## 7 Conclusions  
This paper proposed and evaluated some strategies developed to improve the performance of search procedures over low-dimensionality multimodal domains. This problem definition corresponds to common conditions for optimization problems in mechanical engineering. All the examined strategies can be individually integrated within any existing algorithm. The present analysis assembled them to form a competitive optimization algorithm named S-EPSO. Essentially, this algorithm requires no niching parameters to locate and maintain multiple optima. The first tactic put forward gives socio-emotional personalities to the individuals. Depending on their personality, the particles can naturally adopt various roles during the search evolution. The main idea imitates a simplified representation of socio-emotional relations prevailing during mammal reproduction periods. Some particles echo a female personality, whereas two male personalities form the remaining particle group. Some males are intrepid and explore the landscapes, while others are more prudent. This second group is thus responsible for preserving the found optima and gives the swarm a natural tendency to form clusters around fitting positions. Moreover, less performant males are prone to premature death. The analysis introduces a strategy to help particles visit secluded zones. The proposed approach controls the initial particle distribution. It allots the particles to subdomains of the landscape based on biased decisions reflecting the subdomain's potential. The technique first reduces the domain dimensionality based on a sensitivity index. After that, it evaluates the potential of each subdomain to contain optima. This evaluation rests on a balanced combination of the jaggedness and the mean-average interval descriptors developed in the present analysis. Finally, an intermediate step tries, based on interpolated evaluations, to identify more performant positions for a fraction of the particles. The last part of the study contrasts the S-EPSO performance with those of state-of-the-art algorithms. When compared over seventeen functions of the CEC benchmark ranging from 1 to 5D, S-EPSO demonstrated an excellent overall performance. The comparison showed for 30 specific evaluations, suitable for differentiating among the tested algorithms \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Problem** & **Variable** & \(\boldsymbol{\gamma^{*}-20}\)**,000** & \(\boldsymbol{\gamma^{*}-0.05}\) \\ \hline \multirow{8}{*}{PV} & Best \(f_{PV}\) & 6059.714336 & 6059.714336 \\  & Worst \(f_{PV}\) & 6059.714336 & 6059.714336 \\  & Std. Dev. & 0.0 & 0.0 \\  & \(T_{h}\) & 0.437500 & 0.437500 \\  & \(T_{s}\) & 0.812500 & 0.812500 \\  & \(L\) & 176.636596 & 176.636596 \\  & \(R\) & 42.098446 & 42.098446 \\ \hline \multirow{8}{*}{S SpRe R} & Best \(f_{SR}\) & 2994.554224 & 2994.554224 \\  & Worst \(f_{SR}\) & 2994.554224 & 2994.554224 \\  & Std. Dev. & 0.0 & 0.0 \\  & \(b\) & 3.5000 & 3.5000 \\  & \(m\) & 0.7000 & 0.7000 \\  & \(z\) & 17 & 17 \\  & \(l_{1}\) & 7.3000 & 7.3000 \\  & \(l_{2}\) & 7.715320 & 7.715320 \\  & \(d_{1}\) & 3.350541 & 3.350541 \\  & \(d_{2}\) & 5.286654 & 5.286654 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: S-EPSO results for the PV and SpRe problems with \(\gamma^{*}\) set at 20,000 and 0.05.  
that S-EPSO produced the best performance 14 times, whereas ANDE and NMMSO presented the best results 9 and 10 times, respectively. The global S-EPSO response thus clearly indicates that S-EPSO constitutes a competitive optimization algorithm. Specifically, S-EPSO demonstrated its best performance with the more challenging functions of the benchmark. It outperformed the reference algorithms over most of the evaluations done over the 3 and 5D domains. Finally, the last two real-world problems demonstrate that S-EPSO can handle domains of higher dimensionality than its original frame of reference and that it also performs well in constrained optimization problems.