The No Free Lunch theorems for search and optimization demonstrate that for search/optimization problems in a limited search space, where the points being searched through are not resampled, the performance of any two given search algorithms over all possible problems is the same.
No Free Lunch for Search/Optimization
The no free lunch theorem for search and optimization (Wolpert and Macready 1997) applies to finite spaces and algorithms that do not resample points. All algorithms that search for an extremum of a cost function perform exactly the same when averaged over all possible cost functions. So, for any search/optimization algorithm, any elevated performance over one class of problems is exactly paid for in performance over another class.
I have not clear the meaning of algorithms that do not resample points
What can be an example of an algorithm that do not resample points and one that resample points?
Finally, why does the theorem not apply for algorithms that implement resampling of points?