[Raggamuffin]

Assuming:
1) You want to start in standard tuning,
2) You never want to tune a string more than a whole step above what it would be in standard tuning,
3) You want to minimize the total amount of tuning changes (measured in half steps).

An "optimal" ordering of tunings would be:

EADGBE (Standard)
DADGBE (Drop D)
EADC#AD
EBEC#AD
DBGDAD
ECGDAD
ECFEAD
D#BF#EG#C#
C#CFD#G#C

This requires a total of 48 changes, measured in half steps.

[For the nerdy among us, this is a novel example of the classic traveling salesman problem (TSP) in operations research. In a TSP, a salesman needs to visit "n" cities in the most efficient manner, visiting each city exactly once. TSPs are notoriously difficult to solve because the number of possible solutions (given by n!) gets very large very fast as "n" increases. Even in this relatively simple problem with n=9 "cities" there are 362,880 possible orderings of tunings. Making the assumption that you want to start in standard tuning reduces the possible orderings to 40,320.]