# A Two-Stage Multi-Objective Optimization Algorithm for Solving Large-Scale Optimization Problems
## 3 Proposed Algorithm
### Pareto Optimal Subspace Learning
First, in the first stage of decision variables, we simply divide the decision variables into convergence correlation and diversity correlation; even the grouped decision variables may have different correlations with the objective function, and whether there is a more accurate classification method. It consumes a lot of computing resources in the decision variable grouping stage. Therefore, how to deal with these variables efficiently is a very valuable research problem. In addition, in real society, due to the complexity of decision variables, how to use our algorithm to solve these practical application problems may be an interesting direction. Conceptualization, J.L. ; methodology, T.L. ; software, J.L. ; validation, J.L. ; formal analysis, J.L. ; investigation, T.L. ; resources, T.L. ; data curation, T.L. ; writing--original draft preparation, J.L. ; writing--review and editing, T.L. ; visualization, T.L. ; supervision, J.L. ; project administration, T.L. ; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable, using a publicly available dataset. Not applicable. Data Availability Statement: Data are contained within the article. The authors declare no conflicts of interest. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Problem** & **NSGA-III** & **MOEA/D** & **MOEA/DVA** & **LMEA** & **LSMOEA-VT** \\ \hline DTLZ1 & \(5.4198\times 10^{+1}\) & \(4.5699\times 10^{+2}\) & \(2.8743\times 10^{+2}\) & \(5.9040\times 10^{+1}\) & \(5.3691\times 10^{+1}\) \\ DTLZ2 & \(6.6541\times 10^{+1}\) & \(6.0568\times 10^{+2}\) & \(3.5147\times 10^{+2}\) & \(5.5374\times 10^{+1}\) & \(5.1817\times 10^{+1}\) \\ WFG3 & \(6.6261\times 10^{+1}\) & \(6.4752\times 10^{+2}\) & \(3.5863\times 10^{+2}\) & \(5.2783\times 10^{+1}\) & \(5.0770\times 10^{+1}\) \\ UF9 & \(6.9655\times 10^{+1}\) & \(6.3372\times 10^{+2}\) & \(3.5215\times 10^{+2}\) & \(5.5708\times 10^{+1}\) & \(4.9766\times 10^{+1}\) \\ UF10 & \(6.7915\times 10^{+1}\) & \(6.3627\times 10^{+2}\) & \(3.6118\times 10^{+2}\) & \(6.2106\times 10^{+1}\) & \(5.2047\times 10^{+1}\) \\ LSMOP1 & \(7.9914\times 10^{+1}\) & \(8.2347\times 10^{+2}\) & \(2.5079\times 10^{+2}\) & \(1.60002\times 10^{+2}\) & \(3.4328\times 10^{+2}\) \\ LSMOP2 & \(8.6011\times 10^{+1}\) & \(8.1857\times 10^{+2}\) & \(2.4873\times 10^{+2}\) & \(1.4634\times 10^{+2}\) & \(3.4029\times 10^{+2}\) \\ LSMOP3 & \(8.9809\times 10^{+1}\) & \(8.3215\times 10^{+2}\) & \(2.7383\times 10^{+2}\) & \(1.3938\times 10^{+2}\) & \(3.4699\times 10^{+2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average runtimes (s) of five algorithms on some test problems. ## References

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