What is the fastest and most accurate way to solve an MINLP model with nonlinear constraints, including triangle and quadratic terms? classic solvers, metaheuristics, or ...?
If you use (meta-)heuristics, you do only upper bounding, that is you don't get any proof of optimality. It can certainly be quick though, but the accuracy is unknown.
Can you tell us what your problem looks like? How big is it?
BLOCKS OF VARIABLES 26 SINGLE VARIABLES 216,002 13,194
projected
NON ZERO ELEMENTS 740,984 NON LINEAR N-Z 201,000
DERIVATIVE POOL 10 CONSTANT POOL 41
CODE LENGTH 633,000 DISCRETE VARIABLES 90,000"
Although it is a scheduling problem that binary variables must get reasonable amounts I tried to solve it by RMINLP. Also, I have added penalty terms in the objective function to guarantee the accuracy of binary variables. It is, however, not accurate enough.
For solving your problem it is requiered to make evolve a solutions population. In each iteration you must to verify the fulfilment of your restriction and to add the corresponding value to the objective functions evaluations. For doing it you could different algorithms. In the works attached you can find a clear explanation about the mains ideas.
In my researchgate profile https://www.researchgate.net/profile/Jose-Arzola-Ruiz/research you can find a lot of works thatwhere the previous recommendation is applied.