Nested Optimization

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Archiver
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Nested Optimization

Post by Archiver »


Hi everyone.

I am facing the need to run a nested optimization.
The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.

Is this possible in GAMS and how?

Tks.

Bruno

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Archiver
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Re: Nested Optimization

Post by Archiver »


Bruno,

Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g. https://www.gams.com/modlib/libhtml/cutstock.htm).

Best,
Michael Bussieck - GAMSWorld Coordinator

On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:

Hi everyone.

I am facing the need to run a nested optimization.
The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.

Is this possible in GAMS and how?

Tks.

Bruno

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Archiver
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Re: Nested Optimization

Post by Archiver »


My problem seems to fit into the bilevel class. I'll look into it.

Thank you very much Michael.

Bruno

On Monday, January 18, 2016 at 1:14:55 PM UTC-2, Michael Bussieck wrote:

Bruno,

Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g. https://www.gams.com/modlib/libhtml/cutstock.htm).

Best,
Michael Bussieck - GAMSWorld Coordinator

On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:

Hi everyone.

I am facing the need to run a nested optimization.
The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.

Is this possible in GAMS and how?

Tks.

Bruno

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Archiver
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Re: Nested Optimization

Post by Archiver »


Hello Michael.

I've looked into the bibliography you posted and my problem is slightly different from the bilevel.

On a bilevel problem, an optimized function is a constraint of another function to be optimized.

In my problem, I have a function to be minimized G(x, T) and another function to be minimized W(x, T, x1, T1)

The variables x, T are common to both optimized functions, but one function is not necessarily a constraint of the other.

Do you have any clue as to how this problem can be treated?

Tks a lot!

Bruno

On Wednesday, January 20, 2016 at 5:41:23 AM UTC-2, Bruno Hannud wrote:

My problem seems to fit into the bilevel class. I'll look into it.

Thank you very much Michael.

Bruno

On Monday, January 18, 2016 at 1:14:55 PM UTC-2, Michael Bussieck wrote:

Bruno,

Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g. https://www.gams.com/modlib/libhtml/cutstock.htm).

Best,
Michael Bussieck - GAMSWorld Coordinator

On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:

Hi everyone.

I am facing the need to run a nested optimization.
The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.

Is this possible in GAMS and how?

Tks.

Bruno

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Archiver
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Re: Nested Optimization

Post by Archiver »


If you don’t want to do this as a nested problem, but formulate this in the Nash equilibrium setting, then the tools of EMP will allow you to do this. You set up an equilibrium problem with 2 agents (the G agent and the W agent).

Cheers, Michael

On Jan 20, 2016, at 8:26 AM, Bruno Hannud wrote:

Hello Michael.

I've looked into the bibliography you posted and my problem is slightly different from the bilevel.

On a bilevel problem, an optimized function is a constraint of another function to be optimized.

In my problem, I have a function to be minimized G(x, T) and another function to be minimized W(x, T, x1, T1)

The variables x, T are common to both optimized functions, but one function is not necessarily a constraint of the other.

Do you have any clue as to how this problem can be treated?

Tks a lot!

Bruno

On Wednesday, January 20, 2016 at 5:41:23 AM UTC-2, Bruno Hannud wrote:

My problem seems to fit into the bilevel class. I'll look into it.

Thank you very much Michael.

Bruno

On Monday, January 18, 2016 at 1:14:55 PM UTC-2, Michael Bussieck wrote:

Bruno,

Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g. https://www.gams.com/modlib/libhtml/cutstock.htm).

Best,
Michael Bussieck - GAMSWorld Coordinator

On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:

Hi everyone.

I am facing the need to run a nested optimization.
The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.

Is this possible in GAMS and how?

Tks.

Bruno


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Archiver
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Re: Nested Optimization

Post by Archiver »


Thanks Michael. I’ll try that.

