## 5 Conclusions  
In this paper, we have proposed a novel coupling algorithm named MGSO-BFO. Our proposed algorithm divided the population into two parts to achieve good balance between exploration and exploitation. Part I is in charge of exploitation by GSO and part II is in charge of exploration by BFO. What's more, we introduced the simulation binary crossover (SBX) and polynomial mutation into the MGSO-BFO to enhance the convergence and diversity ability of the algorithm. In order to demonstrate the effectiveness of the proposed algorithm in this paper, we experimentally compare MGSO-BFO with NSGA-II, SPEA2, PNIA and MOEA/D on the benchmark function. The study shows that the non-dominated solution obtained by MGSO-BFA is better than those obtained by NSGA-II, SPEA2, PNIA and MOEA/D in terms of both convergence and diversity. However, we did not consider the expense of computational time in the whole experiment. Future research should include further modifications and take steps to analyze its impact on the convergence of MGSO-BFO. The \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Parameter (D Stands for Dimension)** \\ \hline NSGA-II [22] & \(pc=1,pm=\frac{1}{D}\) \\ \hline SPEA2 [25] & \(pc=1,pm=\frac{1}{D}\) \\ \hline PNIA [26] & \(pc=1,pm=\frac{1}{D}\) \\ \hline MOEA/D [23] & \(\mathrm{T}=20,\delta=0.9,n_{r}=2\) \\ \hline MGSO-BFO & \(p_{ed}=0.25\),\(N_{ed}=4\),\(N_{c}=20\),\(N_{s}=3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter settings of 4 different algorithms. fitness calculation-based selection process can be improved to reduce the computational complexity of MGSO-BFO. Figure 3: The results of dynamic performance comparison. **Author Contributions:** Writing--original draft preparation, Y.W. ; writing--review and editing, Z.C. ; visualization, W.L. **Funding:** This work is supported by the National Natural Science Foundation of China under Grant No. 61806138, No. U1636220 and No. 61663028, Natural Science Foundation of Shanxi Province under Grant No. 201801D121127, PhD Research Startup Foundation of Taiyuan University of Science and Technology under Grant No. 20182002, Zhejiang Provincial Natural Science Foundation of China under Grant No. Y18F030036. **Conflicts of Interest:** The authors declare no conflict of interest. * (20) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Bat algorithm with triangle-flipping strategy for numerical optimization. _Int. J. Mach. Learn. Cybern._**2018**, \(9\), 199-215. [CrossRef]
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