## 4 Experiments and Results
### Experiment 4--Search Performance of MPUSMs-IMFECOA  
To demonstrate the search performance produced by the proposed IMFECOA in conjunction with the MPUSMs, the distribution of individuals in the population evolution process is observed (Figures 9-12). This experiment is validated by changing the underlying surrogate models of MPUSMs and the evolutionary algorithm. This experiment is validated by changing the underlying surrogate models of MPUSMs and the evolutionary algorithm. That is, single and multi-model guided population evolution under different underlying surrogate models exhibits performance suitable for personalized recommendations. Therefore, introduce Restricted Boltzmann Machine (RBM) [42] to build surrogates \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{3}{*}{**Metric**\(\mathbf{\text{Dataset}}\)} & \multicolumn{3}{c|}{**Music**} & \multicolumn{3}{c|}{**CDs**} & \multicolumn{3}{c|}{**Kindle**} & \multirow{3}{*}{**Total**} \\  & **IMFECOA** & \multicolumn{3}{c|}{**1 EDA**} & & & \multicolumn{3}{c|}{**IMFECOA**} & \multicolumn{3}{c|}{**Best**} & \multicolumn{1}{c|}{**Ave**} & \multicolumn{1}{c|}{**Best**} & \multicolumn{1}{c|}{**Ave**} & \multicolumn{1}{c|}{**Best**} & \multicolumn{1}{c|}{**Ave**} & \multicolumn{1}{c|}{**Best**} & \multicolumn{1}{c|}{**Ave**} & \multicolumn{1}{c|}{**Growth**} \\  & **Best** & **Ave** & \multicolumn{1}{c|}{**Best**} & & \multicolumn{1}{c|}{**Ave**} & & \multicolumn{1}{c|}{**Best**} & & \multicolumn{1}{c|}{**Ave**} & & \multicolumn{1}{c|}{**Best**} & \multicolumn{1}{c|}{**Ave**} & \multicolumn{1}{c|}{**Best**} & \multicolumn{1}{c|}{**Ave**} & \multicolumn{1}{c|}{**Growth**} \\ \hline HR & 0.098 & 0.069 & **0.106** & **0.073 \({}^{*}\)** & \(-4.3\%\) & 0.022 & 0.016 & **0.024** & **0.017 \({}^{*}\)** & \(-5.4\%\) & 0.016 & 0.012 & **0.017** & **0.013 \({}^{*}\)** & \(-7.14\%\) & \(-5.6\%\) \\ \hline AJ & 0.997 & 0.976 & **1.0** & **0.992** & \(-1.66\%\) & 0.955 & 0.922 & **0.998** & **0.972** & \(-5.1\%\) & 0.967 & 0.919 & **0.997** & **0.987** & \(-6.9\%\) & \(-4.6\%\) \\ \hline Div & **0.215** & **0.203 \({}^{*}\)** & 0.15 & 0.124 & **6.98\%** & **0.203** & **0.194 \({}^{*}\)** & 0.147 & 0.122 & **59.65\%** & **0.221** & **0.205 \({}^{*}\)** & 0.179 & 0.148 & **38.42\%** & **54.02\%** \\ \hline SSD & **0.77** & **0.591** & 0.687 & 0.575 & **2.93\%** & 0.807 & **0.714 \({}^{*}\)** & **0.868** & 0.681 & **4.88\%** & 0.813 & **0.714 \({}^{*}\)** & **0.91** & **0.693** & **3.30\%** & **3.70\%** \\ \hline Sur & **10.938** & **9.686 \({}^{*}\)** & 10.128 & 0.175 & **5.575** & **6.833** & **6.687** & **6.6** & 6.631 & **0.80\%** & **6.659** & **6.512 \({}^{*}\)** & 0.55 & 6.406 & **16.5\%** & **2.69\%** \\ \hline PMD & **0.222** & **0.215 \({}^{*}\)** & 0.195 & 0.183 & **1.39\%** & **0.205** & **0.202 \({}^{*}\)** & 0.176 & 0.172 & **17.31\%** & **0.219** & **0.214 \({}^{*}\)** & 0.198 & 0.183 & **16.65\%** & **16.65\%** \\ \hline \end{tabular}  
* The mark \({}^{*}\) indicates that the algorithm is significantly different from other algorithms. 2 Bolded values in the table indicate higher performance.  
\end{table} 
Table 5: Combined evaluation results of six metrics for both algorithms. and Genetic Algorithm (GA) [30] to optimize the population. This is because a surrogate model built with an RBM is equally easy to calculate a probabilistic model such that the starting point of the initial population being evolved is the same. In addition, a genetic algorithm can use the same crossover and mutation operators to optimize populations, suitable for comparison with MFEA. Specifically, there are MPUSMs-IMFEAO and DRBM-Social-IGA based on the DRBM-Social surrogate model, and MPUSMs-IMFEAO and RBM-IGA based on the RBM surrogate model. To make the IMFEAO and IGA algorithms comparable, they both use the same crossover operator and mutation operator and set the same crossover probability (\(p=1/3+2/3*tmp\)) and mutation probability (\(1-p\)) for IGA as for IMFEAO.