Distance MAX-MIN problem
Distance MAX-MIN problem
Hi,
I was trying a Max Min problem and was wondering if anyone could help
me out.
Scenario: consider a 2-D point say X to be found out by optimization.
I have a set of say 100 points which i already know.
The objective is to find the minimum distance between X and all the
100 other points and then in the end maximize this distance.
For the above i write the following OBJ equation.
set n/1*100/;
set d/1*2/;
..
..
..
..
variable x(d);
OBJ.. Z=l= sqrt ( sqr(x('1')-tp(n,'1') ) + sqr(x('2')-
tp(n,'2') );
model value/All/
solve value maximizing Z using NLP;
Note: x is a variable to be found out.
tp is the array of 100 numbers i.e. table tp(n,d)
The problem that i am facing is that i am unable to control the value
of 'n' in the equation OBJ. How do i run the value of 'n' from 1 to
100 in the equation.
I tried the following
OBJ(n).. Z=l= sqrt ( sqr(x('1')-tp(n,'1') ) + sqr(x('2')-
tp(n,'2') );
and it worked , but i do not want to follow this method.
Is there any other method how i can control the value of n in the
equation. GAMS does not allow me to use LOOPS inside equations. Any
help will be appreciated.
Sumit
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Re: Distance MAX-MIN problem
Hi,
Thanks for the prompt reply. Yes what you have said is correct i am
actually looking for an alternative method.
I do not want to create 'n' OBJ equations. I want just one OBJ eqn and
then control the value of 'n' inside this eqn..
If i put OBJ(n).. it means that i have
OBJ(1)..
OBJ(2)..
..
..
OBJ(n)..
but i dont want this, i want just one OBJ.. and then i want to control
'n' inside this equation.So essentially i am looking out for an
alternative.
Regards
Sumit
On Sep 14, 3:50 am, "Arne Stolbjerg Drud" wrote:
> > I do not understand your problem. You essentially say: "I have a method that
> > works, but I do not want to use it. Please suggest an alternative."
> >
> > The method you suggest and that works is in my mind the way to do it.
> >
> > Regards
> >
> > Arne Stolbjerg Drud
> >
> > ----------------------------------
> > Arne Stolbjerg Drud
> > ARKI Consulting & Development A/S
> > Bagsvaerdvej 246A, DK-2880 Bagsvaerd, Denmark
> > Phone: (+45) 44 49 03 23, Fax: (+45) 44 49 03 33, email: ad...@arki.dk
> >
> > -----Oprindelig meddelelse-----
> > Fra: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] PÃ¥ vegne
> > af sskhera
> > Sendt: 14. september 2008 01:29
> > Til: gamsworld
> > Emne: Distance MAX-MIN problem
> >
> > Hi,
> >
> > I was trying a Max Min problem and was wondering if anyone could help
> > me out.
> >
> > Scenario: consider a 2-D point say X to be found out by optimization.
> > I have a set of say 100 points which i already know.
> >
> > The objective is to find the minimum distance between X and all the
> > 100 other points and then in the end maximize this distance.
> >
> > For the above i write the following OBJ equation.
> >
> > set n/1*100/;
> > set d/1*2/;
> > ..
> > ..
> > ..
> > ..
> > variable x(d);
> >
> > OBJ.. Z=l= sqrt ( sqr(x('1')-tp(n,'1') ) + sqr(x('2')-
> > tp(n,'2') );
> >
> > model value/All/
> >
> > solve value maximizing Z using NLP;
> >
> > Note: x is a variable to be found out.
> > tp is the array of 100 numbers i.e. table tp(n,d)
> >
> > The problem that i am facing is that i am unable to control the value
> > of 'n' in the equation OBJ. How do i run the value of 'n' from 1 to
> > 100 in the equation.
> >
> > I tried the following
> >
> > OBJ(n).. Z=l= sqrt ( sqr(x('1')-tp(n,'1') ) + sqr(x('2')-
> > tp(n,'2') );
> > and it worked , but i do not want to follow this method.
> >
> > Is there any other method how i can control the value of n in the
> > equation. GAMS does not allow me to use LOOPS inside equations. Any
> > help will be appreciated.
> >
> > Sumit
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Re: Distance MAX-MIN problem
Hi,
Thanks for the reply. Yes i had also tried the same i.e.
OBJ.. smin(n,expression in n);
and used the DNLP solver but it showed the error "cannot handle
function min" which stopped me from going ahead this way.
Will the use of external equations help in any way?
