# [eclipse-users] Help With Model Simplification

From: David Tian <D.Tian-2_at_...14...>
Date: Fri, 3 Nov 2006 15:23:30 +0000
Hi,

The following code is a latex source which presents a model with 128481
variables, 73601 constraints. It has been implemented in ECLiPse using
FD library, but setting up the model only without computing for
solutions already consumes a lot of CPU power and takes alot of memory
several GB. I am wondering whether it is possible to re-model it in a
better way using less no. of constraints.

BTW, Constraints (3) contributes alot to the model complexity: there
are 70400
constraints of (3).

I would really appreciate any help.

I am sorry about the inconvience that the latex source is provided.
This is the only way to show my model.

Many thanks and Best Regards,

David

\documentclass{article}[12pt]
\title{Model Simplification}
\begin{document}
\maketitle
\section{The Model}
Variables: B1 is a 2-d matrix of boolean variables. Dimensions of B1
are 44 and 30. B2 is a 2-d matrix of boolean variables. The dimensions
of B2 are 1600 and 44. B3 is a 1-d matrix of boolean variables. Its
dimension is 1600. S is  varible.\\
Domains: Domains of all the boolean variables are $\{0,1\}$. The domain
of S is $\{1,2,3,\ldots,44\}$.\\
Integer values: D is a 3-d matrix of integer values with dimension 44,
1600 and 30 so that D[a][p][i] refers to the item of D at the ath, pth
and ith position.
\begin{tabbing}
\label{eq}
for\=(p=1,$p<1600$,p++)$\{$\\
\> for\=(a=1,$a<44$,a++)$\{$\\
\>    \> $B2[p][a] \Leftrightarrow \sum_{i = 1,2,\ldots,30} B1[a][i]*D[a][p][i] > 0$ (1)\\
\>$\}$\\
\>$B3[p]\Leftrightarrow \sum_{a=1,2,\ldots,44} B2[p][a] = 1$ (2)\\
\>$\sum_{a=1,2,3,\ldots,44}B2[p][a] \geq 1$ (3)\\
$\}$\\
$\sum_{p = 1,2,3,\ldots,1600}B3[p] = S$ (4)\\
minimize: f = S/44
\end{tabbing}
\section{Number of Variables, Constraints and Search Space Size}
Total number of variables = 44*30 + 1600*44 + 1600 + 1 = 128481. \\
Search space size = $2^{130086}$.\\
The total number of constraints = 1600*44 (constraints 1) + 1600
(constraints 2) + 1600 (constraints 3) + 1 (constraint 4) = 73601.\\
\end{document}

Received on Fri Nov 03 2006 - 15:23:35 CET

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