Home » Stars! 2.6/7 » The Academy » Colonizing Planets
| Re: Colonizing Planets |
Mon, 22 March 2004 20:06   |
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hmmm, smells like a optimisation problem to me... Maybe I should dust off the old textbooks and write something up to solve it.
e.g. starting with a list of individual star habitabilities it should be possible to automatically calculate the max growth and/or max resources. Should be possible to spit out a list of exact %ages for the ideal population for each individual planet.
But, surely somebody has does this before? Anybody hear of a utility already designed to do this?
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| Re: Colonizing Planets |
Mon, 22 March 2004 23:18 |
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OMG... Excel is much more powerfull than I remember... What I expected to take several hours, took me about 10 minutes.... Guess I didn't need to study Optimisation Theory at uni after all, Excel does it all for you now.
It all bears out what has been said before. Get to, and stay at, 25% at your high value worlds asap then gradually fill up your worlds, from the lowest value up.
Here are the results from my testbed, mapping optimal values from 1, 2 and 3 million population on a set of stars {100%,100%,90%,50%,33%,33%,25%,10%,10%,10%} Obviously this doesn't consider the cost of moving population or the cost of terraforming, or the generated resources.
I was kinda disappointed when excel spat out a 26% figure in the first result... At first I thought I misunderstood something about the model, then I realised it just doesn't optimise all that accurately - I can improve the result by moving 5,000 pop off the first world and putting it on a 33% world.... But it only makes about 20 population difference (and since the game works in units of 100...)
Anybody want to see more of this? I could improve the model a lot.
1,000,000 pop:
pop hab maxpop capacity
259,146 1.00 1000000 0.26
254,626 1.00 1000000 0.25
226,261 0.90 900000 0.25
125,000 0.50 500000 0.25
54,807 0.33 330000 0.17
54,230 0.33 330000 0.16
25,930 0.25 250000 0.10
0 0.10 100000 0.00
0 0.10 100000 0.00
0 0.10 100000 0.00
2,000,000 pop
pop hab maxpop capacity
367,583 1.00 1000000 0.37
367,643 1.00 1000000 0.37
334,532 0.90 900000 0.37
203,223 0.50 500000 0.41
149,717 0.33 330000 0.45
149,717 0.33 330000 0.45
127,586 0.25 250000 0.51
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
3,000,000 pop
pop hab maxpop capacity
440,150 1.00 1000000 0.44
440,060 1.00 1000000 0.44
409,790 0.90 900000 0.46
500,000 0.50 500000 1.00
330,000 0.33 330000 1.00
330,000 0.33 330000 1.00
250,000 0.25 250000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
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| Re: Colonizing Planets |
Tue, 23 March 2004 06:02 |
|
 mazda |
 | Lieutenant |
Messages: 655
Registered: April 2003
Location: Reading, UK | |
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Just looking at the figures for 1 million.
1,000,000 pop:
pop hab maxpop capacity
259,146 1.00 1000000 0.26
254,626 1.00 1000000 0.25
226,261 0.90 900000 0.25
125,000 0.50 500000 0.25
54,807 0.33 330000 0.17
54,230 0.33 330000 0.16
25,930 0.25 250000 0.10
0 0.10 100000 0.00
0 0.10 100000 0.00
0 0.10 100000 0.00
Surely you would get more growth by taking the 26k off the 25% world and splitting it onto the two 33% worlds which are not yet at 25% capacity, and would still not be at 25% capacity if you added another 13k pop ?
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| Re: Colonizing Planets |
Tue, 23 March 2004 07:38 |
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| overworked wrote on Tue, 23 March 2004 12:19 |
If you're tying .map and .pxx data in it shouldn't be too hard to add a column calculation where you could punch in the HW (or its location) and get the distance to a target planet from the HW. (Speaking from experience since Leit added such a column to a version of the TT_8 spreadsheet I'm working with.)
