[Ipopt] Using IPOPT to solve NLP subproblems generated by an outer-approximation algorithm

[Ayotte-Sauvé, Étienne]

Hi all,

Recently I've implemented a (non-convex) MINLP problem in GAMS and I've started carrying out numerical tests with an outer-approximation algorithm (DICOPT) using CBC for LP/MIP/RMIP subproblems.

Preliminary tests using an SQP algorithm (SNOPT) for NLP subproblems showed that many of the binary variable choices stemming from the MIP subproblems yielded infeasible NLPs. My first reaction after inspecting the associated solver log files was to add integer cuts to my problem formulation in order to (hopefully) diminish the number of infeasible NLPs. 

After adding these cuts, SNOPT still found infeasible NLP subproblems. However, switching from SNOPT to IPOPT (with the new problem formulation) showed that all these NLP subproblems were "false infeasibles", i.e. IPOPT found a feasible point for each such NLP subproblem.

As a consequence, I am currently using DICOPT + IPOPT + CBC. So far, the objective function values obtained at the DICOPT output are good (i.e. the relative optimality gap is smaller than 10% with respect to the relaxed MINLP) and I have not yet encoutered an infeasible NLP subproblem generated by DICOPT. 

However, the calculation times I obtain with IPOPT are sometimes in the order 60 seconds for a single NLP subproblem. As suggested in older posts by other members of this message board, I have tried using the acceptable_* options to diminish IPOPT calculation times; the performance obtained thus far is not to my satisfaction.

I would like to know if any of you have experience in "speeding up" IPOPT and if so, then I would be very happy to read your suggestions.

Here's an excerpt from an IPOPT log file associated to an NLP subproblem generated by DICOPT.

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
1580 1.5515722e+001 5.55e-009 6.16e-002 -10.6 4.71e-004  -1.6 1.00e+000 1.00e+000h  1
1581 1.5515722e+001 7.81e-010 2.30e-002 -10.6 1.77e-004  -1.1 1.00e+000 1.00e+000h  1
1582 1.5515722e+001 2.42e-009 3.14e+001 -11.0 5.75e-004  -1.6 1.00e+000 5.42e-001h  1
1583 1.5515722e+001 9.89e-010 1.09e+002 -11.0 1.98e-004  -1.2 6.43e-002 1.00e+000h  1
1584 1.5515722e+001 8.90e-009 1.00e-001 -11.0 5.94e-004  -1.7 1.00e+000 1.00e+000h  1
1585 1.5515722e+001 1.25e-009 3.74e-002 -10.7 2.23e-004  -1.2 1.00e+000 1.00e+000h  1
1586 1.5515722e+001 3.94e-009 3.39e+001 -11.0 7.93e-004  -1.7 1.00e+000 5.48e-001h  1
1587 1.5515722e+001 1.58e-009 4.14e+001 -11.0 2.50e-004  -1.3 6.31e-001 1.00e+000h  1
1588 1.5515722e+001 1.42e-008 1.27e-001 -11.0 7.49e-004  -1.8 1.00e+000 1.00e+000h  1
1589 1.5515722e+001 2.00e-009 4.73e-002 -11.0 2.80e-004  -1.3 1.00e+000 1.00e+000h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
1590 1.5515722e+001 3.11e-009 6.00e+001 -11.0 1.02e-003  -1.8 1.00e+000 3.09e-001h  1
1591 1.5515722e+001 2.54e-009 1.26e+001 -11.0 3.15e-004  -1.4 8.57e-001 1.00e+000h  1
1592 1.5515722e+001 2.52e-009 1.96e+003 -11.0 2.36e-002  -1.9 1.00e+000 6.46e-003H 1
1593 1.5515722e+001 3.21e-009 1.34e+002 -11.0 3.54e-004  -1.4 9.31e-001 1.00e+000f   1
1594 1.5515722e+001 1.12e-009 2.23e-001 -11.0 3.46e-004  -1.0 1.00e+000 1.00e+000h  1
1595 1.5515722e+001 4.06e-009 6.72e-002 -11.0 3.97e-004  -1.5 1.00e+000 1.00e+000h  1
1596 1.5515722e+001 5.71e-010 2.51e-002 -11.0 1.49e-004  -1.1 1.00e+000 1.00e+000h  1
1597 1.5515722e+001 5.14e-009 7.55e-002 -11.0 4.45e-004  -1.5 1.00e+000 1.00e+000h  1
1598 1.5515721e+001 7.23e-010 2.82e-002 -11.0 1.67e-004  -1.1 1.00e+000 1.00e+000h  1
1599 1.5515721e+001 6.51e-009 8.49e-002 -11.0 5.00e-004  -1.6 1.00e+000 1.00e+000h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
1600 1.5515721e+001 9.15e-010 3.17e-002 -11.0 1.87e-004  -1.2 1.00e+000 1.00e+000h  1
1601 1.5515721e+001 8.23e-009 9.55e-002 -11.0 5.61e-004  -1.6 1.00e+000 1.00e+000h  1

I apologize in advance for not sending much information about the problem. Confidentiality issues...

Thanks in advance for your help.

Etienne Ayotte-Sauve