Re: [Help-glpk] Irrational numbers

[glpk xypron]

Hello Vijay,

in the example the optimization problem was to find the minimum number of
6000 mm paper roles needed 
to fulfill demand for
4 * 2000 mm and
4 * 1000 mm.

The optimization result will be the same for any width of stock in the interval 
[6000, 7000[ because the widths in demand cannot be combined to any value in 
the interval ]6000, 7000[.

Thus in the example the rounding errors could be avoided by using a paper width 
of 6500 instead of 6000 in the optimization.

Hence I propose to add a preprocessing step to cpsol to identify a reasonable 
tolerance to add to the width of the stock. To determine the tolerance I 
envision the following alternative solutions:

1) Identify the smallest combination of demand elements wider then the width of 
the stock and the largest combination of demand elements equal or smaller then 
the stock. Use the average as width of the stock in the optimization. - This 
leaves You with problem to implement this step with exact mathematics.

2) Limiting all input to integers simply add .5 times the greatest common 
denominator (obviously at least .5) to the width of the stock.

3) Add a field for the rounding tolerance to the input file.

Best regards

Xypron

-------- Original-Nachricht --------
> Datum: Mon, 11 Aug 2008 23:32:08 +0530
> Von: "Vijay Patil" <address@hidden>
> An: address@hidden
> Betreff: [Help-glpk] Irrational numbers

> In one of application using GLPK, I am facing a problem because of not
> being
> able to represent irrational numbers/values correctly (as obj. func.
> coeff.).
> Actually these values are dual values and are obtained from glpk itself.
> Since they are approximated there is a problem (loss of information).
> 
> If you have some experience/expertize dealing with irrational numbers or
> knowledge of floating point representation, you might be interested in
> having a look at the problem.
> 
> http://code.google.com/p/cspsol/issues/detail?id=1#c2
> 
> Any workarounds to deal with this problem?
> 
> Thanks
> -- 
> Vijay Patil

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