## 5 Numerical Tests and Comparisons
### Computational and Statistical Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instances**} & \multirow{2}{*}{**F\&V**} & \multirow{2}{*}{**DPSO**} & \multicolumn{2}{c}{**PAN-**} & \multirow{2}{*}{**HPSO**} & \multirow{2}{*}{**PHPSO**} & \multirow{2}{*}{**Instances**} & \multirow{2}{*}{**F\&V**} & \multirow{2}{*}{**DPSO**} & \multirow{2}{*}{**PAN-**} & \multirow{2}{*}{**HPSO**} & \multirow{2}{*}{**PHPSO**} \\  & & & & & & & & & & & & & \\  & & & & & & & & & & & \\ \hline ta025 & 1.2228 & 1.2228 & 0.9689 & 0.9689 & 0 & ta086 & 1.1755 & 1.1604 & 0.4352 & 0.4352 & 0 \\ ta026 & 2.9389 & 2.9389 & 2.3263 & 2.3263 & 0 & ta087 & 1.2491 & 1.2396 & 0.4628 & 0.4628 & 0 \\ ta027 & 1.5579 & 1.2579 & 1.1232 & 1.1232 & 0 & ta088 & 0.5035 & 0.4935 & 0 & 0 & 0 \\ ta028 & 3.1438 & 3.1438 & 2.63 & 2.63 & 0 & Ta089 & 1.0852 & 1.0701 & 0.3824 & 0.3824 & 0 \\ ta029 & 3.0663 & 3.0663 & 2.4829 & 2.4829 & 0 & ta090 & 0.3783 & 0.5 & 0 & 0 & 0.4575 \\ ta030 & 2.6776 & 2.6776 & 1.218 & 2.128 & 0 & ta091 & 0.6029 & 0.5761 & 0.1025 & 0.1025 & 0 \\ ta031 & 0.5309 & 0.5242 & 0.305 & 0.305 & 0 & ta092 & 0.4659 & 0.428 & 0 & 0 & 0.7522 \\ ta032 & 0.3904 & 0.3816 & 0.1345 & 0.1345 & 0 & ta093 & 0.4476 & 0.4266 & 0 & 0 & 0.7405 \\ ta033 & 0.3633 & 0.3602 & 0.1 & 0.1 & 0 & ta094 & 0.4936 & 0.4664 & 0.0334 & 0.0334 & 0 \\ ta034 & 0.3682 & 0.3638 & 0.1283 & 0.1283 & 0 & ta095 & 0.4635 & 0.4351 & 0 & 0 & 0.7278 \\ ta035 & 0.432 & 0.425 & 0.1837 & 0.1837 & 0 & ta096 & 0.499 & 0.4649 & 0 & 0 & 0.7416 \\ ta036 & 0.4044 & 0.4014 & 0.16 & 0.16 & 0 & ta097 & 0.4638 & 0.4366 & 0 & 0 & 0.5638 \\ ta037 & 0.3379 & 0.3347 & 0.125 & 0.125 & 0 & ta098 & 0.5586 & 0.523 & 0.0621 & 0.0621 & 0 \\ ta038 & 0.3947 & 0.391 & 0.1357 & 0.1357 & 0 & ta099 & 0.5659 & 0.5388 & 0.066 & 0.066 & 0 \\ ta039 & 0.3935 & 0.3932 & 0.1572 & 0.1572 & 0 & ta100 & 0.5911 & 0.5585 & 0.0779 & 0.0779 & 0 \\ ta040 & 0.4571 & 0.4501 & 0.1953 & 0.1953 & 0 & ta101 & 0.9873 & 0.9636 & 0.2122 & 0.2122 & 0 \\ ta041 & 0.3132 & 0.3092 & 0 & 0 & 0.1271 & ta102 & 0.3667 & 0.6266 & 0 & 0 & 0.7785 \\ ta042 & 1.1402 & 1.1346 & 0.5724 & 0.5724 & 0 & ta103 & 0.6347 & 0.6084 & 0.0124 & 0 & 0 \\ ta043 & 0.636 & 0.6346 & 0.2403 & 0.2403 & 0 & ta104 & 1.0478 & 0.169 & 0.2425 & 0.2425 & 0 \\ ta044 & 0.9319 & 0.929 & 0.4709 & 0.4709 & 0 & ta105 & 0.6518 & 0.6373 & 0 & 0 & 0.7306 \\ ta054 & 1.1979 & 1.1951 & 0.6446 & 0.6446 & 0 & ta106 & 1.0966 & 1.0666 & 0.2576 & 0.2576 & 0 \\ ta046 & 0.8167 & 0.8137 & 0.3965 & 0.3965 & 0 & ta107 & 0.645 & 0.6233 & 0 & 0 & 0 \\ ta047 & 0.3134 & 0.3142 & 0 & 0 & 0.1592 & ta108 & 0.9611 & 0.9464 & 0.1955 & 0.1852 & 0 \\ ta048 & 0.9951 & 0.9953 & 0.5039 & 0 & ta109 & 1.0853 & 1.0552 & 0.2642 & 0.2642 & 0 \\ ta049 & 0.9334 & 0.9314 & 0.4952 & 0.4952 & 0 & ta110 & 0.6368 & 0.6159 & 0 & 0 & 0 \\ ta050 & 0.8461 & 0.8455 & 0.4318 & 0.4318 & 0 & ta111 & - & - & 0.07 & 0.07 & 0 \\ ta051 & 1.7498 & 1.752 & 1.0019 & 1.0019 & 0 & ta112 & - & - & 0.05 & 0.05 & 0 \\ ta052 & 0.3752 & 0.3731 & 0.018 & 0.018 & 0 & ta113 & - & - & 0.05 & 0.05 & 0 \\ ta053 & 1.592 & 1.5903 & 0.8841 & 0.8841 & 0 & ta114 & - & - & 0.05 & 0.05 & 0 \\ ta054 & 1.6893 & 1.6915 & 1.0019 & 1.0019 & 0 & ta115 & - & - & 0.07 & 0.07 & 0 \\ ta056 & 1.2087 & 1.2087 & 0.6463 & 0.6463 & 0 & ta116 & - & - & 0.06 & 0.06 & 0 \\ ta057 & 0.3609 & 0.3596 & 0 & 0 & 0.0642 & ta117 & - & - & 0.02 & 0.02 & 0 \\ ta05 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **N** & **Mean** & **StDev** & **SE Mean** \\ \hline PHPSO & 110 & 282,949 & 380,236 & 36,254 \\ DPSO-2008 & 110 & 472,275 & 637,377 & 60,771 \\ Difference & 110 & \(-\)189,326 & 272,438 & 25,976 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Paired \(t\)-test for H\({}_{0}\) = PHPSO = DPSO vs. H\({}_{1}\)= PHPSO \(\
eq\) DPSO on the best-known solutions \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **N** & **Mean** & **StDev** & **SE Mean** \\ \hline PHPSO & 110 & 282,949 & 380,236 & 36,254 \\ P\&V-2003 & 110 & 478,400 & 647,517 & 61,738 \\ Difference & 110 & \(-\)195,451 & 267,281 & 25,484 \\ \hline \hline \end{tabular}
\end{table}