## 4 Numerical Experiments
### Experimental Results  
To verify the reproducibility and stability of the experimental results, we performed 10 iterations for each instance. Table 4 displays the average fitness of different algorithms, as well as a comparison of the best fitness achieved by different methods under varying population sizes. From Table 4, it can be seen that in simpler instances (such as Instance 1), the performance differences among the algorithms are relatively small. However, as the complexity of the instances increases, particularly when the number of joint courses and the total number of courses significantly grow, POGA-DP demonstrates a remarkable advantage in both its average fitness and best fitness compared to these values with the other algorithms. For example, in Instance 15, the average fitness of the GA, PSO, PSM, ACO, and POGA-DP is 1133, 941.3, 1077.1, 1075.4, and 1719.8, respectively, clearly indicating that POGA-DP is far ahead of the other algorithms. This indicates that while POGA-DP performs comparably to the other algorithms when handling low-complexity problems, it exhibits exceptional optimization capabilities as the complexity of the problem increases, especially when there are many joint courses. In this study, a new classroom utilization metric was proposed, aimed at more effectively allocating classroom resources and improving the quality of the scheduling results. The classroom utilization rate of the scheduling results is calculated using the following formula:  
\[Occupancy=\frac{1}{\sum_{r\in R}\sum_{k\in K}\theta_{r,k}}\sum_{r\in R}\sum_{ w\in W}\sum_{k\in K}\frac{\theta_{r,k}\delta_{r,w,k}}{20N_{r}} \tag{25}\]  
In practical applications, due to factors such as the length of the semester, holidays, and activities, the scheduling of teaching events often does not span the entire semester. After assigning a suitable classroom \(r\) to teaching event \(m\), if this teaching event occurs only from week 1 to week 10 and no other teaching events are scheduled for \(r\) in subsequent weeks in this period, the space resources of the classroom will be significantly wasted. By considering dimensions such as weeks and time slots in the Occupancy metric, this approach reflects the actual usage of the classroom better. Table 5 presents a comparison of the GA and POGA-DP in solving the UCSP-BJFU with different instances, detailing the \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{6}{c}{**Average Fitness**} & \multicolumn{6}{c}{**Best Fitness**} \\ \cline{2-11}  & **GA** & **PSO** & **PSM** & **POGA-DP** & **ACO** & **GA** & **PSO** & **PSM** & **POGA-DP** & **ACO** \\ \hline Instance 1 & 41.0 & 33.7 & 38.5 & 41.0 & 39.8 & 41 & 35 & 41 & 41 & 40 \\ Instance 2 & 73.4 & 60.5 & 76.4 & 106.7 & 75.2 & 82 & 66 & 79 & 108 & 78 \\ Instance 3 & 131.1 & 109.0 & 130.2 & 206.8 & 128.5 & 144 & 115 & 138 & 212 & 136 \\ Instance 4 & 139.8 & 114.7 & 140.7 & 245.2 & 138.1 & 153 & 126 & 146 & 263 & 145 \\ Instance 5 & 233.6 & 178.9 & 242.8 & 449.6 & 238.4 & 262 & 194 & 254 & 459 & 250 \\ Instance 6 & 56.8 & 55.3 & 57.2 & 72.0 & 56.5 & 57 & 59 & 61 & 73 & 60 \\ Instance 7 & 100.0 & 97.2 & 105.9 & 143.3 & 103.8 & 102 & 98 & 108 & 146 & 105 \\ Instance 8 & 338.3 & 278.4 & 331.6 & 544.5 & 330.2 & 360 & 297 & 348 & 551 & 342 \\ Instance 9 & 602.5 & 506.6 & 572.1 & 924.0 & 580.3 & 631 & 524 & 599 & 932 & 590 \\ Instance 10 & 929.6 & 732.5 & 897.0 & 1437.2 & 910.7 & 977 & 722 & 922 & 1448 & 915 \\ Instance 11 & 40.0 & 34.4 & 49.8 & 77.0 & 46.2 & 40 & 36 & 52 & 77 & 48 \\ Instance 12 & 63.3 & 58.9 & 64.6 & 100.9 & 62.5 & 66 & 61 & 67 & 101 & 65 \\ Instance 13 & 175.9 & 133.6 & 175.3 & 244.0 & 172.8 & 184 & 140 & 177 & 248 & 174 \\ Instance 14 & 551.3 & 452.8 & 561.4 & 905.1 & 550.6 & 583 & 472 & 578 & 912 & 570 \\ Instance 15 & 1133 & 941.3 & 1077.1 & 1719.8 & 1075.4 & 1183 & 970 & 1104 & 1739 & 1098 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of fitness values.