## 5 Conclusions and Perspectives  
In this paper, a new Distributed Bi-behaviors Crow Search Algorithm (DB-CSA) is proposed for the dynamic treatment of both convergence and diversity concepts, based on two new mechanisms: distributed bi-behavior profiles, characterized by a large Gaussian Beta-1 and narrow Gaussian Beta-2 functions for exploitation and exploration enhancement, respectively. All quantitative results were analyzed using the non-parametric Wilcoxon signed rank test with a 0.05 significance level. The experimental studies showed that the proposed DB-CSA is significantly better than the state-of-the-art methods. The novel DB-CSA-II algorithm achieved good results for solving dynamic multi-objective problems characterized by different types of dynamic change in the POS and the POF including 2 or 3 conflicting objective functions. The comparative study (1) included seven transfer-learning based methods (MMTL-MOEA/D, KF-MOEA/D, PPS-MOEA/D, SVR-MOEA/D, Tr-MOEA/D, and RI-MOEA/D) used the MIGD metric and the five popular DMOEAs (DNSGA-II, dCOEA, PPS, MOEA/D and SGEA) to solve twenty-one DMOPs with different types of changes on both POF and POS using the IGD and HVD quality indicators and it is proved that the proposal relative results are better for all test beds. Based on the comparative study (2), we can resume the efficiency of DB-CSA system compared to thirteen MaOEAs (MSOPS-II, MOEA/D, HypE, PICEA-g, SPEA/SDE, GrEA, NSGA-III, KnEA, RVEA, Two_Arch2, \(\theta\)-DEA, MOEA/DD, AnD) for solving sixteen many-objective optimization problems (9 WFG and 7 MaF) with 2, 3 and 7 objectives, as well as the more complex DTLZ and WFG test suites with 3, 5, 8, 10 and 15 objectives compared to the seven MaOEAs (PMEA-MA, PMEA*-MA, SPEA2/SDE, NSGA-II/SDR, MaOEA/IGD, VaEA, SPEA). All results confirmed the relevance of the proposed DB-CSA approach and its capacity to correctly manage convergence and diversity concepts when solving DMOPs and MaOPS. For future works, it is recommended to investigate the impact that the beta-profiles have on performances when solving a DMOP characterized by a time-varying POS and POF, a dynamic spread or the dynamic density of the approximated solution set with a nonlinear correlation between the decision variables. Both variants of the DB-CSA method are worthy of consideration when solving a set of Evolutionary Transfer Multi/Many-objective Optimization Problems. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12199627/s1](https://www.mdpi.com/article/10.3390/app12199627/s1)]([https://www.mdpi.com/article/10.3390/app12199627/s1](https://www.mdpi.com/article/10.3390/app12199627/s1)), Table S1: MIGD results (Mean and Standard Deviation) of the 6 DMOEAs [15] compared to the standard CSA and the proposed DB-CSA algorithm for solving FDA and dMOP functions; Table S2: IGD results (Mean and Standard Deviation) of the 5 DMOEAs [11] compared to the standard CSA and the proposed DB-CSA algorithm for solving FDA and dMOP functions; Table S3: HVD results (Mean and Standard Deviation) of the 5 DMOEAs [11] compared to the standard CSA and the proposed DB-CSA algorithm for solving FDA and dMOP \begin{table}
\begin{tabular}{l c c c c c c} \hline
**DMOPs** & **MMTL-MOEA/D** & **KF-MOEA/D** & **PPS-MOEA/D** & **SVR-MOEA/D** & **Tr-MOEA/D** & **DB-CSA-II** \\ \hline FDA1 & 5.83 & 3.55 & **3.11** & 4.85 & 42.54 & 10.32 \\ FDA2 & 5.40 & 3.46 & **3.08** & 4.63 & 45.27 & 12.86 \\ FDA3 & 5.09 & 3.92 & **3.64** & 4.78 & 57.71 & 14.96 \\ FDA4 & 10.06 & 9.78 & 13.32 & **9.66** & 132.59 & 21.92 \\ FDA5 & **9.94** & 10.24 & 14.83 & 11.52 & 115.52 & 19.85 \\ dMOP1 & **7.05** & 7.25 & 8.96 & 8.34 & 80.23 & 9.05 \\ dMOP2 & 7.74 & **4.02** & 4.93 & 4.47 & 73.53 & 9.29 \\ dMOP3 & 5.63 & **3.52** & 4.15 & 4.61 & 75.55 & 9.73 \\ \hline \end{tabular}
\end{table} 
Table 11: Run-times of DMOEAs for Solving FDA and dMOP Test Suites (Unit: Seconds).