Briefly: try breadth-first (and see how it goes).
We know that GC3 implements tech cost creep, which increases tech costs in rp per level as you gain techs. We don't know the equation for the cost creep function. But I think it's pretty intense, in the ballpark of 4x or 5x rp cost per tech by the time you reach Age of War.
- I have an annotated screenshot posted on my Steam wall that shows a 25% tech level award from surveying an Artifact decaying to about 7% (by counting pixels in PSP) over many dozens of turns, while I ignored it and researched other stuff. Assuming that the awarded rps stayed constant while the cost for that tech level stretched out, creep for that one level must have increased its cost by 390%(!!).
[TechAgeDefs.xml] shows that each Age is defined by a threshold of <RequiredTechPoints>.
- <RequiredTechPoints> 0 = AgeOfExpansion
- <RequiredTechPoints>3000 = AgeOfWar
- <RequiredTechPoints>6000 = AgeOfAscension
- <RequiredTechPoints>9000 = AgeOfVictory (but its <DisplayName> is still AGE_OF_ASCENSION)
[TechDefs.xml] shows that tech level has two attributes.
- <ResearchCost>: This must be the base rps you need, before tech cost creep is added in. At start of game, there's obviously no cost creep yet, so all tier 2 techs cost their base amounts.
- <TechPoints>: This must be your progress toward each Age. I note a curious correlation:
- 142 for every tech with <Option>AgeOfExpansion
- 095 for every tech with <Option>AgeOfWar, except ... (these are probably *gasp* XML bugs)
- [_] 176: GenericResearchCoordination
- [_] 176: GenericFortification
- 176 for every tech with <Option>AgeOfAscension, except ...
- [_] 095: GenericNeroLinking (while his ROMs burned?)
- 0 for every tech with <Option>AgeOfVictory (c.f. GenericBeyondMortality)
- 142 for every tech that omit any <Prerequ><TechAge><Option>AgeOf__ entry. These techs are all in Age of Expansion (but don't explicitly state that).
- [_] GenericDiplomaticRelations
- [_] GenericDiplomaticOptimization{1,2,3}
- [_] GenericCulturalInfluence
- [_] GenericCulturalOptimization{1,2,3}
- [_] GenericXenoCommerce
- [_] GenericCommerceSpecialization{1,2,3}
- [_] GenericXenoEconomics
- [_] GenericInterstellarBanking
- [_] GenericInterstellarTrade
- [_] GenericTradeOptimization{1,2,3}
Some conjectures based on this:
- There seems to be no TechPoints creep. They don't reward you more as you amass more of them. Dang! killjoys
- In Age of Expansion, you're limited to taking 142 TechPoints per tech. Then 3000 / 142 = 21.127, i.e. your 22nd tech level advances you to Age of War, and you'll overshoot by several pixels.
- Your 21st tech gives you 2,982 / 3,000 TechPoints = 99.40% of the AoE pixel bar.
- Your 22nd tech gives you 3,124 / 6,000 TechPoints = 4.13% of the AoW pixel bar.
- From my tedious notes, this is consistent with every Beta 1 game I've played. I always hit AoW at exactly 22 techs, and leak into the Age of War bar by several pixels.
- In Age of War, you can take 95, 142, or 176 TechPoints per tech. Let's ignore the 176s (which I think are just XML bugs).
- If you take only 95-TP AoW techs, then +2,876 more / 95 = 30.274, so your 31st AoW tech level puts you into Age of Ascension. (I think there aren't even 31 techs total.)
- If you take only 142-TP AoE techs, then +2,876 / 142 = 20.254, so you must go back for 21 more AoE tech levels.
- If you take half of each, so that your average TechPoints is 118.5 TP, then you need 25 more tech levels (and the 25th can be from either Age).
- In Age of Ascension, you can fill in the tech tree and quietly reach Age of Victory after another 20-30 techs.
