I didn't find deep informations on Wikipedia about all-pairs shortest path, in particular I do not know what is the best algorithm to solve this problem beyond Floyd-Warshall's one, then I do not know if the following observation is too irrelevant or trivial.
In maxplus algebra we revisited linear algebra substituting the usual operations with the max-operation and plus-operation instead of addition and multiplication respectively. In particular we obtain an equivalent theory by taking minimum instead of maximum, then having a minplus algebra (with the obvious changing in the associated semiring, i.e. taking $+\infty$ instead of $-\infty$ as neutral element for the first operation).
Trying to see what the usual graph-theoretic-interpretation of matrix multiplication become in the minplus algebra (with $+\infty$ in the entries corresponding to non-existing edge and $0$s on the diagonal), I see that the $k$-th power of the adjacency matrix gives the shortest paths of length at most $k$. Then, all-pairs shortest path could be solved in $n^\omega \log n$ (where $\omega$ is the present lowest exponent for matrix multiplication) instead of $n^3$ like FW-alg.
Did I made big mistakes about all that?
I consider that maybe the lower bounds on matrix multiplication are not valid changing operations... but then seems plausible that it could be possible to have an exponent less than $3$ also for minplus algebraic matrix multiplication; among other things, the multiplication is far more computationally expensive than addition, and so is taking minimum respect to addition.