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Pythagoras, he say...
distance = sqrt( (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) )
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| Re: Colonizing Planets |
Tue, 23 March 2004 10:54 |
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| Staz wrote on Tue, 23 March 2004 07:38 |
| overworked wrote on Tue, 23 March 2004 12:19 |
If you're tying .map and .pxx data in it shouldn't be too hard to add a column calculation where you could punch in the HW (or its location) and get the distance to a target planet from the HW. (Speaking from experience since Leit added such a column to a version of the TT_8 spreadsheet I'm working with.)
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Pythagoras, he say...
distance = sqrt( (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) )
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I don't think the formula is the difficulty...
It's whether or not the spreadsheet has all the references on-hand. For a single planet at a time you can of course just look-up the numbers and punch them in.
If you're doing a larger calculation based on 30-50 planets than perhaps it would be better to do some additional front-end work and automate the calculation for all the planets in the galaxy?
- Kurt
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| Re: Colonizing Planets |
Tue, 23 March 2004 14:05 |
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| Kotk | 
 | Commander |
Messages: 1227
Registered: May 2003 | |
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Uhh ... people, what you are modeling here???  It sounds like you got ready terraformed planets with stations or even deathstars everywhere with 0 travel time between them and the question is how to grow pop there?  Actual picture is a tiny bit different.
Okay ... i try to give idea of the actual picture ... Lets say we get AR, 1-immune and 1 in 5 hab without TT. Its to illustrate the task.
Distances:
AR has to have over 30 green planets to be competive. 30 is probably no enough to get 25k by 2450 but it can compete with others. Now even if we talk of AR with as wide hab as 1 in 5 it means territory of 50 planets. In dense universe it means about 200,000 square ly territory. Lets say our AR got wonderful neighbours and did wonderful diplo so it has almost square rectangular area like 400x500ly ... still the distances to travel are quite significant.
Orbitals:
Dock has max pop 500,000, station has 1,000,000. Ultra has max pop 2,000,000 (and costs about the same as Station). AR wont have it before 2430. Deathstar has max pop 3,000,000 and wont occur before the game is pretty much winnable for our AR already lets say for simplifying it is available at turn 45. Also lets say for simplifying that any orbital besides dock takes 2 years to build. Any models must take into account that available orbitals affect the growth. Only orbitals affect the max pop of AR, planet value has nothing to do with it.
Planets and terraforming:
Initially its quite good luck if 1 or 2 of the 10 greens our AR finds by scouting 50 planets are above 70%.
At max terra the picture is way different. About 30 of 50 planets are green. The green planets are roughly like that: about 35% planets have above 90% value (half of these fully 100%), about 35% are between 70% and 90% and only about 30% of greens are below 70%. Terraforming costs 3k per planet at worst case. Its initially quite slow process but once the planet turns green both its resources and pop start to grow quite rapidly. So any model without terraforming is flawed model.
Resources generated by pop of AR:
Are rather odd. Any model of AR should take it into account.
Example: Very first 50,000 pop at red world generates about 17% more resources than that same 50,000 pop when dropped on the top of 250,000 pop on 100% world. However if we drop second portion of 50,000 pop onto red world we get over two times less from it (so filling 100% world to 1,000,000 is more profitable). Reds and yellows and planets below 25% all generate resources as 25% planets.
No, guys, i am far from  trying to model it all scientifically, but please avoid makeing false assumptions based on overly simplified models. 
[edit: added the resources by AR for completeness sake]
[Updated on: Tue, 23 March 2004 15:27] Report message to a moderator
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| Re: Colonizing Planets |
Tue, 23 March 2004 19:02 |
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heh, don't forget I have diverged from talking about AR specifically and am just trying to maximise population growth. I suppose at the moment it is only really a realistic model for a CA race (instaforming.) For other races you'd only really be able to use it for a guide (I suggested before generating 2 reports - one for current hab, one for future hab.) I think the main use seems to be to remind you when you want to be colonising those low-hab worlds, and it shows that at that point you generally want to max those low hab worlds as soon as you colonise them.
Regarding the dodgy figures for the 1 million pop... I told you Excel's algorithms are dodgy. I've tweaked both my technique and the algorithms themselves to give some better values.
