I would like to know which would be the best constraint solvers (commercial or open source) designed to handle complex optimization problems of several tens of thousands of variables and several thousand constraints, and why?
Ideally, a solver capable of tackling using efficient heuristics, in a distributed computing context.
Thank you in advance for your suggestions, best regards.
There is no single best solver for all "complex optimization problems of several tens of thousands of variables and several thousand constraints". So this question cannot really be answered. In general, however, one would look at commercial solvers such as Cplex (but distributed mip is deprecated) and Gurobi. I think most modelers use a reasonable SMP machine (just easier and they can easily be equipped with enough cores and memory that distributed MIP is not worthwhile).
Note that a model with 10k variables and equations is not very large these days. The model may still be difficult, and a lot depends on the skill of the modelers.