## 4 Experiments and Results
### Experimental Setup  
Three datasets from Amazon [41] are selected for the experiment, and the statistical information of the datasets is described in Table 2. Based on the dataset, the experiments mainly use item IDs, user IDs, review time, categories, and rating information. Each experimental dataset is composed of evaluation data from \(U_{sum}\) randomly selected users in the dataset. In each experimental dataset, one user is selected as the experimental subject, and the remaining users who are similar will provide social knowledge for that user. If all items evaluated by a user have a total of \(J\) categories, the items are expressed as \(x=\{x_{1},x_{2},\cdots,x_{J}\}\), where \(x_{1,2,\ldots,J}\in\{0,1\}\). The evaluation data of the experimental subjects are processed as follows.  
Considering the actual situation of interactive behavior, the set \(C\) of historical evaluation items of a user is sorted by review time. Then, it is divided to obtain multiple training sets (sliding window) and item pools containing the items to be searched at different interactions, as shown in Figure 3. In these experiments, the set \(C\) is divided into two parts, one for the first 70% of items as the set \(C_{HI}\) regarded as the historical interactive items, and the other as the fixed set \(C_{F}\) of items to be searched. The last 30% of the set \(C_{HI}\), named \(C_{I}\), is considered as the result of 10 actual interactions. The training items are obtained from the set \(C_{HI}\) through a sliding window with a fixed length of \(0.4*|C_{HI}|\). \(0.1*|C_{I}|\) items following the sliding window is seen as the actual result of the interaction, and all the data after the sliding window in \(C\) are regarded as an item pool to be searched, so that the item pool decreases gradually as the interaction proceeds. To be relevant, the updated history items in experiments include sliding window data and the Top-N list, except for the first interaction. However, the \(R_{topN}\) used for model management is still calculated from the Top-N list rather than real interaction results.  
In these experiments, MPUSMs and their derived models are created based on Dual-RBM [13], so the parameters (number of units in the hidden and visible layers) of the Dual-RBM and the training method are the same as in [13]. In addition, the parameters (\(\alpha\), \(\beta\)) related to the calculation of scores for MPUSMs and partial-MPUSMs are referred to [13]. Moreover, IMFEOA is built based on MFEA [16], so the parameter \(rmp\) is referenced to [16]. In addition, the population to be optimized by IMFEOA will evolve until no new individuals can be searched for, so that unknown items can be fully explored (\(G\) = 100). The remaining parameters are deliberately set to be identical to SC-DRBMIEDA [13] in order to be able to compare with it in the same context. Detailed parameter configurations are given  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **\# of Users** & **\# of Items** & **\# of Ratings** \\ \hline Digital\_Music (Music) & 478,235 & 266,414 & 836,006 \\ \hline CDs\_and\_Vinyl (CDs) & 1,578,597 & 486,360 & 3,749,004 \\ \hline Kindle\_Store (Kindle) & 1,406,890 & 430,530 & 3,205,467 \\ \hline \hline \end{tabular}
\end{table}
Table 2: # of users, items and ratings of the datasets.  
Figure 3: The data set division of the user.  
in Table 3. The user surrogate models and algorithm descriptions used for comparison in these experiments are shown in Table 4.