Nested Optimization

[Bruno Hannud]

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

[Michael Bussieck]

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/solvers/jams/index.html?cp=0_3_23#EMP_BILEVEL_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

[Bruno Hannud]

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

Thank you very much Michael.

Bruno

[Bruno Hannud]

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 

[Michael Ferris]

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 

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[Steven Dirkse]

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

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[Bruno Hannud]

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

[Bruno Hannud]

Thanks Michael. I’ll try that.

Bruno

Sent with Unibox

On Jan 20, 2016, at 3:10 PM, Michael Ferris <fer...@cs.wisc.edu> 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 <bruno....@gmail.com> 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/solvers/jams/index.html?cp=0_3_23#EMP_BILEVEL_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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[Bruno Hannud]

Steve,

Thanks to have mentioned this.

Bruno

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