From: David Tian <D.Tian-2_at_postgrad.manchester.ac.uk>

Date: Fri, 3 Nov 2006 15:23:30 +0000

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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