# Memory-Enhanced Dynamic Multi-Objective Evolutionary Algorithm Based on \(L_{p}\) Decomposition
## 3 Memory-Enhanced Dynamic Multi-Objective Evolutionary Algorithm Based on \(L_{p}\) Decomposition
### Detailed Description of dMOEA/D-\(L_{p}\) and Its Time Complexity Analysis
To skillfully monitor environmental change and quickly respond to the new environment, an improved environment detection operator is presented and a subproblem-based memory scheme is adopted which allows the evolutionary algorithm to store good solutions from old environments and reuse them as necessary. We conducted two sets of experimental studies. In the first set of experiments, we compared dMOEA/D-\(L_{p}\) against dMOEA/D-TCH, dMOEA/D-WS, and dMOEA/D-PBI to test the effectiveness of the \(L_{p}\) decomposition method for dynamic multi-objective optimization. In the second set of experiments, we compared dMOEA/D-\(L_{p}\) with two other popular algorithms (DNSGA-II and QICCA) to test the overall performance of the algorithm. Simulation results demonstrated the effectiveness of the \(L_{p}\) decomposition method for decomposition-based dynamic multi-objective optimization. Comparison results also revealed that the proposed dMOEA/D-\(L_{p}\) had quick tracking performance and better convergence, it was superior and preferable in solving dynamic multi-objective optimization problems. Conceptualization, X.X. and Y.T. ; Formal analysis, S.L. ; Funding acquisition, Y.T. ; Investigation, X.X. ; Methodology, X.X. ; Project administration, W.Z. ; Validation, Y.T. and W.Z. ; Writing--original draft, X.X. ; Writing--review & editing, Y.T. Table 5.0 Solution sets obtained by three algorithms at \(t=13.2\) on FDA5 in case of \(\tau_{T}=15\), \(n_{T}=5\). Table 5.1 Solution sets obtained by three algorithms at \(t=10.8\) on FDA5 in case of \(\tau_{T}=15\), \(n_{T}=5\). Funding: This research was funded by the [National Natural Science Foundation of China] grant numbers [61401260, 61572298, 61602283], and the [Natural Science Foundation of Shandong, China] grant numbers [BS2014 DX006, ZR2016 FB10]. This research was funded by the National Natural Science Foundation of China (grant numbers: 61401260, 61572298, 61602283), and the Natural Science Foundation of Shandong, China (grant numbers: BS2014 DX006, ZR2016 FB10). The authors declare no conflict of interest. ## References

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