Bruno


Sent with Unibox

> On Jan 20, 2016, at 3:10 PM, Michael Ferris wrote:
>
> If you don’t want to do this as a nested problem, but formulate this in the Nash equilibrium setting, then the tools of EMP will allow you to do this. You set up an equilibrium problem with 2 agents (the G agent and the W agent).
>
> Cheers, Michael
>
> On Jan 20, 2016, at 8:26 AM, Bruno Hannud wrote:
>
> Hello Michael.
>
> I've looked into the bibliography you posted and my problem is slightly different from the bilevel.
>
> On a bilevel problem, an optimized function is a constraint of another function to be optimized.
>
> In my problem, I have a function to be minimized G(x, T) and another function to be minimized W(x, T, x1, T1)
>
> The variables x, T are common to both optimized functions, but one function is not necessarily a constraint of the other.
>
> Do you have any clue as to how this problem can be treated?
>
> Tks a lot!
>
> Bruno
>
> On Wednesday, January 20, 2016 at 5:41:23 AM UTC-2, Bruno Hannud wrote:
>
> My problem seems to fit into the bilevel class. I'll look into it.
>
> Thank you very much Michael.
>
> Bruno
>
> On Monday, January 18, 2016 at 1:14:55 PM UTC-2, Michael Bussieck wrote:
>
> Bruno,
>
> Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g.https://www.gams.com/modlib/libhtml/cutstock.htm).
>
> Best,
> Michael Bussieck - GAMSWorld Coordinator
>
> On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:
>
> Hi everyone.
>
> I am facing the need to run a nested optimization.
> The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.
>
> Is this possible in GAMS and how?
>
> Tks.
>
> Bruno
>
>
> --
> To unsubscribe from this group and stop receiving emails from it, send an email togamsworld+unsubscribe@googlegroups.com.
> To post to this group, send email to gamsworld@googlegroups.com.
> Visit this group at https://groups.google.com/group/gamsworld.
> For more options, visit https://groups.google.com/d/optout.
>
> --
> You received this message because you are subscribed to a topic in the Google Groups "gamsworld" group.
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> To unsubscribe from this group and all its topics, send an email to gamsworld+unsubscribe@googlegroups.com.
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> For more options, visit https://groups.google.com/d/optout.

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Archiver
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Re: Nested Optimization

Post by Archiver »

Bruno,

You mention two functions to be minimized, but this can be interpreted in different ways. I can think of two such:

A) one agent controls all variables (x, T, x1, T1) and wants to minimize both G(x,T) and W(x,T,x1,T1). This is sometimes called multi-objective programming or goal programming. There are different ways to set this up that allow the one controlling agent to "trade off" gains in G for losses in W, or vice versa.

B) there are two agents. Agent 0 controls variables (x,T), and agent 1 controls variables (x1,T1). Agent 0 then optimizes G(x,T). Agent 1 optimizes W(x,T,x1,T1) wrt only (x1,T1) but views (x,T) as parameters. The interesting wrinkle is that they are not fixed, like parameters often are, but not endogenous to agent 1 either. This is the Nash equilibrium case that Ferris mentioned.

-Steve

On Wed, Jan 20, 2016 at 9:26 AM, Bruno Hannud wrote:

Hello Michael.

I've looked into the bibliography you posted and my problem is slightly different from the bilevel.

On a bilevel problem, an optimized function is a constraint of another function to be optimized.

In my problem, I have a function to be minimized G(x, T) and another function to be minimized W(x, T, x1, T1)

The variables x, T are common to both optimized functions, but one function is not necessarily a constraint of the other.

Do you have any clue as to how this problem can be treated?

Tks a lot!

Bruno

On Wednesday, January 20, 2016 at 5:41:23 AM UTC-2, Bruno Hannud wrote:

My problem seems to fit into the bilevel class. I'll look into it.

Thank you very much Michael.

Bruno

On Monday, January 18, 2016 at 1:14:55 PM UTC-2, Michael Bussieck wrote:

Bruno,

Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g. https://www.gams.com/modlib/libhtml/cutstock.htm).

Best,
Michael Bussieck - GAMSWorld Coordinator

On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:

Hi everyone.

I am facing the need to run a nested optimization.
The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.

Is this possible in GAMS and how?

Tks.

Bruno

--
To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.
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Visit this group at https://groups.google.com/group/gamsworld.
For more options, visit https://groups.google.com/d/optout.




--
Steven Dirkse, Ph.D.
GAMS Development Corp., Washington DC
Voice: (202)342-0180 Fax: (202)342-0181
sdirkse@gams.com
http://www.gams.com
Archiver
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Posts: 7876
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Re: Nested Optimization

Post by Archiver »


Steve,

Thanks to have mentioned this.

