I am solving a series of large-scale LPs (between 5 to 10 millions of variables and about the same number of constraints). I am using the barrier method (which I gather might be the fastest method for such problems) and it takes between 5~10 hours to find the optimal solution.
I wonder what might be the best way to find a good solution in a shorter period of time. For example, if I use TimeLimit =2 hours, are there any tricks or best practices that I can follow to maximize the chance of finding a good solution (as close as possible to the optimal solution)?
To be more specific, are there solution methods that might be better to be used in this case? Is primal or dual simplex preferred to the barrier method? Are there any settings or parameters that I need to change?
I appreciate any sort of help or insight about this issue.
P.S. just a bit more details: I use the barrier method and it returns a solution that is quite far from the optimal solution. I use the primal and dual simplex, but it does not return any solution (it returns - inf for a maximization problem).
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