# Optimization Algorithms for Detection of Social Interactions
## 4 Results  
In this section, all the experiments and comparisons performed on the two proposed algorithms, Opt-IA and Hybrid-IA, are presented, in order to assess their efficiency and robustness in detecting highly linked communities. Different social networks have been taken into account for the experimental analyses conducted on the two algorithms, and for their comparison with other efficient metaheuristics which are present in literature. The instances are well-known networks used for the community detection problem and their characteristics are summarized and reported in Table 1. _Gravy's Zebra_[16] is a network created by [PERSON] et al. in which a link between to nodes indicates that a pair of zebras appeared together at least once during the study. In _Zachary's Karate Club_[17] network, collected by [PERSON] in 1977, a node represents a member of the club and an edge represents a tie between two members of the club. _Bottlenose Dolphins_[18] is an undirected social network of dolphins where an edge represents a frequent association. _Books about US Politics_[19] is a network of books sold, compiled by [PERSON], where edges represent frequent co-purchasing of books by the same buyers. Another network considered is _American College Football_[1], a network of football games between colleges. _Jazz Musicians_[20] is the collaboration network between Jazz musicians. Each node is a Jazz musician and an edge denotes that two musicians have played together in a band. These specific networks have been chosen because they are the most used as test benches and, consequently, allowed us to compare our algorithms with several others and, in particular, with different metaheuristics. Although there exist bigger networks in literature, large and meaningful comparisons are more difficult to develop. For all experiments carried out and presented in this section, both Opt-IA and Hybrid-IA maintain a population of B cells of size \(d=100\), whereas the number of generated clones depends upon the approach used. Since Opt-IA needs high variability, \(dup=10\) has been set for larger networks (\(|V|\geq 100\)), and \(dup=4\) for smaller ones (\(|V|<100\)); \(dup=2\), has been, instead, set in Hybrid-IA for all tested network types. Moreover, the \(m\) and \(P_{die}\) parameters in Opt-IA have been set to 1 and 0.02, respectively; however, for Hybrid-IA, \(\rho\) and \(\tau_{B}\) have been set to 1.0 and 5. Note that all parameters of Opt-IA have been determined through careful tuning experiments, whilst those of Hybrid-IA have been identified both from the knowledge learned by previous works [11; 12], and from a preliminary and not in-depth experiments. As described above, the maximum number of generations has been taken into account as stopping criterion. For all experiments performed in this research work, it was fixed \(MaxGen=1000\) for Opt-IA, and \(MaxGen=100\) for Hybrid-IA. Note that a higher iterations number has been \begin{table}
\begin{tabular}{l r r} \hline \hline _Name_ & \(|V|\) & \(|E|\) \\ \hline Grevy’s Zebras [16] & 28 & 111 \\ Zachary’s Karate Club [17] & 34 & 78 \\ Bottlenose Dolphins [18] & 62 & 159 \\ Books about US Politics [19] & 105 & 441 \\ American College Football [1] & 115 & 613 \\ Jazz Musicians Collaborations [20] & 198 & 2742 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The social networks used in the experiments. considered for Opt-IA due to its blind search, which, for obvious reasons, requires larger time steps to reach acceptable solutions. Initially, the experimental analysis has been focused on the inspection of the efficiency of both algorithms, Opt-IA and Hybrid-IA, in terms of convergence and solution quality found. In Figure 1, the convergence behavior of both Opt-IA and Hybrid-IA on the _Books about US Politics_ network is showed.