If it weren't for the restriction that all the discrepancies be equal I wouldOriginally Posted by jakemalloy
consider using either simulated annealing of a genetic optimisation algorithm
This is my dilemma:
Situation: n number of people are in a network. Each pair has a mutual distance they desire to be from each other. If there are discrepencies, all members compromise equally to adjust for the closest fit possible. E.G., A and B 1 unit; B and C 2 units; A and C 4 units. (Keep in 2D) Therefore, A and B add 1/3 unit, B and C add 1/3 unit, and A and C reduce 1/3 unit. Thus, each is as close to the desired distance as possible and all adjust equally.
Occassionally arbitrary choices must be made, e.g., four members all wanting to be 1 unit from each other. Some will have to adjust away and some toward. Which member goes which direction is arbitrary.
So, Any good way to do this?
I need some analysis help.
What I have so far:
Finding and adjusting for a third point is cake.
For example. ab = 1, bc = 1, ac = 5. Find the discrepancy (3). Divide by 3 and adjust each by the result. [A little more involved to get a computer to do it but I can manage]
It works irrespective of which point is plotted first, which is a good thing. And each adjusts equally. I donít know if this is helping or hurting my ability to generalize.
When I get to 2D it gets a lot harder for me. So, I started looking what I think is the simplest form in which a fourth point would be added. The first three points are equidistant. Letís say, ab = 2, ac = 2, and bc = 2. And say the desired distance from D is the same, so that ad = 1, bd = 1, and cd = 1. So, the result will look something like the right hand picture. Then I found the ratio of AD:AB to be x: x(sqrt(3)). Then by guess and check I found the number that if each adjusted by it would actually produce the needed picture to be approx. .098076 [for some reason Iím blanking on how to find the real number by a method better than guess and check; feel free to advise me on this point]. Below is some guessing
New AB New AD Orig. - New AB Orig. - New AD closeness to equality
1.90194 1.098086 0.09806 0.098086 -2.6E-05
1.90193 1.09808 0.09807 0.09808 -9.8E-06
1.90192 1.098074 0.09808 0.098074 5.98E-06
1.901925 1.098077 0.098075 0.098077 -1.9E-06
1.901924 1.098076 0.098076 0.098076 -3.3E-07
1.901923 1.098076 0.098077 0.098076 1.24E-06
1.9019237 1.098076 0.098076 0.098076 1.4E-07
1.9019236 1.098076 0.098076 0.098076 2.98E-07
So, first I need the method by which I can find the exact number that would work in the case.
Second, I need to know what the significance of this number is, or how it should generalize.
Third, I need to make sure that if I would have encountered D before C, that the result would be the same.