47 and DMU49, but with very close values, indicating very little skewed frequency distributions (see Figure 15).