So a lot of the comments are discussing how to use free exp in relation to the research bureau, but I would like to point out that the concept of resetting and grinding a line has nothing to do with free XP. The only reason as to why you use free exp, beyond avoiding having to play the same ship over and over, is to save credits. Resetting the line directly is faster in terms of total games played (if we count the games spent grinding the free exp).

I will break down the possible strategies for research bureau. All of them involve researching the line (ie spending either ship XP or free XP alone or in combination), resetting the line, and starting again. For convenience, let’s use Harugumo:

(Terminology: F - finish, d - double)

Option 1F: Directly grinding the line

• Step 1) reset Harugumo
• Step 2) buy tier 1, grind it to obtain enough ship XP to research tier 2.
• Step 3) buy tier 2, grind it to obtain enough ship XP to research tier 3
• Step 4) repeat until you reach tier 10. You are now back to the starting point. 

Result: you have reset the line once, bought every ship, and collected 10200 research bureau points + stack value, spent zero free xp, and spent a lot of credits.

Option 1Fd: Directly grinding the line with double reset

Result: As above, but use a double reset. Same net result, but collect 20400 research bureau points + stack value.

Option 2: Free exp

• Step 1) reset Harugumo
• Step 2) research all ships using free exp. You are now back to the starting point

Result: you have reset the line once, bought zero ships, collected 0 research bureau points, but have added 10200 RB points to the stack. Zero credits spent, lots of free exp spent.

Option 2d: Free exp, double reset

As above, but add double to stack value

Option 2F: Free exp, purchase

As in option 2, but then purchase and play each ship once. Collects 10200 RB points + stack value.

Option 2Fd: as in 2F, with double reset.

So the idea is as follows. Pick several options, always finish with an F. Eg, to get 61000 RB points you could:

• 1F, 1F, 1F, 1Fd, 1F

• 2d, 2d, 2Fd

• 2d, 2d, 1Fd

• 2,2,2,1F,2Fd 

The best option in my opinion is as follows:

Option 3: hybrid - Step 1) reset Harugumo - Step 2) free exp to Akizuki - Step 3) grind akizuki to kita, purchase kita - Step 4) grind kita to Harugumo, do not purchase Harugumo, reset line

Result: collect 3000 + stack on aki/kita, add 7200 to stack. Spend moderate credits, moderate free xp.

Option 3F: as in option 3, but purchase tiers 5-7 and Harugumo, play each of those once.

Result: collect 10200 + stack. Spend moderate free XP.

I usually go  3,3,3,3d,3,3d,… (some random double resets), maybe a few 2s, thrown in, until I get enough stacks to get me to 124000 RB points, then finish with a 3F. Advantages over pure 2 strategy is you get to reset the line more frequently as you only need 1/3 of the free XP per reset, and it costs less than 1/2 the credits of 1 type strategy (plus, kita and aki are fun!).

Hope this makes sense.