Re: [Help-glpk] typo in mip gap formula on wikibook page

[Michael Hennebry]

On Thu, 2 May 2013, Andrew Makhorin wrote:

> The mip gap has the same meaning as the relative error (please see
> http://en.wikipedia.org/wiki/Approximation_error ), so changing the
> formula would confuse the user. A requirement to make the result
> "immune ... and never greater than 100%" looks too artificial.

http://en.wikipedia.org/wiki/Approximation_error:
> There are two features of relative error that should be kept in mind.
> Firstly, relative error is undefined when the true value is zero as
> it appears in the denominator (see below).
> Secondly, relative error only makes sense when measured on a ratio scale,
> (i.e. a scale which has a true meaningful zero), otherwise it would be
> sensitive to the measurement units. For example, when an absolute error
> in a temperature measurement given in Celsius is 1° and the true value
> is 2°C, the relative error is 0.5 and the percent error is 50%.
> For this same case, when the temperature is given in Kelvin,
> the same 1° absolute error with the same true value of 275.15° K gives
> a relative error of 3.63e-3 and a percent error of only 0.363%.
> Celsius temperature is measured on an interval scale,
> whereas the Kelvin scale has a true zero and so is a ratio scale.

My suggestion has the effect of inducing a true zero.
BTW I didn't make it up.
I first encountered it in early literature on TSPs.

On Thu, 2 May 2013, Andrew Makhorin wrote:
> Probably, in order to avoid a meaningless result when the lower and
> upper objective bounds have different signs, the mip gap should not be
> computed at all.

Why print the mip gap at all?
The answer to that question should tell you whether to print it.

Also using the current mip gap in a stopping
criterion is not necessarily a good idea.
If one has enough knowledge to use it, one might as well use absolute error.
Temperatures near room temperature are an example.

--
Michael   address@hidden
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword."  --  Lily