Benders' Decomposition

GAMS
1

Hello,

I am implementing a Benders’ decomposition Algorithm in GAMS to solve a MIP problem. The master problem contains integer variables and is difficult to solve. It seems that GAMS solve it each time from the scratch. Is there anyway that, I can force GAMS to keep the solution of Master problem from previous iteration, and use it to solve the new master problem?

I appreciate your response.

Majid

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2

Hi Majid,

Check this link:

http://www.amsterdamoptimization.com/pdf/benders.pdf


Cheers,
Pedro

On Fri, Oct 31, 2014 at 3:58 PM, Majid wrote:

Hello,

I am implementing a Benders’ decomposition Algorithm in GAMS to solve a MIP problem. The master problem contains integer variables and is difficult to solve. It seems that GAMS solve it each time from the scratch. Is there anyway that, I can force GAMS to keep the solution of Master problem from previous iteration, and use it to solve the new master problem?

I appreciate your response.

Majid

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3

Hi Majid



You can use modelname.solvelink =2; which keeps Gams open (?, I did not find a clear explanation in the documentation…Perhaps somebody could explain this to me in layman terms.)



Cheers

Renger


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From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of Majid
Sent: Friday, October 31, 2014 4:58 PM
To: gamsworld@googlegroups.com
Subject: Benders’ Decomposition



Hello,



I am implementing a Benders’ decomposition Algorithm in GAMS to solve a MIP problem. The master problem contains integer variables and is difficult to solve. It seems that GAMS solve it each time from the scratch. Is there anyway that, I can force GAMS to keep the solution of Master problem from previous iteration, and use it to solve the new master problem?



I appreciate your response.



Majid

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4

Dear Majid,

The statement ‘master_model_name.solvelink=2’ just speed up by keeping GAMS in memory and I think its not related to your question.
About Benders Decomposition I have to say it is really easy to implement using GAMS. I recommend you study the Erwin Kalvelagen paper regarding B.D. It is available on the Internet.

Regards,

Morteza Shabanzadeh
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On Friday, October 31, 2014 7:28 PM, Majid wrote:


Hello,

I am implementing a Benders’ decomposition Algorithm in GAMS to solve a MIP problem. The master problem contains integer variables and is difficult to solve. It seems that GAMS solve it each time from the scratch. Is there anyway that, I can force GAMS to keep the solution of Master problem from previous iteration, and use it to solve the new master problem?

I appreciate your response.

Majid

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5

Hello,

I think my question fits right in this topic.

I use BONMIN on a windows platform for a MINLP model. The model is hard to solve. It consists of a few smooth, nonlinear equations and a lot of linear equations. The integer variables are embedded in the linear equations. I would like to know wheter the Benders Decomposition is suitable to break my model into a NLP and a MIP model to speed up computational time. Or is there any other possibility to divide a MINLP model?

Thanks in advance,

Michael



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6

Thanks.

I already studied Erwin’s BD note, and my implementation is based on that. But my question is, how to use the solutions from the previous steps. The problem is that my master problem is very difficult to solve, and when GAMS solves it in each iteration from scratch, the solution time will be very large.

I know that CPLEX has this feature when you call it from c++ or Python. I just want to know if there is something similar in GAMS.

Thanks

On Fri, Oct 31, 2014 at 1:35 PM, wrote:

Hello,

I think my question fits right in this topic.

I use BONMIN on a windows platform for a MINLP model. The model is hard to solve. It consists of a few smooth, nonlinear equations and a lot of linear equations. The integer variables are embedded in the linear equations. I would like to know wheter the Benders Decomposition is suitable to break my model into a NLP and a MIP model to speed up computational time. Or is there any other possibility to divide a MINLP model?

Thanks in advance,

Michael



\

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7

Dear Majid,
“How to use the solutions from the previous steps” for what? For solving the master or using in subproblem?

On Fri, Oct 31, 2014 at 9:19 PM, Majid Taghavi wrote:

Thanks.

I already studied Erwin’s BD note, and my implementation is based on that. But my question is, how to use the solutions from the previous steps. The problem is that my master problem is very difficult to solve, and when GAMS solves it in each iteration from scratch, the solution time will be very large.

I know that CPLEX has this feature when you call it from c++ or Python. I just want to know if there is something similar in GAMS.

Thanks

On Fri, Oct 31, 2014 at 1:35 PM, wrote:

Hello,

I think my question fits right in this topic.

I use BONMIN on a windows platform for a MINLP model. The model is hard to solve. It consists of a few smooth, nonlinear equations and a lot of linear equations. The integer variables are embedded in the linear equations. I would like to know wheter the Benders Decomposition is suitable to break my model into a NLP and a MIP model to speed up computational time. Or is there any other possibility to divide a MINLP model?

Thanks in advance,

Michael



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8

Dear Hossein,

To solve the master problem in the current step, which is the same problem from previous step plus a cut.

Thanks

On Fri, Oct 31, 2014 at 1:56 PM, Hossein Karimi wrote:

Dear Majid,
“How to use the solutions from the previous steps” for what? For solving the master or using in subproblem?

On Fri, Oct 31, 2014 at 9:19 PM, Majid Taghavi wrote:

Thanks.

I already studied Erwin’s BD note, and my implementation is based on that. But my question is, how to use the solutions from the previous steps. The problem is that my master problem is very difficult to solve, and when GAMS solves it in each iteration from scratch, the solution time will be very large.

I know that CPLEX has this feature when you call it from c++ or Python. I just want to know if there is something similar in GAMS.

Thanks

On Fri, Oct 31, 2014 at 1:35 PM, wrote:

Hello,

I think my question fits right in this topic.

I use BONMIN on a windows platform for a MINLP model. The model is hard to solve. It consists of a few smooth, nonlinear equations and a lot of linear equations. The integer variables are embedded in the linear equations. I would like to know wheter the Benders Decomposition is suitable to break my model into a NLP and a MIP model to speed up computational time. Or is there any other possibility to divide a MINLP model?

Thanks in advance,

Michael



\

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