## 3 Computational Experiments
### Second Experimental Campaign: Large Instances
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(1N\)} & \multicolumn{3}{c}{\(CHa\)} & \multicolumn{3}{c}{\(CH_{-}IPa\)} \\ \cline{2-9}  & \([\mathbf{-10,10]}\) & \([\mathbf{-100,100]}\) & \([\mathbf{-1K,1K}]\) & \(\mathbf{P-EL}\) & \([\mathbf{-10,10]}\) & \([\mathbf{-100,100]}\) & \([\mathbf{-1K,1K}]\) & \(\mathbf{P-EL}\) \\ \hline
100 & 2.3 & 22.9 & 263.7 & 3165.4 & 0.7 & 5.2 & 79.2 & 3057.5 \\
200 & 1.1 & 14.0 & 134.8 & 3800.4 & 0.2 & 3.5 & 32.7 & 3583.8 \\
500 & 0.6 & 5.8 & 45.6 & 3086.2 & 0.0 & 0.4 & 6.1 & 2462.2 \\
1000 & 0.2 & 2.1 & 18.1 & 3782.4 & 0.0 & 0.1 & 1.1 & 2776.3 \\
2000 & 0.0 & 0.8 & 14.0 & 3129.2 & 0.0 & 0.0 & 0.5 & 1374.0 \\
5000 & 0.0 & 0.3 & 3.2 & 3461.1 & 0.0 & 0.0 & 0.1 & 272.3 \\ \hline
**AVG** & **0.7** & **7.7** & **79.9** & **3404.1** & **0.1** & **1.5** & **20.0** & **2254.4** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Absolute objective function values—\(CHa\) and \(CH\_IPa\)—large instances. Figure 4: Objective function values obtained by \(CH\_1 Pa\) compared to the size of the instances. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{\(CH\_1 Pa\)} \\ \cline{2-5}
**Instance** & \(\mathbf{[-10,10]}\) & \(\mathbf{[-100,100]}\) & \(\mathbf{[-1K,1K]}\) & **P-EL** \\ \hline Rand\_100\_02 & 0 & 0 & 0 & 0 \\ Rand\_100\_03 & 0 & 0 & 0 & 0 \\ Rand\_100\_04 & 0 & 0 & 0 & 0 \\ Rand\_100\_05 & 0 & 0 & 0 & 0 \\ Rand\_100\_10 & 0 & 0 & 0 & 0 \\ Rand\_100\_20 & 0 & 0 & 0 & 0 \\ Rand\_200\_02 & 0 & 0 & 0 & 0 \\ Rand\_200\_03 & 0 & 0 & 0 & 0 \\ Rand\_200\_04 & 0 & 0 & 1 & 0 \\ Rand\_200\_05 & 0 & 0 & 0 & 0 \\ Rand\_200\_10 & 0 & 0 & 1 & 1 \\ Rand\_200\_20 & 0 & 0 & 0 & 1 \\ Rand\_500\_02 & 1 & 0 & 1 & 0 \\ Rand\_500\_03 & 1 & 0 & 0 & 1 \\ Rand\_500\_04 & 0 & 1 & 1 & 1 \\ Rand\_500\_05 & 0 & 1 & 1 & 1 \\ Rand\_500\_10 & 1 & 2 & 1 & 1 \\ Rand\_500\_20 & 3 & 3 & 3 & 3 \\ Rand\_1000\_02 & 2 & 2 & 2 & 2 \\ Rand\_1000\_03 & 2 & 3 & 3 & 2 \\ Rand\_1000\_04 & 2 & 3 & 3 & 3 \\ Rand\_1000\_05 & 4 & 4 & 4 & 4 \\ Rand\_1000\_10 & 7 & 8 & 7 & 8 \\ Rand\_1000\_20 & 11 & 11 & 11 & 12 \\ Rand\_2000\_02 & 8 & 9 & 9 & 9 \\ Rand\_2000\_03 & 10 & 12 & 12 & 11 \\ Rand\_2000\_04 & 12 & 15 & 14 & 14 \\ Rand\_2000\_05 & 13 & 15 & 15 & 14 \\ Rand\_2000\_10 & 25 & 27 & 27 & 25 \\ Rand\_2000\_20 & 48 & 51 & 53 & 55 \\ Rand\_2000\_2 & 42 & 50 & 52 & 53 \\ Rand\_5000\_03 & 57 & 67 & 71 & 65 \\ Rand\_5000\_04 & 73 & 85 & 90 & 83 \\ Rand\_5000\_05 & 88 & 103 & 112 & 101 \\ Rand\_5000\_10 & 217 & 204 & 202 & 201 \\ Rand\_5000\_20 & 366 & 350 & 371 & 328 \\ \hline
**AVG** & **27.6** & **28.5** & **29.6** & **27.7** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CPU time (milliseconds) of the proposed \(CH\_1 Pa\)  
Figure 5: Relationship between the number of \(1 Pa\) iterations and \(|N|\). In the following tables, the results obtained by \(CH_{-1}Pa\) are compared with those obtained by using the iterated neighborhood search procedure described in Section 2.2. In each Table, both the best among the first random paths (\(RP\)) and the best path after the improvement phase (\(RPR\)) are reported. Tables 7 and 8 show, respectively, the number of optimal solutions and the computational times in milliseconds, identified by \(CH_{-1}Pa\), \(RP\) and \(RPR\). It can be seen from these tables that \(CH_{-1}Pa\) produces the maximum number of optimal solutions in about \(\frac{1}{50}\) of the computational time required by the \(RP\) and \(RPR\) iterative techniques. In particular, \(CH_{-1}Pa\) is able to find more 30% optimal solutions than \(RPR\) for costs [\(-100\), \(100\)] and \(P\)-\(EL\), and about 180% for cost [\(-1K\), \(1K\)]. These results also show that \(1 Pa\) applied to the \(RP\) significantly increases the number of optimal solutions identified by the \(RP\), passing from 181 to 319 optimal solutions identified; the greatest effect is on instances with cost \(P\)-\(EL\) and [\(-1K\), \(1K\)].