How to speed up Solver

1st thought: I recall sitting in a presentation by a researcher in my field. He was describing calculations that would take months to complete. Some problems just by their nature require a lot of operations to solve and, therefore, take time. Since you provide no information about the problem you are solving (other than a snippet of the code that calls Solver), it is impossible for us to make any specific suggestions.

Have you done some of the common things recommended? Turned screen updating off at the start of your procedure? Are any of your formulas unnecessarily using full column references?

One way or another, speeding a these things up is about reducing the number of operations. Do you have multiple formulas (array formulas searching a range, in particular) that are duplicating effort? Can you restructure the spreadsheet to reduce this duplication?

With a Newton-Raphson type algorithm, one way to reduce the number of iterations needed is to give it a better "initial guess"? I obviously cannot tell what is in your by changing cells before the procedure runs. A few lines of code that can put a better "initial guess" into these cells before Solver runs can significantly reduce the number of iterations Solver needs to solve the problem, thus reducing the time needed.

Those are a few suggestions of common things that can speed this kind of thing up.