Originally posted by: jdpfreefly

Hi, everyone,

        l'm want to do a lagrangian relaxation(LR) in a multicommodity network flow problem. I  had searched in this forum, there are already somebody asked this question, but nobody answered.  my wonder is there is so many callback routine, I have no idea how to get start to build a  basic framework to initialize LR method. Is there anyone had did this method, can sharing some C programming code.

      Or some sentences about advice or comments is also ok.

     Thank you!

      Best wishes to you and you family!

      A freshman in operation research field.

Originally posted by: jdpfreefly

please! anyone who once did lagrangian relaxation based on C callback cplex, if you  see this topic  please give me some advice or even a simple sentence. Thank  you! 

God bless me, I'm crazy, down to the bottom. Thank you who care about this topic.

Originally posted by: suji248

Hello,

May I ask you few questions?

Firstly did you try to solve the problem without the LR method ?  If yes what was the run time of the solver ?

LR  or any other decomposition methods is helpful when you are not able to solve the original problem to optimality using CPLEX. 

Also to solve the problem in LR method you  need to have good knowledge  about your model. Like for example if you know the Hard constraints in your model it will be little easy to start. Else if you consider all the constraints to be hard it may not be a good idea.

https://www.or-exchange.org/questions/9917/dualizing-more-than-one-constraint-while-designing-lagrangian

And the biggest problem using LR is convergence issue which I faced . Also here are the few notes which could help you 

Also the exact value of  the Multiplier( Lambda)  needs to calculated  after a lot of trail n error methods or you can use these below mentioned paper link to calculate it.

http://people.brunel.ac.uk/~mastjjb/jeb/natcor_ip_rest.pdf

Originally posted by: jdpfreefly

Thank you very much! 

suji248, @suji248, it's so kind of you.

Firstly, I had not yet to other decomposition methods to solve this problem. As this problem is 0-1 MLP, according recently journal paper said, the LR associated with branch-and-bound is the most efficient to solve this type problem. So, I want to learn LR associated with BB, but i stuck with the first step.

I had tried use some solver like mipsolver and netsolver in CPLEX to sovle it, but it's too huge to process(system environment: windows 7, visual studio 2012, intel core i5 + 8G).

I am learn the materials that you posted it to me. 

Thank you!

Best regards!