Note that TechPoints per age is linear and flat, but ResearchCost in rps has that creep -- which could be linear, supra-linear, polynomial, or exponential. I further infer the following:
- As you take tech levels in a branch, the downstream techs in that branch all creep upward. Completely separate branches may also increase mildly.
- Wild guess: Every tech level adds:
- a flat inflation penalty(?) to all other techs (similar to the Ideology trees, so there is precedent for this)
- a large creep penalty to all downstream techs in that branch (as noted, this can reach +390%!)
- Paul has mentioned in a few streams that tech specializations (rounded-rectangle option choices) are handled specially.
- Each specialization costs as much as its most expensive downstream tech -- to penalize you for coming back to it later?
- Taking 2 or 3 specializations adds the "large creep penalty" 2x or 3x over -- to penalize you for choosing "all of the above"? The entire subtree after that gets that much more costly.
- Ugh ... this really, really hurts the small ship stack idea of taking all 3 Interstellar Specializations (+1 move, +1 sensor, +2 range). The entire non-weapon ship components tree will see all 3 of those creep kicks. Gahh ... maybe I'm playing it wrong, and a beeliner will kill me.
I conjecture that we maximize Age advancement for minimal rps spent by going breadth-first, to minimize cost creep penalties that drain away total rps spent. (When you're in the 75% "tech creep tax bracket", 75% of your rps essentially go to cost creep, and only 25% to the base <ResearchCost>.)
- Take only 1 of each specialization. Mnemonic: Each specialization adds a luxury tax.
- Take low-tier techs first.
Now, such a timeline is probably not competitive due to other in-game considerations, e.g. you just won't grow pop and build stuff as fast as an empire that is willing to drill to tier 3-4 in some critical techs. And obviously, a pure breadth-first style is nonsensical, because you'll reach Age of War while having zero Age of War techs eligible to be researched immediately. (I have done that, and it is ... somewhat embarrassing 
)
But the converse might also be true: beelining might actually be slower, because you're paying compounding creep costs to stay in one branch to tier 5, and maybe adding inflation costs to all other branches' low tiers. When we take creep and inflation into account, it means that all total orderings are not equal (for a given set of partially-ordered tech sub-trees). Put another way, let breadth-first be your default choice (even if you know it's stupid), and ask yourself: Is the benefit I gain for re-ordering it in this other way worth the inflation and creep cost of drilling depth-first? So it adds a bit of bean-counting pressure to our tech paths.
Come to think of it, it might actually be less efficient to beeline for a tier-4 research tech that gives only "+10% to research", if you later have to go back and finish a small ship stack of 6-9 techs in completely different branches. "+10%" is only 1 Research Laboratory-on-an-island per planet, and only for those planets actually doing research, and when added into your other research bonuses, it might actually be only a +1.5% gain in your total rps per turn. If the tech inflation for having taken a tier-4 makes your sideline techs more expensive by +2% each, you actually lose, in "total rps before inflation" spent. You'd have been better off doing the entire small ship stack first.
Here's something I'll try in Beta 2:
- Plan ahead for the subset (sub-forest?) of 22 AoE techs you want to end up with. Choose them to give you coverage where you want it, for the type of game you want to play. They should probably include some food, manuf/research, ship, and wealth/approval techs, and then your choice of weapons, diplomacy, trade, or influence.
- Make sure that your sub-forest of techs reaches the AoE/AoW boundary in 1+ tech branch, so that you're ready to research into AoW as soon as you get there.
- Within your sub-forest of techs, take them breadth-first as much as possible.
- Adjust dynamically, depending on the "hotness" of your game. If you think you have time and opportunity to get a production boost, maybe you can afford a slightly sub-optimal drilling, and just pay the creep tax. If you sense you're in a race, then lean toward ruthless streamlining. And so on.
I admit that, up to now, I've ignored all of the above, and researched techs based purely on their benefits. Whatever the cost later, I just pay it without noticing. That approach works against the Beta 1 null AIs, but surely we'll eventually encounter smarter opponents (new AI or multi-player), and then many of our pet strategies will get sintered in open competition.
