Lack of hard +300% productivity cap

[Rycieos]

As explained in the FFF that introduced Quality, the game now has a hard cap at +300% productivity:

This is also why we created an overall machine limit on productivity to be +300% (modifiable by mods if needed), so even when some mods add machines with more module slots and/or better productivity modules, [the recycling loop] will always be prevented from getting broken accidentally.

This is important with the infinite technologies that give productivity, like steel, processing units, and low density structures, where it is possible to get +250% from research, and +50% from the foundry or electromagnetic plant.

I do not know if the linear solver handles this correctly (the math is way too complicated for me to manually test), but I know that the one step matrix solver does not:

$ python3 ./scripts/one_step_matrix_solver.py --additional-prod 0
q1 input per q5 output: 79.87855759632308
recipe q1 uses 2 quality modules and 2 prod modules
recipe q2 uses 2 quality modules and 2 prod modules
recipe q3 uses 2 quality modules and 2 prod modules
recipe q4 uses 2 quality modules and 2 prod modules
recipe q5 uses 0 quality modules and 4 prod modules

$ python3 ./scripts/one_step_matrix_solver.py --additional-prod 50
q1 input per q5 output: 24.24642624603618
recipe q1 uses 2 quality modules and 2 prod modules
recipe q2 uses 1 quality modules and 3 prod modules
recipe q3 uses 1 quality modules and 3 prod modules
recipe q4 uses 1 quality modules and 3 prod modules
recipe q5 uses 0 quality modules and 4 prod modules

$ python3 ./scripts/one_step_matrix_solver.py --additional-prod 300
q1 input per q5 output: 0.0003611924996120015
recipe q1 uses 0 quality modules and 4 prod modules
recipe q2 uses 0 quality modules and 4 prod modules
recipe q3 uses 0 quality modules and 4 prod modules
recipe q4 uses 0 quality modules and 4 prod modules
recipe q5 uses 0 quality modules and 4 prod modules

$ python3 ./scripts/one_step_matrix_solver.py --additional-prod 1000
q1 input per q5 output: 0.023587769271446946
recipe q1 uses 4 quality modules and 0 prod modules
recipe q2 uses 4 quality modules and 0 prod modules
recipe q3 uses 4 quality modules and 0 prod modules
recipe q4 uses 4 quality modules and 0 prod modules
recipe q5 uses 0 quality modules and 4 prod modules

The last two outputs are incorrect, as with the cap at +300%, no additional prod modules would do anything, and the --additional-prod 1000 should be capped to 300.

Arguably, this 300 value should be configurable, as it is a value configurable by mods.

I attempted to implement this in one_step_matrix_solver.py, but was unable to get it working.

[scottmsul]

Thanks for the report. The linear solver should implement the 300% cap correctly. I haven't dedicated as much time towards the one step matrix solver since I don't use it as much anymore. I probably won't look into this with high priority but maybe at some point. Note that it's more complicated than capping the --additional-prod flag at 300 since the 300 cap has to also include any applied prod modules.

[Rycieos]

Note that it's more complicated than capping the --additional-prod flag at 300 since the 300 cap has to also include any applied prod modules.

Correct. That part was easy to implement. But my specific scenario was ~+250% productivity, where a few modules would make a difference but any more would hit the cap.

I realize that the matrix solver is out of favor compared to the linear solver, but I couldn't get the linear solver to do what I wanted. Not to derail the conversation, but in case this is something only the matrix solver can do: I have a belt of common processing units, and I want to legendary all of them. I'm trying to find the sweet spot for productivity research and do a recycle -> craft processing units loop.

[scottmsul]

Try this command:

python ./scripts/factorio_solver.py --input-items processing-unit=1 sulfuric-acid=0 --output-item processing-unit --productivity-research processing-unit=2.5 --allowed-recipes processing-unit processing-unit-recycling --building-cost 0 --module-cost 0 --allow-byproducts --check-speed-modules

[Rycieos]

Thanks, that works perfectly. I'm not sure what flags fixed the "no optimal solution found" issue I was having, but this seems to work exactly like I want. The only thing supprising is that at +200% prod from research, the rare step wants full productivity:

$ ./scripts/factorio_solver.py --input-items processing-unit=1 sulfuric-acid=0 --output-item processing-unit --productivity-research processing-unit=2.0 --allowed-recipes processing-unit processing-unit-recycling --building-cost 0 --module-cost 0 --allow-byproducts --check-speed-modules
Solution:
Objective value = 1.0000000000000018

Inputs used:
input__normal__processing-unit: 1.0000000000000018
input__normal__sulfuric-acid: 18.3651592506768

Byproducts:

Buildings used: 18.889509052390306

Modules used: 87.90378102439412

Machine layout:
Processing unit in Electromagnetic plant: normal 3Q2P, uncommon 3Q2P, rare 5P, epic 3Q2P, legendary 5P
Processing unit (recycling) in Recycler: normal 4Q, uncommon 4Q, rare 4Q, epic 4Q

Which has to be a bug, right? That's +375% productivity (50% from electromagnetic plant, 200% from research, 125% from modules). Which is over the cap.

And if you specify +225% from research:

$ ./scripts/factorio_solver.py --input-items processing-unit=1 sulfuric-acid=0 --output-item processing-unit --productivity-research processing-unit=2.25 --allowed-recipes processing-unit processing-unit-recycling --building-cost 0 --module-cost 0 --allow-byproducts --check-speed-modules
Solution:
Objective value = 1.0000000000000027

Inputs used:
input__normal__processing-unit: 1.0000000000000027
input__normal__sulfuric-acid: 18.365159250676818

Byproducts:

Buildings used: 18.88950905239033

Modules used: 87.90378102439423

Machine layout:
Processing unit in Electromagnetic plant: normal 3Q2P, uncommon 3Q2P, rare 5P, epic 3Q2P, legendary 5P
Processing unit (recycling) in Recycler: normal 4Q, uncommon 4Q, rare 4Q, epic 4Q

All of the machines call for more than is useful.

But regardless, you are correct that the linear solver handles it more correctly.

[scottmsul]

Once it gets to +300% it's lossless from any method, and I had set the module/building costs to zero in the example I provided, so in that configuration it might be wasteful with respect to those, as long as it "works".

Try setting the module and building costs to a greater value and it should give more reasonable results.

[Rycieos]

Interesting. Setting module cost to 1 does improve it:

$ ./scripts/factorio_solver.py --input-items processing-unit=1 sulfuric-acid=0 --output-item processing-unit --allowed-recipes processing-unit processing-unit-recycling --building-cost 0 --module-cost 1 --allow-byproducts --check-speed-modules --productivity-research processing-unit=2.20
Solution:
Objective value = 15.487952712173746

Inputs used:
input__normal__processing-unit: 1.59508931500244
input__normal__sulfuric-acid: 19.756975186792648

Byproducts:

Buildings used: 5.555323591518066

Modules used: 13.892863397171304

Machine layout:
Processing unit in Electromagnetic plant: normal 5Q, uncommon 4Q1P, rare 4Q1P, epic 4Q1P, legendary 3Q2P
Processing unit (recycling) in Recycler: normal, uncommon 4Q, rare 4Q, epic 4Q

Only remaining issue is that the legendary craft can't make use of quality modules at all, but that is a minor issue that can be easily ignored.

Since the linear solver handles this correctly, feel free to deprioritize or close this issue. Thanks for all your help!