I am fairly new to Mixed Integer Linear Programming and I was hoping someone could clarify a performance question for me. Basically I am performing a calculation with about 34 decision variables and my calculation time is around 5 seconds. I would like to ideally get the calculation time down into the sub 1 second range.
Currently I am using the CBC solver & MATLAB, but as I understand it this is a single-threaded solver. Most of the MILP solvers I've seen seem to pride themselves on large project performance with 1k+ variables and knocking compute time down from days to hours but only a few of the expensive ones are even multi-threaded. Processor speed would seem to only go so far with such a problem so there has to be something that could be done on the software side.
In a situation like I have what factors play a role in the calculation time? In theory would a solution like Gurobi be able to ramp up and make a discernible difference over CBC on such a small problem?
When solving MIPs, multi-threading usually doesn't help that much, compared to other applications. One thing more sophisticated solvers do better than CBC is presolving. It may very well happen, that all decision variables can be eliminated/fixed in the root node. In general, it is not possible to predict the solving time of a MIP based on its size. The solving process is simply too complex. To answer your question: I do suppose that you will see a significant speedup when trying another solver (Gurobi, Xpress, CPLEX, SCIP, etc.). It is not guaranteed though, and you might also witness a slowdown.