Hi

I am a newbie and am trying to understand how to use CPLEX for LP relaxations of MIPs

The original problem may involve multiple objectives

Minimize OBJ1 followed by 
Minimize OBJ2

the constraints, variables are the same for both models OBJ1 and OBJ2

In reality while the problem is a MIP (say one of the variables is mixed integer), still we only want to solve the LP relaxation (while using cutting planes to come as close to the MIP solution as possible)

Is it possible to do something like

a) Solve OBJ1  (LP problem only)

Then add Cutting Planes/Gomory cuts (constraints) to the problem to come close to the MIP, but it should still be an LP (how to identify/add these cuts, constraints, does CPLEX provide this, how to get it?)

b) Next solve OBJ2 (LP problem only), using the warm start from OBJ1 optimal solution

Then add Cutting Planes to this problem to again come close to the MIP, but it should still be an LP

The motivation is that the LP relaxation may be faster than the actual MIP solve for large datasets, so what is the way to solve an LP, (but still try to make the solution a bit close to an LP)?

Can you point out any example, or article where something similar has been attempted?

Thank you in advance for your help

Dinesh

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Dinesh
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Greetings!

Dear Dinesh,

Here's a solution of your problem, To get and use Gomory cuts or cutting plane constraints from CPLEX for LP, you can enable the CPLEX automatic cut generation feature. This feature allows CPLEX to dynamically generate Gomory cuts and other cutting plane constraints during the solution process. Simply activate the "CutPass" parameter in your CPLEX code or through the CPLEX Optimization Studio interface. This will instruct CPLEX to utilize Gomory cuts and cutting plane constraints to enhance the LP solution process and improve the quality of the solution.

I hope this information is very helpful for your problem.

Hi

I am a newbie and am trying to understand how to use CPLEX for LP relaxations of MIPs

The original problem may involve multiple objectives

Minimize OBJ1 followed by 
Minimize OBJ2

the constraints, variables are the same for both models OBJ1 and OBJ2

In reality while the problem is a MIP (say one of the variables is mixed integer), still we only want to solve the LP relaxation (while using cutting planes to come as close to the MIP solution as possible)

Is it possible to do something like

a) Solve OBJ1  (LP problem only)

Then add Cutting Planes/Gomory cuts (constraints) to the problem to come close to the MIP, but it should still be an LP (how to identify/add these cuts, constraints, does CPLEX provide this, how to get it?)

b) Next solve OBJ2 (LP problem only), using the warm start from OBJ1 optimal solution

Then add Cutting Planes to this problem to again come close to the MIP, but it should still be an LP

The motivation is that the LP relaxation may be faster than the actual MIP solve for large datasets, so what is the way to solve an LP, (but still try to make the solution a bit close to an LP)?

Can you point out any example, or article where something similar has been attempted?

Thank you in advance for your help

Dinesh