Originally posted by: srinit34

the help pages for backtracking tolerance say this:

If a cutoff tolerance (upper cutoff or lower cutoff) has been set by the user, then that value is used as the incumbent until an integer feasible solution is found.

Question - Does this mean that any solution found overrides the cutoff, or that the solution found will override the cutoff only if the solution is better than the cutoff? I think the latter.

Also, the best node is defined like this:

the best remaining objective function value of any unexplored node (best node);

Question - Is this referring to the LP relaxation value of the node? I think so.

By definition (in CPLEX) a "solution" is a vector that satisfies the cutoff. So yes, a solution will overwrite the cutoff, but something that is worse than the cutoff will never be considered a solution. So CPLEX is doing what you expected.

For the second question: yes, this refers to the LP relaxation.