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\title{
Applying Constraint Logic Programming  Languages for  Modelling Multi-objective
Decision Making under Uncertainty  (Summary)\\ 
(Aug.\ 1996 -- Feb \ 1997)
}
\author{ John Darlington \and Yike Guo}

\date{Imperial College/ Fujitsu Parallel Computing Research Centre}


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\samepage \begin{tabular}{|l|l|}
\hline
  Logical Expression  & Constraint  \\ 
\hline
 $P_1\vee ...\vee P_n$ & $\delta_1 +...+\delta_n\geq 1$  \\ 
\hline
$P_1\wedge P_2$ &$\delta_1=1,\delta_2=2$ \\ 
\hline
... & ...  \\ 
\hline
\end{tabular}
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\hspace*{-1cm}
\begin{tabular}[t]{|c|c|c|c|c|c|c|c|c|} \hline
  \raisebox{-1.5ex}[0cm][0cm]{Problem} &
  \raisebox{-1.5ex}[0cm][0cm]{Entries} &
  \multicolumn{2}{c|}{MGBAS} &
 \multicolumn{2}{c|}{GBAS} &
 \multicolumn{2}{c|}{TGBAS} &
 \multicolumn{1}{|c|}{GRIN} \\ \cline{3-9}
  & & Size & Time & Size & Time & Size &  Time & Size \\ \hline\hline
  mat3x7.1 & 0-20 & 17 & 0.46 & 568 & 1462.96 & 272 & 55.96 & 31
\\  \hline
  mat4x8.1 & 0-20 & 157 & 25.91 &5245&13509.32& 2352 & 447.68
& 294 \\  \hline
  mat4x8.2 & 0-20 & 112 & 17.82 &3742&9638.23& 1640 & 335.76 &
205 \\  \hline
  mat4x8.3 & 0-20 & 251 & 54.84 &8386&21599.41& 3848 & 783.44
& 481 \\  \hline
  mat5x10.1 & 0-4 & 121 & 31.53 &4002&10307.69& 1632 & 335.24
& 204  \\  \hline
  mat5x10.2 & 0-4 & 142 & 90.56 &4696&12095.35& 2800 & 559.60
& 350  \\  \hline
  mat5x10.3 & 0-4 & 112 & 63.69 &3742&9638.41& 3312 & 671.52 &
414  \\  \hline
  mat6x12.1 & 0-3 & 134 & 121.73&4477&13531.15& 4467 & 895.36
& 561 \\  \hline
  mat6x12.2 & 0-3 & 103 & 89.87 &3441&8862.07 & 3304 & 671.52
& 413  \\  \hline
  mat6x12.3 & 0-3 & 267 & 278.32&8920&22975.54& 5672 &
1119.20 & 709 \\  \hline
  mat8x16.1 & 0-1 & 87 & 7.67   &658&1520.44 & 568  & 121.84 &
126  \\  \hline
  mat8x16.2 & 0-1 & 101 & 12.53 &760&1857.29 & 650  & 135.89 &
168 \\  \hline
\hline
\end{tabular}
\end{center}

\label{mgba}
\end{table*}
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