Mbot at 13:32, 8 November 2011

2011-11-08T13:32:51Z

← Older revision		Revision as of 08:32, 8 November 2011
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	<pre>		<pre>
	Problem type appears to be: mip		Problem type appears to be: mip
	Time for symbolic processing: 0.~~020405~~ seconds		Time for symbolic processing: 0.020054 seconds
	Starting numeric solver		Starting numeric solver
	===== * * * =================================================================== * * *		===== * * * =================================================================== * * *
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	FuncEv 58		FuncEv 58
	CPU time: 0.~~031200~~ sec. Elapsed time: 0.~~010000~~ sec.		CPU time: 0.015600 sec. Elapsed time: 0.011000 sec.
	a total of 3 disks are in use		a total of 3 disks are in use
	files on one of them: 4 8 10 12 14		files on one of them: 4 8 10 12 14

Mbot at 21:23, 2 November 2011

2011-11-02T21:23:58Z

← Older revision		Revision as of 16:23, 2 November 2011
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	==Variables==		==Variables==

			<pre>
	maxuse A maximal number of disks		maxuse A maximal number of disks
	capacity Storage available on each disk		capacity Storage available on each disk
	sizes Filesizes		sizes Filesizes
			</pre>

	==Reference==		==Reference==

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== Before leaving on holiday, you wish to backup your most important files onto fl..."

2011-11-02T21:00:32Z

Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== Before leaving on holiday, you wish to backup your most important files onto fl..."

New page

{{Part Of Manual|title=the TomSym Manual|link=[[TomSym|TomSym Manual]]}}

==Problem description==

Before leaving on holiday, you wish to backup your most important files onto floppy disks. You have got empty disks of 1.44Mb capacity. The sixteen files you would like to save have the following sizes: 46kb, 55kb, 62kb, 87kb, 108kb, 114kb, 137kb, 164kb, 253kb, 364kb, 372kb, 388kb, 406kb, 432kb, 461kb, and 851kb.

Assuming that you do not have any program at hand to compress the files and that you have got a sufficient number of floppy disks to save everything, how should the files be distributed in order to minimize the number of floppy disks used?

==Variables==

maxuse A maximal number of disks
capacity Storage available on each disk
sizes Filesizes

==Reference==

Applications of optimization... Gueret, Prins, Seveaux

<source lang="matlab">
% Marcus Edvall, Tomlab Optimization Inc, E-mail: tomlab@tomopt.com
% Copyright (c) 2005-2009 by Tomlab Optimization Inc., $Release: 7.2.0$
% Written Oct 7, 2005. Last modified Apr 8, 2009.
</source>

==Problem setup==

<source lang="matlab">
maxuse = 10;
capacity = 1440;
sizes = [46;55;62;87;108;114;137;164;253;364;372;388;406;432;461;851];

f = length(sizes);
d = maxuse;

save = tom('save',f,d,'int');
use = tom('use',d,1,'int');

% All variables are binary
bnds = {0 <= save <= 1, 0 <= use <= 1};

% An item must be stored on one unit
con1 = {sum(save,2) == 1};

% Stay below capacity of storage unit
con2 = {(sizes'*save)' <= capacity*use};

% Objective
objective = sum(use);

constraints = {bnds, con1, con2};
options = struct;
options.solver = 'cplex';
options.name = 'Backing up files';
sol = ezsolve(objective,constraints,[],options);

PriLev = 1;
if PriLev > 0
files = length(sizes);
filepos = sol.save;
disks_in_use = sum(sol.use);
disp(['a total of ' num2str(disks_in_use) ' disks are in use'])
for d = 1:maxuse,
files_on_disk = filepos(:,d); % what files on disk d
if (abs(sum(files_on_disk)) >= 0.5), % disk d is not empty?
file_ids = find(files_on_disk);
disp([' files on one of them: ' num2str(file_ids') ])
end
end
end

% MODIFICATION LOG
%
% 051010 med Created.
% 060112 per Added documentation
% 060125 per Moved disp to end
% 060314 med checking for empty disc changed
% 090308 med Converted to tomSym
</source>

<pre>
Problem type appears to be: mip
Time for symbolic processing: 0.020405 seconds
Starting numeric solver
===== * * * =================================================================== * * *
TOMLAB - TOMLAB Development license 999007. Valid to 2011-12-31
=====================================================================================
Problem: --- 1: Backing up files f_k 3.000000000000000000
f(x_0) 0.000000000000000000

Solver: CPLEX. EXIT=0. INFORM=101.
CPLEX Branch-and-Cut MIP solver
Optimal integer solution found

FuncEv 58
CPU time: 0.031200 sec. Elapsed time: 0.010000 sec.
a total of 3 disks are in use
files on one of them: 4 8 10 12 14
files on one of them: 1 2 6 7 9 11 15
files on one of them: 3 5 13 16

</pre>

TomSym Backing Up Files - Revision history

Mbot at 13:32, 8 November 2011

Mbot at 21:23, 2 November 2011

Mbot: Created page with "{{Part Of Manual|title=the TomSym Manual|link=TomSym Manual}} ==Problem description== Before leaving on holiday, you wish to backup your most important files onto fl..."