Can I get the total time or total steps required to calculate the best solution? Or the time to get the next best solution? The user is impatient and doesn't know the next best solution or how long the entire calculation will take.
No, but you can display the time elapsed since the current best solution was discovered. So when I come back to the computer and the solver has been running for 20 minutes, I can decide:
IMPORTANT: You cannot make any predictions about the next best solution based on the time elapsed since the last improvement. I'm only saying that showing that information can improve the user experience.