"Wesam ELSHAMY" <wesamelshamy@[EMAIL PROTECTED]
> wrote in message
news:1181746797.361598.126120@[EMAIL PROTECTED]
> On Jun 13, 7:55 am, "Vista" <a...@[EMAIL PROTECTED]
> wrote:
>> automatic parametric space exploration and boundary detection.
>>
>> Hi all,
>>
>> I am not sure where to ask about my "strange" question, so as an
initial
>> attempt, I post it here.
>>
>> I have a parameterized function f(x, y, z, u, v), which takes values on
>> {0,
>> 1}, i.e. either 0 or 1.
>>
>> Through experimenting I've found that when plotting out in 2D there is
a
>> clear linear cut in the parameter space.
>>
>> If I plot f(1, y, z, 5, 7) as a mesh of grid size 0.1, the cut is a
>> straight
>> line, the region below this line has f=1, and the region above this
line
>> has
>> f=0.
>>
>> If I plot f(2, y, z, 5, 7) as a mesh of grid size 0.1, the cut is a
>> straight
>> line, the region below this line has f=1, and the region above this
line
>> has
>> f=0. The only difference is that this line ****fted.
>>
>> ...
>>
>> If I plot f(x, 1, z, 5, 7) and f(x, 2, z, 5, 7) etc., still there is a
>> linear cut splitting the space.
>>
>> ...
>>
>> If I plot f(x, y, 1, 5, 7) and f(x, y, 2, 5, 7) etc., still there is a
>> linear cut splitting the space.
>>
>> ...
>>
>> It looks like there is a space-cutting plane in my parameter space.
>>
>> But the grid size is 0.1, I still have a hard time figuring out what
will
>> happen when grid size becomes 0.01 and 0.001, etc.
>>
>> But still, I would like to discover how to define this cutting plane
>> mathematically... ba
>>
>> My function is too complicated, and can only be computed numerically,
so
>> I
>> had a hard time finding a closed form for this cutting plane.
>>
>> Is there a way to determine the cutting plane using some automatifc
>> procedure?
>>
>> I mean, it looks like some kind of optimization procedure, it seeks the
>> finest boundry in the space such that on the left of the cut, f=1 and
on
>> the
>> other side of the cut, f=0. It also looks like a regression problem.
But
>> so
>> far I am still not sure how to model it.
>>
>> Can anybody give me some suggestions and comments?
>>
>> Thanks a lot!
>
> Since you posted your message in a GA newsgroup, my solution to your
> problem will be GA related.
>
> I recommend using a Multi-objective Evolutionary Algorithm (MOEA)
> procedure for your problem. You may try the SPEA2 algorithm (http://
> www.tik.ee.ethz.ch/sop/publicationListFiles/zlt2001a.pdf). For more
> MOEA algorithms check out http://www.lania.mx/~ccoello/EMOO/
>
> The parameters of your function (x, y, z) will be evolved by the
> algorithm and you can set your fitness function to reflect the
> absolute rate of change of your complex function f(). The diversity
> maintenance mechanism will help maintaining a good diversity along the
> plane, however you will need a big population size to cover a good
> ****tion of this plane.
>
> Alternatively you may try a Multi-Objective Particle Swarm
> Optimization (MOPSO) procedure (http://www.lania.mx/~ccoello/EMOO/
> coello04.pdf.gz). Based on my experience, PSO algorithms are faster
> than GA algorithms for this kind of problems.
>
> Wesam Elshamy
>
Thanks Wesam.
Let me describe my problem with an simpler example.
Let's say I have a 2D plane.
I draw a straight line to split the plane to two parts: Left and Right.
The
equation for the straightline is y=a*x+b.
In the left part the values of F(x, y) are 1s, while in the right part the
values of F(x, y) are 0s.
You can query the value of F for any x and y. That's to say, you give me a
location (x, y), I will tell you the function value F(x, y).
What's the most efficient way to discover the value of "a" and "b"?
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