Regards,
Sumit
On Sep 15, 12:17 am, "Arne Stolbjerg Drud" wrote:
> > From a syntax point of view you can write:
> >
> > OBJ .. Z =E= smax(n, expression in n );
> >
> > However, Smax is a non-differentiable function so you will also have to
> > change the solve statement to
> >
> > Solve ... using DNLP;
> >
> > The DNLP solvers we have are trying to solve the model as if it was an NLP
> > model, ignoring any non-differentiable properties. In your case this means
> > that the solver probably would get stuck somewhere on the way to an optimal
> > solution. The non-differentiable property also means, that a locally optimal
> > solution may not be recognized as locally optimal since there are no
> > well-defined gradients.
> >
> > So again I will encourage you to use your original formulation with N
> > constraints defining the objective.
> >
> > Regards
> >
> > Arne Stolbjerg Drud
> >
> > ----------------------------------
> > Arne Stolbjerg Drud
> > ARKI Consulting & Development A/S
> > Bagsvaerdvej 246A, DK-2880 Bagsvaerd, Denmark
> > Phone: (+45) 44 49 03 23, Fax: (+45) 44 49 03 33, email: ad...@arki.dk
> >
> > -----Oprindelig meddelelse-----
> > Fra: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] PÃ¥ vegne
> > af sskhera
> > Sendt: 14. september 2008 19:21
> > Til: gamsworld
> > Emne: Re: Distance MAX-MIN problem
> >
> > Hi,
> >
> > Thanks for the prompt reply. Yes what you have said is correct i am
> > actually looking for an alternative method.
> > I do not want to create 'n' OBJ equations. I want just one OBJ eqn and
> > then control the value of 'n' inside this eqn..
> >
> > If i put OBJ(n).. it means that i have
> >
> > OBJ(1)..
> > OBJ(2)..
> > ..
> > ..
> > OBJ(n)..
> >
> > but i dont want this, i want just one OBJ.. and then i want to control
> > 'n' inside this equation.So essentially i am looking out for an
> > alternative.
> >
> > Regards
> > Sumit
> >
> > On Sep 14, 3:50 am, "Arne Stolbjerg Drud" wrote:
> >
>> > > I do not understand your problem. You essentially say: "I have a method
> > that
>> > > works, but I do not want to use it. Please suggest an alternative."
> >
>> > > The method you suggest and that works is in my mind the way to do it.
> >
>> > > Regards
> >
>> > > Arne Stolbjerg Drud
> >
>> > > ----------------------------------
>> > > Arne Stolbjerg Drud
>> > > ARKI Consulting & Development A/S
>> > > Bagsvaerdvej 246A, DK-2880 Bagsvaerd, Denmark
>> > > Phone: (+45) 44 49 03 23, Fax: (+45) 44 49 03 33, email: ad...@arki.dk
> >
>> > > -----Oprindelig meddelelse-----
>> > > Fra: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] PÃ¥
> > vegne
>> > > af sskhera
>> > > Sendt: 14. september 2008 01:29
>> > > Til: gamsworld
>> > > Emne: Distance MAX-MIN problem
> >
>> > > Hi,
> >
>> > > I was trying a Max Min problem and was wondering if anyone could help
>> > > me out.
> >
>> > > Scenario: consider a 2-D point say X to be found out by optimization.
>> > > I have a set of say 100 points which i already know.
> >
>> > > The objective is to find the minimum distance between X and all the
>> > > 100 other points and then in the end maximize this distance.
> >
>> > > For the above i write the following OBJ equation.
> >
>> > > set n/1*100/;
>> > > set d/1*2/;
>> > > ..
>> > > ..
>> > > ..
>> > > ..
>> > > variable x(d);
> >
>> > > OBJ.. Z=l= sqrt ( sqr(x('1')-tp(n,'1') ) + sqr(x('2')-
>> > > tp(n,'2') );
> >
>> > > model value/All/
> >
>> > > solve value maximizing Z using NLP;
> >
>> > > Note: x is a variable to be found out.
>> > > tp is the array of 100 numbers i.e. table tp(n,d)
> >
>> > > The problem that i am facing is that i am unable to control the value
>> > > of 'n' in the equation OBJ. How do i run the value of 'n' from 1 to
>> > > 100 in the equation.
> >
>> > > I tried the following
> >
>> > > OBJ(n).. Z=l= sqrt ( sqr(x('1')-tp(n,'1') ) + sqr(x('2')-
>> > > tp(n,'2') );
>> > > and it worked , but i do not want to follow this method.
> >
>> > > Is there any other method how i can control the value of n in the
>> > > equation. GAMS does not allow me to use LOOPS inside equations. Any
>> > > help will be appreciated.
> >
>> > > Sumit
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