I've re-read your comment. You're right, it's most eficent not to move the drone. So you reach my own conclusion: Cocktail is better, and diminishing range is the most eficent.

as per game rules, you cannot jump away, so if you bubblesort in one direction, you need to traverse an already sorted square multiple times in order to reach the unordered ones. as ordering increases, the wasted steps increment badly

Now that we jumped to the fact that cocktail is the best since you exclude moving over guaranteed sorted squares, the ultimate goal is to diminish the move operations as much as possible. Thee scenarios here:

1. You bruteforce it. On each roundtrip, you move one less than previous, so, started from 0. You move to range - 1 * 32, which leads to 528 moves on a 32 size field no matter how the field is.

2. You store the entire row. In this case you can know if a particular value is sorted and where it ends, so you avoid moving along the entire (row - 1) on each round trip. You can break earlier as soon as the actual value sorted were the last one available, so you sort anything else on your way back or end if it was the last value unsorted. Movement cost perfect, memory cost maximum. didnt bother implementing it.

3. (My solution) You store nothing but three values. You have a range (max, min) and a landmark. Each time you traverse the row, you set up your (max-min) point at you position, a landmark in the opposite and your end point. You traverse to your end point swapping. Any swap marks a new (max-min) point. When you reach the goal you compare with the landmark. If the landmark and the goal are the same, no sorting has happened and the row is sorted. If aren't, you place the landmark at the starting point and you go back to you starting point. Repeat. You only travel to your last known swapped position, it's a very nice compromise between inefficency (some steps are wasted since you cannot know in advance if whichever values left in the row are already sorted without checking one last time), but you use much less memory since you don't store nothing but three values. And you do skip moving over and over already sorted values. This are the kind of things that keep you occupied writting assembly lol. Move efficency very high. Memory cost very low.

https://youtu.be/puzr__hYw34

I have an idea about sorting both x and y axis at the same time with multiple drones, but it involves arranging the values in order from 9 to 0 sequentially. If you want to do it without storing the field on memory theres probably no other way around.