# Exploring Evolutionary Algorithms for Multi-Objective Optimization in Seismic Structural Design
## 4 Results
### Most Productive Countries and Networks of Global Collaboration  
Table 5 lists the top ten most productive countries according to the quantity of publications and citations. First place went to Iran (\(n=168\)), next to China (\(n=143\)) and USA (\(n=110\)). With 54 and 45 publications, respectively, Italy and Greece ranked fifth and sixth. With between 18 and 41 publications for each, the remaining five countries are Japan, the UK, Turkey, Korea, and Canada. The USA scored first (\(n=1814\)) based on the number of citations, followed by Iran (\(n=1701\)), China (\(n=1081\)), and Italy (\(n=1028\)). At the point of this study, they were the only four nations to obtain more than 1000 citations. Following, in order, were Turkey and Greece with 821 and 586 citations, respectively, and then the United Kingdom and Canada with 522 and 231 citations. There were limited citations for Spain, Israel, Canada, and three other top ten countries. Figure 5: One hundred of the most popular author keywords as word clouds. Figure 6: Co-occurrence network for the top 100 author keywords in popularity. Based on the data we were able to obtain, articles about multi-objective optimization of structural systems with seismic design using evolutionary computation, metaheuristics, and nature-inspired algorithms have been published in 46 countries. Figure 7 depicts the cross-country cooperation network of 26 partner countries. In Figure 7, every node stands for a country. Nodes' sizes represent the number of publications, and the level of cross-country collaboration is shown by the thickness of the lines connecting nodes. Six distinct clusters can be found. Iran, Germany, Korea, and five other countries (Canada, Thailand, the UK, Japan, and Portugal) make up the largest group (red). Six nations make up the second cluster (green), with China at the center. The third group consisted of Turkey, Italy, Austria, and Colombia (purple), while the fourth group (blue) had Argentina, Mexico, Spain, and Chile. The last two clusters, Cyprus and Greece and India and Afghanistan, respectively, have just two partners. A few nations that are absent from Table 5 but included in Figure 7 are Chile, Spain, Mexico, Argentina, Colombia, Cyprus, and Austria. Because these countries have international cooperation with other countries in this field, they are not among the top 10 countries with the highest production. In this study, the research productivity of countries was evaluated according to the total number of publications. However, it should be noted that such an evaluation does not take into account important factors such as the population of each country. Research productivity should be normalized relative to the population in order to evaluate the scientific contributions of a country more fairly. Countries with larger populations may  
Figure 7: Network of 26 countries that are partners engaged in cross-border collaboration. \begin{table}
\begin{tabular}{c l c c c c} \hline \hline
**Order** & **Country** & **Total Papers** & **\%** &
\begin{tabular}{c} **Total** \\ **Citations** \\ \end{tabular} & **\%** \\ \hline
1 & Iran & 168 & 25.30 & 1701 & 20.97 \\
2 & China & 143 & 21.53 & 1081 & 13.33 \\
3 & Usa & 110 & 16.56 & 1814 & 22.37 \\
4 & Italy & 54 & 8.13 & 1028 & 12.67 \\
5 & Greece & 45 & 6.77 & 586 & 7.22 \\
6 & Japan & 41 & 6.17 & 150 & 1.85 \\
7 & UK & 33 & 4.96 & 522 & 6.43 \\
8 & Turkey & 28 & 4.21 & 821 & 10.12 \\
9 & Korea & 24 & 3.61 & 174 & 2.14 \\
10 & Canada & 18 & 2.71 & 231 & 2.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ranking of the top ten countries about output in terms of publications and citations. naturally have more researchers and therefore more publication potential. Normalized metrics such as the number of publications per population may provide more accurate results when comparing the scientific productivity of countries. For example, countries with smaller populations may be more productive in terms of scientific contributions relative to their populations.