Challenges with MINLP Problems Using Knitro

[Diego Fernandes Pantuza]

I am currently working on solving a MINLP (Mixed Integer Nonlinear Programming) problem and have been using Knitro as the solver, which initially showed promising results for this type of problem.

At first, I focused on developing an NLP model that could find a local optimal solution quickly. After some adjustments to the solver settings, I was able to achieve this goal: the solver now finds the optimal solution in about 3 seconds, even without using a previous solution as a starting point.

However, when binary variables were introduced into the model, Knitro started to struggle significantly. While the root node relaxation is solved quickly, the branch-and-bound iterations take a long time to converge and, in many cases, produce infeasible solutions — even in scenarios where the binary variables do not affect other constraints in the model.

Please find below a screenshot with the problem characteristics:

I would like to know:

• Have you encountered similar issues when using Knitro?
• Do you have any suggestions on what might be causing this difficulty in finding feasible solutions?

Thank you very much for your attention and support.

Best regards,

[richard.waltz]

Hi,

It's hard to say much without looking more closely at your model.  The problem characteristics show many quadratic equality constraints in your model, which makes it highly non-convex and difficult when combined with binary variables.  If possible, can you please contact Artelys Knitro support <support...@artelys.com> and share your model with us so we can investigate?

Regards,

-Richard Waltz