With the new revised system I get this result for 1,000,000 pop:
pop hab maxpop capacity
250,758 1.00 1000000 0.25
250,799 1.00 1000000 0.25
225,000 0.90 900000 0.25
125,000 0.50 500000 0.25
74,222 0.33 330000 0.22
74,222 0.33 330000 0.22
0 0.25 250000 0.00
0 0.10 100000 0.00
0 0.10 100000 0.00
0 0.10 100000 0.00
Which is, of course, pretty much exactly what we originally predicted.  That population on the 25% world has been lifted off. Interesting point is the extra 800 pop being held on the 100% worlds. I've tried taking it off manually and putting it on the 33% worlds, but this actually reduced the total pop growth. OTOH moving any more off the 33% to the 100% doesn't increase growth either. Clearly the extra 800 pop grows at above 33% of the normal rate, but only just! I never realised before that the curve was so tight.
Don't forget these values are based on the formulas, not the actual game values... The game does some weird stuff with the 100 pop units. Partly rounding issues, but I'm also pretty sure it carries over sub-100 pop values. Anybody got more info on this?
Here are updated tables for 2, 2.25, 2.5, 2.75, and 3 million. I'm 99% confident that these numbers generate max growth to within 100 pop. Notice the 37%-38% hold at the 100% worlds for 2, 2.25, and 2.5 million(!) (warning this may be unique to the set of hab values I chose for my test):
2 million
pop hab maxpop capacity
367,620 1.00 1000000 0.37
367,631 1.00 1000000 0.37
334,508 0.90 900000 0.37
203,191 0.50 500000 0.41
149,672 0.33 330000 0.45
149,672 0.33 330000 0.45
127,704 0.25 250000 0.51
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
2.25 million
pop hab maxpop capacity
384,312 1.00 1000000 0.38
384,306 1.00 1000000 0.38
351,500 0.90 900000 0.39
223,394 0.50 500000 0.45
178,244 0.33 330000 0.54
178,244 0.33 330000 0.54
250,000 0.25 250000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
2.5 million
pop hab maxpop capacity
371,704 1 1000000 0.37
371,705 1 1000000 0.37
338,652 0.9 900000 0.38
207,939 0.5 500000 0.42
330,000 0.33 330000 1.00
330,000 0.33 330000 1.00
250,000 0.25 250000 1.00
100,000 0.1 100000 1.00
100,000 0.1 100000 1.00
100,000 0.1 100000 1.00
2.75 million
pop hab maxpop capacity
425,116 1.00 1000000 0.43
425,108 1.00 1000000 0.43
393,807 0.90 900000 0.44
295,972 0.50 500000 0.59
330,000 0.33 330000 1.00
330,000 0.33 330000 1.00
250,000 0.25 250000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
3 million
pop hab maxpop capacity
440,114 1.00 1000000 0.44
440,168 1.00 1000000 0.44
409,718 0.90 900000 0.46
500,000 0.50 500000 1.00
330,000 0.33 330000 1.00
330,000 0.33 330000 1.00
250,000 0.25 250000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
100,000 0.10 100000 1.00
Comments? Suggestions?
The plan is to pull in planet data from the .p files to show distance from homeworld, and to generate double sets of results for current hab and terraformed hab. The purpose is to create a guide rail to manage your growth by.
...
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| Re: Colonizing Planets |
Mon, 20 September 2004 00:16 |
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Here are some little teasers. I've been reading *that* thread, and I thought I'd revist this one with a little taste of the results I got *after* all the above optimisations.
1) travel time -> I constructed a much more complicated model, that incorporated transit times has on the decision making. The model is very ugly, but I got some solid results. Hold points are higher on the high value worlds. This is because population in transit aren't growing (less significant to IT and IS, more significant to AR)
2) 'hold' -> to max growth I added the ability to hold population in freighters. Which leads to:
3) Resources -> I also modified the model to 'max out total earned resources by year x'. It was interesting seeing the break points where the model indicates to hold population in orbit to max out growth, for long term resources.
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