Hello members,

I am solving my optimization(minimization) problem iteratively by adding the columns in my RMP with the same set of constraints but during some of the iteration, my objective value getting increased. Logically objective value should not get degraded as the columns which were there in the previous iteration are the subset of columns in the iteration where the objective value was degraded so if there is no improvement in objective then the solution in the previous iteration should repeat. I am attaching the file contains objective values at each iteration. 

Settings I am using,

CPLEX Parameter File Version 12.2.0.0
CPX_PARAM_LPMETHOD          4
CPX_PARAM_BARALG               3
CPX_PARAM_BAREPCOMP      0.01
CPX_PARAM_BARCROSSALG  -1
CPX_PARAM_TILIM                    3600
CPX_PARAM_EPMRK                0.99999

Thanks in advance!

------------------------------
Rajat Mishra
------------------------------

#DecisionOptimization

You have a rather liberal convergence criterion for the barrier solver (BarEpComp = 0.01, when the default is 1e-8). Your objective values decrease monotonically until about the 40th iteration, at which point changes are small (less than 2e-5 times the objective value). So I think this is just a consequence of your parameter setting. You could try a smaller value for BarEpComp and see if convergence is more monotone.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

Hello Paul,
I have tried with a smaller value of BarEpComp (1e-12). With this setting, I was able to get a good result in the small problem but in large problems (2181), this setting also not performing well. Please provide guidance.
Thanks!

------------------------------
Rajat Mishra
------------------------------

Original Message:
Sent: Tue March 09, 2021 05:11 PM
From: Paul Rubin
Subject: LP objective value fluctuation

You have a rather liberal convergence criterion for the barrier solver (BarEpComp = 0.01, when the default is 1e-8). Your objective values decrease monotonically until about the 40th iteration, at which point changes are small (less than 2e-5 times the objective value). So I think this is just a consequence of your parameter setting. You could try a smaller value for BarEpComp and see if convergence is more monotone.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

If this is a MIP model, you can try reducing the relative gap tolerance (EpGap). Also, you should try warm-starting each iteration with the previous iteration's solution. Beyond that, though, you may just have to accept that a certain amount of rounding error is inevitable, and so a succeeding solution may be worse by a trivial fraction of the objective value.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

Original Message:
Sent: Mon March 15, 2021 02:06 AM
From: Rajat Mishra
Subject: LP objective value fluctuation

Hello Paul,
I have tried with a smaller value of BarEpComp (1e-12). With this setting, I was able to get a good result in the small problem but in large problems (2181), this setting also not performing well. Please provide guidance.
Thanks!

------------------------------
Rajat Mishra
------------------------------


Original Message:
Sent: Tue March 09, 2021 05:11 PM
From: Paul Rubin
Subject: LP objective value fluctuation

You have a rather liberal convergence criterion for the barrier solver (BarEpComp = 0.01, when the default is 1e-8). Your objective values decrease monotonically until about the 40th iteration, at which point changes are small (less than 2e-5 times the objective value). So I think this is just a consequence of your parameter setting. You could try a smaller value for BarEpComp and see if convergence is more monotone.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University

------------------------------
Rajat Mishra
------------------------------

Original Message:
Sent: Mon March 15, 2021 01:49 PM
From: Paul Rubin
Subject: LP objective value fluctuation

If this is a MIP model, you can try reducing the relative gap tolerance (EpGap). Also, you should try warm-starting each iteration with the previous iteration's solution. Beyond that, though, you may just have to accept that a certain amount of rounding error is inevitable, and so a succeeding solution may be worse by a trivial fraction of the objective value.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------


Original Message:
Sent: Mon March 15, 2021 02:06 AM
From: Rajat Mishra
Subject: LP objective value fluctuation

Hello Paul,
I have tried with a smaller value of BarEpComp (1e-12). With this setting, I was able to get a good result in the small problem but in large problems (2181), this setting also not performing well. Please provide guidance.
Thanks!

------------------------------
Rajat Mishra


Original Message:
Sent: Tue March 09, 2021 05:11 PM
From: Paul Rubin
Subject: LP objective value fluctuation

You have a rather liberal convergence criterion for the barrier solver (BarEpComp = 0.01, when the default is 1e-8). Your objective values decrease monotonically until about the 40th iteration, at which point changes are small (less than 2e-5 times the objective value). So I think this is just a consequence of your parameter setting. You could try a smaller value for BarEpComp and see if convergence is more monotone.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University

Rather than using barrier (other than maybe on the first RMP), have you tried using one of the simplex algorithms and warm-starting each RMP with the optimal basis from the prior problem?

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University
------------------------------

Original Message:
Sent: Wed March 17, 2021 12:33 AM
From: Rajat Mishra
Subject: LP objective value fluctuation

I am solving the LP model by using column generation in which at each iteration I am creating some columns and based on reduced cost are adding into my RMP and then solving the LP problem at each iteration. So basically my objective value fluctuating in each iteration.

------------------------------
Rajat Mishra
------------------------------


Original Message:
Sent: Mon March 15, 2021 01:49 PM
From: Paul Rubin
Subject: LP objective value fluctuation

If this is a MIP model, you can try reducing the relative gap tolerance (EpGap). Also, you should try warm-starting each iteration with the previous iteration's solution. Beyond that, though, you may just have to accept that a certain amount of rounding error is inevitable, and so a succeeding solution may be worse by a trivial fraction of the objective value.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University


Original Message:
Sent: Mon March 15, 2021 02:06 AM
From: Rajat Mishra
Subject: LP objective value fluctuation

Hello Paul,
I have tried with a smaller value of BarEpComp (1e-12). With this setting, I was able to get a good result in the small problem but in large problems (2181), this setting also not performing well. Please provide guidance.
Thanks!

------------------------------
Rajat Mishra


Original Message:
Sent: Tue March 09, 2021 05:11 PM
From: Paul Rubin
Subject: LP objective value fluctuation

You have a rather liberal convergence criterion for the barrier solver (BarEpComp = 0.01, when the default is 1e-8). Your objective values decrease monotonically until about the 40th iteration, at which point changes are small (less than 2e-5 times the objective value). So I think this is just a consequence of your parameter setting. You could try a smaller value for BarEpComp and see if convergence is more monotone.

------------------------------
Paul Rubin
Professor Emeritus
Michigan State University