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%% Title:

{\LARGE On-Line Supplement for:\\ The Multidimensional Knapsack Problem:\\ Structure and Algorithms}\\[12pt]

% Authors and addresses:

\footnotesize

\mbox{\large Jakob Puchinger}\\
NICTA Victoria Laboratory\\
Department of Computer Science \& Software Engineering\\
University of Melbourne, Australia\\
\mbox{jakobp@csse.unimelb.edu.au}\\[6pt]

\mbox{\large G\"unther R.\ Raidl}\\
Institute of Computer Graphics and Algorithms\\
Vienna University of Technology, Austria\\
\mbox{raidl@ads.tuwien.ac.at}\\[6pt]

\mbox{\large Ulrich Pferschy}\\
Department of Statistics and Operations Research\\
University of Graz, Austria\\
\mbox{pferschy@uni-graz.at}

\normalsize

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\begin{table}[!htb]
\caption{Objective values of the MKP obtained with different algorithm
variants and total CPU times of 1800 seconds per instance, for the last column
of 14400 seconds, compared to best known approach (VV~2005); $n=500$ $m=5$.}
\label{tab:Appendix1}
\bigskip

\centering
\begin{tabular}{|r|r|r|r|r|}
\hline
\multicolumn{1}{|c|}{VV 2005} & \multicolumn{1}{c|}{CPLEX} & \multicolumn{1}{c|}{CPLEX C} &
\multicolumn{1}{c|}{CPLEX\_MA\_D C s}
& \multicolumn{1}{c|}{CPLEX\_MA\_D C el}\\
\hline
\hline
120148 & 120148 & 120148 & 120148 & 120148 \\
117879 & 117879 & 117879 & 117879 & 117879 \\
121131 & 121131 & 121131 & 121131 & 121131 \\
120804 & 120804 & 120804 & 120804 & 120804 \\
122319 & 122319 & 122319 & 122319 & 122319 \\
122011 & 122024 & 122024 & 122024 & 122024 \\
119127 & 119127 & 119127 & 119127 & 119127 \\
120568 & 120568 & 120568 & 120568 & 120568 \\
121575 & 121575 & 121575 & 121575 & 121586 \\
120717 & 120717 & 120717 & 120717 & 120717 \\
218426 & 218428 & 218428 & 218428 & 218428 \\
221202 & 221202 & 221202 & 221202 & 221202 \\
217542 & 217542 & 217542 & 217534 & 217542 \\
223560 & 223560 & 223560 & 223560 & 223560 \\
218965 & 218966 & 218966 & 218966 & 218966 \\
220527 & 220530 & 220530 & 220530 & 220530 \\
219989 & 219989 & 219989 & 219989 & 219989 \\
218215 & 218215 & 218215 & 218215 & 218215 \\
216976 & 216976 & 216976 & 216976 & 216976 \\
219719 & 219719 & 219719 & 219719 & 219719 \\
295828 & 295828 & 295828 & 295828 & 295828 \\
308086 & 308086 & 308086 & 308086 & 308086 \\
299796 & 299796 & 299796 & 299796 & 299796 \\
306480 & 306480 & 306480 & 306480 & 306480 \\
300342 & 300342 & 300342 & 300342 & 300342 \\
302571 & 302571 & 302571 & 302571 & 302571 \\
301339 & 301339 & 301339 & 301339 & 301339 \\
306454 & 306454 & 306454 & 306454 & 306454 \\
302828 & 302822 & 302828 & 302828 & 302828 \\
299910 & 299904 & 299906 & 299906 & 299910 \\
\hline
\end{tabular}
\end{table}
                                     
\begin{table}[!htb]
\caption{Objective values of the MKP obtained with different algorithm
variants and total CPU times of 1800 seconds per instance, for the last column
of 14400 seconds, compared to best known approach (VV~2005); $n=500$ $m=10$.}
\label{tab:Appendix2}
\bigskip