Bruno


Sent with Unibox

> On Jan 20, 2016, at 4:06 PM, Steven Dirkse wrote:
>
> Bruno,
>
> You mention two functions to be minimized, but this can be interpreted in different ways. I can think of two such:
>
> A) one agent controls all variables (x, T, x1, T1) and wants to minimize both G(x,T) and W(x,T,x1,T1). This is sometimes called multi-objective programming or goal programming. There are different ways to set this up that allow the one controlling agent to "trade off" gains in G for losses in W, or vice versa.
>
> B) there are two agents. Agent 0 controls variables (x,T), and agent 1 controls variables (x1,T1). Agent 0 then optimizes G(x,T). Agent 1 optimizes W(x,T,x1,T1) wrt only (x1,T1) but views (x,T) as parameters. The interesting wrinkle is that they are not fixed, like parameters often are, but not endogenous to agent 1 either. This is the Nash equilibrium case that Ferris mentioned.
>
> -Steve
>
> On Wed, Jan 20, 2016 at 9:26 AM, Bruno Hannud wrote:
>
> Hello Michael.
>
> I've looked into the bibliography you posted and my problem is slightly different from the bilevel.
>
> On a bilevel problem, an optimized function is a constraint of another function to be optimized.
>
> In my problem, I have a function to be minimized G(x, T) and another function to be minimized W(x, T, x1, T1)
>
> The variables x, T are common to both optimized functions, but one function is not necessarily a constraint of the other.
>
> Do you have any clue as to how this problem can be treated?
>
> Tks a lot!
>
> Bruno
>
> On Wednesday, January 20, 2016 at 5:41:23 AM UTC-2, Bruno Hannud wrote:
>
> My problem seems to fit into the bilevel class. I'll look into it.
>
> Thank you very much Michael.
>
> Bruno
>
> On Monday, January 18, 2016 at 1:14:55 PM UTC-2, Michael Bussieck wrote:
>
> Bruno,
>
> Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g. https://www.gams.com/modlib/libhtml/cutstock.htm).
>
> Best,
> Michael Bussieck - GAMSWorld Coordinator
>
> On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:
>
> Hi everyone.
>
> I am facing the need to run a nested optimization.
> The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.
>
> Is this possible in GAMS and how?
>
> Tks.
>
> Bruno
>
> --
> To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.
> To post to this group, send email to gamsworld@googlegroups.com.
> Visit this group at https://groups.google.com/group/gamsworld.
> For more options, visit https://groups.google.com/d/optout.
>
>
>
>
> --
> Steven Dirkse, Ph.D.
> GAMS Development Corp., Washington DC
> Voice: (202)342-0180 Fax: (202)342-0181
> sdirkse@gams.com
> http://www.gams.com
>
> --
> You received this message because you are subscribed to a topic in the Google Groups "gamsworld" group.
> To unsubscribe from this topic, visit https://groups.google.com/d/topic/gamsw ... nsubscribe.
> To unsubscribe from this group and all its topics, send an email to gamsworld+unsubscribe@googlegroups.com.
> To post to this group, send email to gamsworld@googlegroups.com.
> Visit this group at https://groups.google.com/group/gamsworld.
> For more options, visit https://groups.google.com/d/optout.

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Archiver
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Re: Nested Optimization

Post by Archiver »


Michael, can you point me to a sample program so that I see how is its structure (the bilevel bibliography has 2 such samples which were very instructive).

Cheers.

Bruno

On Wednesday, January 20, 2016 at 3:12:33 PM UTC-2, Michael Ferris wrote:

If you don’t want to do this as a nested problem, but formulate this in the Nash equilibrium setting, then the tools of EMP will allow you to do this. You set up an equilibrium problem with 2 agents (the G agent and the W agent).

Cheers, Michael

On Jan 20, 2016, at 8:26 AM, Bruno Hannud wrote:

Hello Michael.

I've looked into the bibliography you posted and my problem is slightly different from the bilevel.

On a bilevel problem, an optimized function is a constraint of another function to be optimized.

In my problem, I have a function to be minimized G(x, T) and another function to be minimized W(x, T, x1, T1)

The variables x, T are common to both optimized functions, but one function is not necessarily a constraint of the other.

Do you have any clue as to how this problem can be treated?

Tks a lot!

Bruno

On Wednesday, January 20, 2016 at 5:41:23 AM UTC-2, Bruno Hannud wrote:

My problem seems to fit into the bilevel class. I'll look into it.

Thank you very much Michael.

Bruno

On Monday, January 18, 2016 at 1:14:55 PM UTC-2, Michael Bussieck wrote:

Bruno,

Can you be more specific with your request. GAMS has the possibility to formulate bilevel optimization problems (http://www.gams.com/help/topic/gams.doc ... L_PROGRAMS) but also to have decomposition schemes where you have a master and a sub problem that interact with each other (see e.g. https://www.gams.com/modlib/libhtml/cutstock.htm).

Best,
Michael Bussieck - GAMSWorld Coordinator

On Friday, January 15, 2016 at 4:26:20 PM UTC-5, Bruno Hannud wrote:

Hi everyone.

I am facing the need to run a nested optimization.
The program would consist of an upper level optimization, and a lower level optimization, nested within the upperlevel optimization.

Is this possible in GAMS and how?

Tks.

Bruno


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Visit this group at https://groups.google.com/group/gamsworld.
For more options, visit https://groups.google.com/d/optout.

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