In ksolve++ this is called UTM (unidirectional turn metric), where e.g. U = 1 move, U2 = 2 moves, and U' = U3 = 3 moves. I don't know of any other solver that supports it (ksolve+ doesn't), but it's fun to play around with (e.g. 3x3x3 <U L, F R B>).
Also, something important to remember if this is added (which I remember debugging for a while in ksolve++): because a move and it's inverse don't have the same weight, you need to apply the inverses of the generators to go from positions at depth d to positions at depth d+1 when you're doing table generation, so that the moves go in the right direction when you're solving a position.
In ksolve++ this is called UTM (unidirectional turn metric), where e.g. U = 1 move, U2 = 2 moves, and U' = U3 = 3 moves. I don't know of any other solver that supports it (ksolve+ doesn't), but it's fun to play around with (e.g. 3x3x3 <U L, F R B>).
Also, something important to remember if this is added (which I remember debugging for a while in ksolve++): because a move and it's inverse don't have the same weight, you need to apply the inverses of the generators to go from positions at depth d to positions at depth d+1 when you're doing table generation, so that the moves go in the right direction when you're solving a position.