\centering
\begin{tabular}{|r|r|r|r|r|}
\hline
\multicolumn{1}{|c|}{VV 2005} & \multicolumn{1}{c|}{CPLEX} & \multicolumn{1}{c|}{CPLEX C} &
\multicolumn{1}{c|}{CPLEX\_MA\_D C s}
& \multicolumn{1}{c|}{CPLEX\_MA\_D C el}\\
\hline
\hline
117811 & 117800 & 117809 & 117809 & 117809 \\
119232 & 119175 & 119181 & 119181 & 119217 \\
119215 & 119211 & 119211 & 119211 & 119211 \\
118813 & 118813 & 118813 & 118813 & 118813 \\
116509 & 116502 & 116514 & 116514 & 116514 \\
119504 & 119504 & 119481 & 119504 & 119504 \\
119827 & 119777 & 119790 & 119794 & 119800 \\
118329 & 118323 & 118323 & 118323 & 118323 \\
117815 & 117779 & 117781 & 117781 & 117815 \\
119231 & 119211 & 119203 & 119228 & 119228 \\
217377 & 217377 & 217377 & 217377 & 217377 \\
219077 & 219066 & 219066 & 219077 & 219077 \\
217806 & 217847 & 217847 & 217847 & 217847 \\
216868 & 216868 & 216868 & 216868 & 216868 \\
213850 & 213846 & 213846 & 213859 & 213859 \\
215086 & 215073 & 215086 & 215075 & 215086 \\
217940 & 217887 & 217931 & 217931 & 217931 \\
219984 & 219984 & 219984 & 219984 & 219984 \\
214375 & 214352 & 214375 & 214352 & 214375 \\
220899 & 220852 & 220846 & 220886 & 220886 \\
304387 & 304387 & 304387 & 304353 & 304387 \\
302379 & 302348 & 302356 & 302371 & 302379 \\
302416 & 302408 & 302416 & 302416 & 302416 \\
300757 & 300747 & 300743 & 300747 & 300757 \\
304374 & 304357 & 304357 & 304374 & 304366 \\
301836 & 301767 & 301796 & 301796 & 301836 \\
304952 & 304949 & 304949 & 304949 & 304952 \\
296478 & 296456 & 296459 & 296456 & 296459 \\
301359 & 301353 & 301353 & 301353 & 301357 \\
307089 & 307089 & 307089 & 307089 & 307089 \\
\hline
\end{tabular}
\end{table}
                                           
\begin{table}[!htb]
\caption{Objective values of the MKP obtained with different algorithm
variants and total CPU times of 1800 seconds per instance, for the last column
of 14400 seconds, compared to best known approach (VV~2005); $n=500$ $m=30$.}
\label{tab:Appendix3}
\bigskip

\centering
\begin{tabular}{|r|r|r|r|r|}
\hline
\multicolumn{1}{|c|}{VV 2005} & \multicolumn{1}{c|}{CPLEX} & \multicolumn{1}{c|}{CPLEX C} &
\multicolumn{1}{c|}{CPLEX\_MA\_D C s}
& \multicolumn{1}{c|}{CPLEX\_MA\_D C el}\\
\hline
\hline
116056 & 115957 & 116014 & 116014 & 116014 \\
114810 & 114701 & 114810 & 114810 & 114810 \\
116712 & 116661 & 116661 & 116661 & 116699 \\
115329 & 115268 & 115241 & 115241 & 115253 \\
116525 & 116396 & 116413 & 116420 & 116516 \\
115741 & 115726 & 115726 & 115741 & 115726 \\
114181 & 114072 & 114058 & 114024 & 114181 \\
114348 & 114270 & 114290 & 114290 & 114290 \\
115419 & 115419 & 115287 & 115419 & 115419 \\
117116 & 117023 & 117023 & 117023 & 117104 \\
218104 & 218033 & 218073 & 218041 & 218073 \\
214648 & 214645 & 214621 & 214626 & 214626 \\
215978 & 215898 & 215918 & 215903 & 215942 \\
217910 & 217863 & 217827 & 217836 & 217841 \\
215689 & 215625 & 215601 & 215601 & 215635 \\
215890 & 215848 & 215847 & 215847 & 215860 \\
215907 & 215831 & 215883 & 215883 & 215883 \\
216542 & 216425 & 216419 & 216448 & 216466 \\
217340 & 217287 & 217333 & 217312 & 217312 \\
214739 & 214701 & 214701 & 214701 & 214701 \\
301675 & 301656 & 301656 & 301656 & 301656 \\
300055 & 300004 & 300055 & 299992 & 300016 \\
305087 & 305069 & 305051 & 305051 & 305062 \\
302032 & 302001 & 302008 & 302008 & 302008 \\
304462 & 304406 & 304423 & 304423 & 304423 \\
297012 & 296959 & 296959 & 296959 & 296959 \\
303364 & 303329 & 303322 & 303322 & 303335 \\
307007 & 306920 & 306940 & 306961 & 307007 \\
303199 & 303158 & 303199 & 303199 & 303199 \\
300572 & 300524 & 300499 & 300509 & 300572 \\
\hline
\end{tabular}
\end{table}

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