## 5 Results Using Test Data Obtained with FEM Model
### The Use of Memory Assistance  
Although ABC was the best among the tested methods, the calculation times using ABC were longer than the calculation times using other methods. Although the pre-calculation of time-consuming Bessel functions was used (Section 2.2), it will be useful to shorten the calculation time. We used Memory Assistance [70].  
We used two different Memory Assistances:  
* Short-Term Memory Assistance (STMA): After each iteration, the whole population is saved into memory, and, in each iteration, the population members are compared with members from only one previous iteration. In this approach, only memory is used for one population set. In the presented case, this is ((5 parameters + OF) \(\times\) 30 population members) memory locations.
* Long-Term Memory Assistance (LTMA): Each population member is compared with all the members written into memory, obtained from all the previous iterations. If the calculated member is not found in the memory, it is added to the memory. The search in the memory starts from the last added to the first added. When the same population member is found, the search is finished. Theoretically, ((5 parameters + OF) \(\times\) 30 population members \(\times\) 600 iterations) locations of memory can be used.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Calculation** & \multicolumn{4}{c}{**Method**} \\
**Times/Subarea** & **DE/rand/1/exp** & **DE/rand/2/exp** & **DE/best/1/bin** & **TLBO** & **ABC** \\ \hline \(t\) (s)/AD & 4.22 & 4.88 & 16.67 & 7.25 & 33.25 \\ \(t\) (s)/AE & 4.83 & 5.34 & 17.90 & 5.45 & 39.12 \\ \(t\) (s)/AF & 14.60 & 14.95 & 14.27 & 4.01 & 41.07 \\ \(t\) (s)/BD & 5.11 & 15.20 & 30.87 & 5.79 & 35.66 \\ \(t\) (s)/BE & 5.18 & 5.96 & 11.22 & 9.20 & 33.40 \\ \(t\) (s)/BF & 4.50 & 5.05 & 29.05 & 3.73 & 36.35 \\ \(t\) (s)/CD & 4.31 & 5.86 & 15.92 & 3.80 & 32.99 \\ \(t\) (s)/CE & 5.00 & 13.84 & 26.81 & 5.19 & 31.43 \\ \(t\) (s)/CF & 4.70 & 5.32 & 35.77 & 6.00 & 34.34 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Mean calculation times for 50 independent runs.  
Figure 9: Convergence of the evolutionary methods for (**a**) AD subarea, (**b**) AE subarea, (**c**) AF subarea, (**d**) BD subarea, (**e**) BE subarea, (**f**) BF subarea, (**g**) CD subarea, (**h**) CE subarea and (**i**) CF subarea.  
The STMA algorithm is presented in Figure 10 and the LTMA algorithm is shown in Figure 11.  
The expression \"record\" used in Figures 10 and 11 means one set of parameters + OF's values (\(\rho_{1}\), \(h_{1}\), \(\rho_{2}\), \(h_{2}\), \(\rho_{3}\), OF). An appropriate precision must be set, as these are differences in the parameters for which duplication may be identified. These values depend on the physical background of the problem, and they determine the decimal accuracy of the calculated parameters. The precisions used for the identification of duplications are presented in Table 15.  
Figure 11: Algorithm presenting Long-Term Memory Assistance (LTMA).  
Figure 10: Algorithm presenting Short-Term Memory Assistance (STMA).  
From Table 16, it can be seen that with the use of Memory Assistance, the calculation time was shortened by 21% in both cases, using STMA and LTMS. Although the mean number of duplications in the case of LTMA was 2643, which is higher than 1682 in the case of STMA, the memory handling time was longer in the case of LTMA compared to STMA. The advantage of STMA is its much lower use of memory space, and, accordingly, it can be concluded that STMA is a better choice for the presented problem.  
It is important to emphasize that the use of Memory Assistance is not required; it is just a suggestion if we want to reduce the time of soil parameters' determination.