Talk:Fitness proportionate selection

Optimal Data Structures Algorithms

There are better algorithms than Log(n). Check http://hypirion.github.io/roulette-tree/ — Preceding unsigned comment added by 191.85.0.220 (talk) 01:05, 22 September 2017 (UTC)

Untitled

This page is a bit of a mess: There are basically 2 slightly conflicting versions of the page here. The 2nd one is shorter, less clear, and more opinionated, so I'm going to remove it.

fitness -> probability of selection function

Could someone give an example of a function to relate fitness to probability of selection? Seems like a simple concept, but I'm having a hard time wrapping my head around it.

Article claims that: Selecting N chromosomes from the population is equivalent to playing N games on the roulette wheel, as each candidate is drawn independently.

What if multiple outcomes are the same ? —Preceding unsigned comment added by 62.167.10.135 (talk) 21:43, 15 January 2008 (UTC)

And what if all fitness values are 0 in that formula? —Preceding unsigned comment added by 193.49.62.52 (talk) 13:01, 8 February 2011 (UTC)

I'll bite - it's rather simple, because I've done it. Suppose we're evolving a program to compute square root from a population of random programs. We evaluate fitness of each individual as the root mean square error with respect to ten test values of square root. That is, we run the program with each of ten input values, and record the error of the program's output (the putative square root of the input). The root mean square error over the ten sample points is the fitness of that individual. And we repeat that for each individual. Since we want to select individuals with lower error, we invert the RMS error, i.e., normalize the fitness as 1/RMS, so that more fit individuals have larger values and less fit individuals have smaller values of fitness. Now we sum the fitness values over the population. Let's say that value is 52. The fitness value of the most fit individual is let's say, 7. The probability of selecting that individual is some function f(7,52). The simplest (and maybe not the best, but commonly used), is f ~ 7/52 or 14%. That mean's that there's an 86% probability that the most fit individual will NOT be selected, when aspirationally, we should like that one to be in the next generation. And analogously, unfit individuals may get lucky and be selected. This phenomenon is called stochastic noise: since there was no direct competition between any of the candidates selected among each other, or between those selected and those not, we don't actually know if the fitness spectrum is the correct ranking. As a side note, if all fitness values are all zero (or some other value), the genetic paradigm will not produce any useful evolution. An initial population with variable fitness is required, or the fitness function needs to be adjusted to discriminate marginal differences in fitness among a population with very low or almost uniform fitness. Sbalfour (talk) 16:21, 8 May 2019 (UTC)