**6. Conclusions**

In recent years, in order to enable MOEAs to handle MaOPs with various characteristics, various MOEAs have been proposed. However, these MOEAs also had their own disadvantages. For example, MOEAs that rely on reference vectors cannot well represent the characteristics of the whole PF when generating reference vectors, which results in the performance degradation of MOEAs. This paper made full use of the advantages of DLS in many-objective optimization (better to maintain convergence and diversity), and proposed DL-TPCEA in combination with the BCE framework. The effective combination of the two strategies can further explore the entire decision space. At the same time, the convergence factor in DLS is further improved according to the evolutionary state of the population in BCE, and then the dynamic convergence factor is proposed to better use the important element of the evolutionary state of the population. This effective combination greatly improves the performance of DL-TPCEA. When compared with five state-of-the-art MOEAs, DL-TPCEA has significant advantages. Finally, in order to verify the performance advantage of DL-TPCEA over the weight-sum based algorithm, DL-TPCEA was compared with the two weight-sum based algorithms, and the results showed that DL-TPCEA still had significant advantages.

In addition, the original DLS used *Iε*+ to maintain individual convergence and a diversity maintenance mechanism based on *Lp*-norm distance to maintain diversity. In this paper, the *CV* indicator is used to maintain individual convergence, and the comparison between *CV* and *Iε*+ should be the future research direction. In addition, there are still many excellent strategies that can be used to maintain convergence and diversity, and this paper does not compare these strategies. The future direction of work can start from this point and be improved under the framework of DL-TPCEA to achieve better results. We used dynamic learning factors to combine DLS and BCE more effectively, but there are more ways to combine them more effectively in the future. In terms of the selection of the initial value of the dynamic convergence factor, suggestions in relevant paper [94] can also be referred to ge<sup>t</sup> a better initial value.

**Author Contributions:** Conceptualization, G.L. and G.-G.W.; methodology, G.L.; software, G.L.; validation, G.-G.W. and S.W.; formal analysis, S.W.; investigation, G.L.; resources, G.L. and G.-G.W.; data curation, G.L.; writing—original draft preparation, G.L.; writing—review and editing, G.-G.W. and S.W.; visualization, G.L.; supervision, G.L., G.-G.W. and S.W.; project administration, G.-G.W. and S.W.; funding acquisition, G.-G.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, gran<sup>t</sup> number U1706218, 41576011, 41706010 and 61503165.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
