# Multi-Objective Evolutionary Neural Architecture Search with Weight-Sharing Supernet
## 6 Conclusions  
This paper explores the NAS problem by utilizing multi-objective evolutionary algorithms. Specifically, a multi-objective evolutionary NAS framework based on a weight-sharing supernet is designed that combines the characteristics of EC-NAS with gradient-based NAS. In this framework, the candidate network architectures are regarded as the individuals in the population. In addition, the idea of the one-shot model is combined, where all the network architectures are treated as subnets on a weight-sharing supernet. By sharing the weight parameters of the supernet, the population evaluation's efficiency is significantly improved. To prevent the evolutionary algorithms from prematurely converging to the small model region due to the small model trap during the search phase, we further propose a bi-population MOEA/D-based NAS method. This method divides the original population in the traditional MOEA/D into two sub-populations, which optimize toward different directions to achieve the simultaneous search for models with different sizes. Furthermore, the introduced communication mechanism between sub-populations further ensures that the algorithm can sufficiently explore the entire search space. Experiments on CIFAR-10 and Mini-ImageNet datasets validate the effectiveness and transferability of the proposed method. In the future, we may consider expanding the proposed NAS framework and method to other search spaces. Although the proposed NAS method can reduce the time consumed by the population evaluation to a large extent, this process still accounts for a significant portion of the running time. Thus, we may consider adopting surrogate models to achieve quick predictions of the network's performance. Lastly, this work only focuses on the search for CNNs, while, in practical applications, there are also requirements for designing other networks like RNNs. Therefore, multiple search spaces may be adopted to design various types of neural networks in future work. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Architecture**} & **Top-1** & **Top-5** & **\#Params** & **Search Cost** & \multirow{2}{*}{**Search Method**} \\  & **Acc (\%)** & **Acc (\%)** & **(M)** & **(GPU Days)** & \\ \hline ResNet34 & 76.88 & 91.73 & 21.34 & - & Manual Design \\ MobileNet-V2 & 76.77 & 92.46 & 2.35 & - & Manual Design \\ NASNet & 77.25 & 91.37 & 5.24 & 2000 & Reinforcement Learning \\ DARTS-V2 & 74.97 & 90.78 & 4.60 & 4 & Gradient Based \\ GDAS-LEVEL2 & 74.84 & 90.83 & 5.47 & 0.21 & Gradient Based \\ AmoebaNet-A & 76.76 & 91.10 & 4.65 & 3150 & Evolution \\ CARS-C & 75.20 & 90.74 & 4.07 & 0.4 & Evolution (MO) \\ CARS-E & 75.26 & 90.94 & 4.26 & 0.4 & Evolution (MO) \\ CARS-F & 75.92 & 90.79 & 4.42 & 0.4 & Evolution (MO) \\ CARS-G & 76.14 & 91.34 & 4.56 & 0.4 & Evolution (MO) \\ Bi-MOEA/D-NAS-1 & 76.46 & 91.36 & 3.73 & 0.5 & Evolution (MO) \\ Bi-MOEA/D-NAS-2 & 76.99 & 91.38 & 3.96 & 0.5 & Evolution (MO) \\ Bi-MOEA/D-NAS-3 & 76.89 & 91.40 & 4.17 & 0.5 & Evolution (MO) \\ Bi-MOEA/D-NAS-4 & 77.10 & 91.58 & 4.66 & 0.5 & Evolution (MO) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test performance of the network architectures on Mini-ImageNet. **Author Contributions:** Methodology, J.L. and Y.G. ; formal analysis, J.L. ; investigation, J.L. ; writing--original draft preparation, J.L. and K.Z. ; writing--review and editing, J.L., K.Z., Y.L. ([PERSON]) and Y.G. ; supervision, Y.L. ([PERSON]) and Y.G. ; funding acquisition, Y.L. ([PERSON]) and Y.G. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported in part by the Guangdong Regional Joint Funds for Basic and Applied Research under grant 2021B1515120078, in part by the Guangdong Natural Science Funds for Distinguished Young Scholars under grant 2022B1515020049, in part by the National Natural Science Foundation of China under grant 62276100, and in part by the TCL Young Scholars Program.