## 6 Experiments
### All Maximum Cliques with Minimum Sum of Their Weights in Complete Weighted Graph  
ALG_1 to ALG_9 were compared with each other, and the results of these comparisons are included in Tables 1 and 2. These tables contain the averages of 10 measurements. The obtained results are the averages of the smallest sum of the weights of all determined maximal cliques, and these averages are given in thousands. The weight of a single edge is generated as a number between 1 and 100. The parameters that changed during the tests were as follows: \(m\)--the number of vertices in any part of the graph; \(d\)--the number of graph parts; \(lm\)--the number of ants; \(lc\)--the number of cycles; \(p\)--the pheromone evaporation coefficient. The use  
Table 1 shows the results obtained when the number of vertices in each part of the graph \(m\) changes while the number of graph parts \(d\), the number of ants \(lm\), the number of cycles \(lc\), and the evaporation rate \(\rho\) are constant. It can be seen that ALG_6 and ALG_7 show increasingly better results compared to the other algorithms as the number of vertices in the graph section increase.  
Figure 4 presents the deviation in the results obtained by the other proposed algorithms in relation to the baseline algorithm ALG_1 [5]. The deviation is calculated according to the formula  
\[\frac{W_{ALG\_1}-W_{ALG\_x}}{W_{ALG\_1}} \tag{22}\]  
where  
WALG_1 represents the minimum sum of the weights of all maximum clicks obtained from ALG_1; WALG_x represents the minimum sum of the weights of all maximum clicks obtained from the remaining algorithms (ALG).  
It is clear that ALG_6 and ALG_7 achieve increasingly better results compared to the original algorithm ALG_1 from the literature [5] as the number of vertices in each part of the graph increases. Therefore, when the search space becomes larger, ALG_6 and ALG_7 perform better than the other algorithms.  
Table 2 shows the results obtained when the number of vertices in each part of the graph \(m\) is constant; the number of graph parts \(d\) changes; and the number of ants \(lm\), the number of cycles \(lc\), and the evaporation rate \(\rho\) are constant. It can be seen that ALG_6 and ALG_7 show increasingly better results compared to the other algorithms as the number of graph sections increases.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**d:** & **20** & **25** & **30** & **35** & **40** \\ \hline ALG\_1 & 206.6 & 336.0 & 496.4 & 689.0 & 912.6 \\ ALG\_2 & 205.0 & 332.4 & 492.3 & 684.7 & 907.2 \\ ALG\_3 & 204.4 & 332.5 & 492.8 & 684.5 & 907.1 \\ ALG\_4 & 204.6 & 331.5 & 492.6 & 683.5 & 906.6 \\ ALG\_5 & 204.2 & 332.8 & 492.9 & 683.4 & 906.9 \\ ALG\_6 & 201.7 & 328.8 & 487.1 & 677.2 & 897.8 \\ ALG\_7 & 200.9 & 328.3 & 487.3 & 677.4 & 899.2 \\ ALG\_8 & 203.1 & 331.2 & 490.0 & 681.6 & 902.1 \\ ALG\_9 & 203.3 & 331.4 & 490.6 & 681.0 & 902.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Sumed weights of maximum cliques: \(m=20\), \(lm=10\), \(lc=30\), \(\rho=0.995\).  
Figure 4: Sumed weights of maximum cliques: \(m\) changes, \(d=25\), \(lm=10\), \(lc=30\), \(\rho=0.995\).  
Figure 5 also shows how the deviation in the results obtained by the other proposed algorithms changes in relation to the base algorithm ALG_1 [5] as the number of graph parts increases. Here it can be seen that the increase in the dimensions of the maximum cliques determined reduces the benefits gained by the proposed ant colony algorithms compared to those gained by the previously published algorithm [5].