Two ideas are presented.
First, new proofs show that a subset of algorithms can have
identical performance over a subset of
functions,  even when the subset of functions is not closed under
permutation.
We refer to these as focused sets.
In some cases
focused sets correspond to the orbit
of a permutation group; in other cases, the focused sets
must be computed heuristically.   In the smallest case,
two algorithms can have identical performance
over just two functions in a focused set.
These results particularly exploit the case where
search is limited to m steps, where m is
significantly smaller than the size of the search space.
These proofs emphasize the need for search algorithms
to understand and exploit problem
structure.
Second,  the problem structure of elementary
landscapes is reviewed, particularly for the
Traveling Salesman Problem.   These results suggest
that current algorithms may not adequately
(or at least explicitly) exploiting all of the
available problem structure.