Minimizing pollution

[lvl19]

I've been thinking about this for a while, and new expansion was a nice deadline. The question is: What is the absolute minimum amount of pollution required per research. To my knowledge, nobody has attempted to solve this before. Now there are a few complications, but tl;dr: minimum 1.087 pollution per set of mining productivity science packs. It's always possible that I've made a mistake in the math, but that should be the theoretical minimum value. That assumes infinite mining productivity, so in practice you'll always get slightly higher numbers, but you can get arbitrarily close. Unless the mining productivity caps at some value, which is entirely possible.

I made an example 26 spm base. It reaches ~1.14 pollution/science at 1k mining prod. Blueprint is too large, but have a save. For comparison, the base pollutes about the same as 3 unmoduled mining drills.

[shopt]

I haven't looked at your maths yet, but even if mining productivity isn't hard capped, it believe it would be effectively capped at filling a steel chest in a single tick. You would then have the practical issue of making sure the chest is then fully emptied before the miner runs again, presumably using some circuitry and a power switch.

I'm also curious how you went about working out where (if anywhere) the breakeven on productivity vs efficiency is.

[lvl19]

The tradeoff isn't between productivity vs. efficiency but productivity vs speed. All machines should be at the minimum 20% power use, which also means 20% pollution output. While not strictly necessary, there just isn't a situation with vanilla modules where that isn't the case. So what I did was for each possible set of productivity modules, add as many speed modules as you can while still maintaining -80% energy consumption. This is made easier, because it's somewhat easy to show that it's never optimal to have two lower tier modules in the same machine. So for assembling machines, there are only 13 Pareto optimal module configurations to explore.
Then I went through all the recipes in order. Once you know how much pollution it costs to produce the ingredients of a recipe, you can compare the 13 different options and choose the one with the lowest pollution.
The one thing this approach doesn't handle well is oil processing, since it's the only one with multiple outputs and alternative recipes. Luckily the vanilla oil demand is very petroleum heavy, so it was pretty easy in the end to find the correct marginal costs for each of the 3 oils.
With the extreme mining productivity, the optimal result used surprisingly few productivity modules. Only purple and yellow science were fully prod3 moduled (in addition to the rocket silo and labs which don't pollute anyway).

[Skev]

From the wiki: Modules that list "+x% pollution" increase pollution multiplier, not a flat pollution rate. Final pollution value is (pollution multiplier * energy usage multiplier * base pollution), meaning heavily boosted buildings are likely to account for most of the pollution produced in a factory.

Since pollution is a multiple of energy usage, Efficiency modules can reduce the energy usage of anything with a module slot to 0. Inserters don't generate pollution, so unless I've missed something you can stop polluting altogether.

[lvl19]

Efficiency modules have a hard coded cap of -80%, i.e. they cannot reduce the energy usage to below 20%.