# Enhanced Hybrid Algorithms for Inverse Problem Solutions in Computed Tomography
## 5 Discussion  
In this section, we discuss the conclusions drawn from the results obtained from the tests included in Examples 1, 2, and 3 from Section 4. Example 1 aimed to compare and select the optimal metaheuristic optimization algorithm for further research. Based on experience, knowledge, and a review of the scientific literature, the optimization multi-agent algorithms chosen were ABC and JS. Therefore, we compared these two algorithms. In this comparison, the ABC algorithm performed significantly better and was subsequently used to create the hybrid algorithm (see Example Section 4.2). In each of the tests conducted, the value of the fitness function was significantly lower for ABC than for JS, as can be seen in Figures 6, 9, 12, 15 and 18. Figures 6-8 present the results of identifying the polygon using a single circle. These figures compare the outcomes obtained from the two tested metaheuristic algorithms. Figure 6 shows the fitness function values over successive iterations for both algorithms. It is evident that ABC achieved significantly lower objective function values in every iteration. Figure 7 displays the result of identifying the polygon shape using a single circle. Using only one circle, of course, does not closely approximate the polygon's shape; however, as shown in the figure, the circle covers a large portion of the original polygon. The circle was slightly better fitted in the case of ABC. The energy absorption level is shown in Figure 8. In this case, JS achieved a slightly better value, but overall (shape identification and energy absorption values), ABC produced better results. Figures 9-20 show analogous results for the cases using two, three, four, and five circles, respectively. All the tests show that ABC far outperforms the JS. In particular, Figures 16 and 19 illustrate this well, showing the recreation of the polygon shape using four and five circles, respectively. In the case of ABC, the circles cover the polygon relatively well, while for JS, the coverage does not  
Figure 33: The shapes and arrangement of the polygons in the domain. look as good. It is also worth noticing that the time needed to perform the calculations grew according to the amount of circles used for the identification (ranging from around 22,000 ms with one circle to around \(237,000\) ms with five circles). Because of ABC's overall better performance, it was used in the next series of tests using the hybrid approach. It is important to note that the value of fitness function tends to drop significantly during first few iterations, but the decrease then slows significantly; this observation might suggest that this approach is not the most time-efficient and perhaps some of the time needed for evaluation may be saved by reducing the number of iterations without a significant difference to the fitness function value. In the second example, we developed a hybrid algorithm based on ABC (metaheuristic multi-agent optimizer) and the Hooke-Jeeves (HJ) and Nelder-Mead (N-M) methods (deterministic methods). In this example, we compared both deterministic methods within the hybrid algorithm by testing their performance in the problem of localization for a single polygon. Both methods produced very similar results. However, the primary goal of this example was to compare the performance of the hybrid algorithm with that of the algorithm based solely on ABC (Example 1). It turned out that the hybrid algorithm performed significantly better in addressing the problem considered. This is confirmed by the calculation results. For example, Figure 31 presents the fitness function values obtained for the ABC and hybrid algorithms. In particular, for three and five circles, the hybrid algorithm returned significantly better results. A visual comparison of the figures related to shape identification using circles (between Examples 1 and 2) already suggests that the hybrid algorithm performed significantly better on the problem than the metaheuristic algorithm.