adjusted fitness in NEAT algorithm

Question

I'm learning about NEAT from the following paper: http://nn.cs.utexas.edu/downloads/papers/stanley.ec02.pdf

I'm having trouble understanding how adjusted fitness penalizes large species and prevents them from dominating the population, I'll demonstrate my current understanding through an example and hopefully some one will correct my understanding.

Let's say we have two species, A and B, species A did really well last generation and were given more children, this generation they have 4 children and their fitnesses are [8,10,10,12] while B has 2 and their fitnesses are [9,9] so now their adjusted fitnesses will be A[2, 2.5, 2.5, 3] and B[4.5, 4.5].

Now onto distributing children, the paper states: "Every species is assigned a potentially different number of offspring in proportion to the sum of adjusted fitnesses f'_i of its member organisms"

So the sum of adjusted fitnesses is 10 for A and 9 for B thus A gets more children and keeps growing, so how does this process penalizes large species and prevent them from dominating the population?

Answer 1

Great question! I completely agree that this paper (specifically the part you quoted) says that the offspring are assigned based on the sum of adjusted fitnesses within a species. Since adjusted fitness is calculated by dividing fitness by the number of members of a species, this would be mathematically equivalent to assigning offspring based on the average fitness of each species (as in your example). As you say, that, in and of itself, should not have the effect of curtailing the growth of large species.

Unless I'm missing something, there is not enough information in the paper to determine whether A) There are additional implementation details not mentioned in the paper that cause this selection scheme to have the stated effect, B) This is a mistake in the writing of the paper, or C) This is how the algorithm was actually implemented and speciation wasn't helpful for the reasons the authors thought it was.

Regarding option A: Immediately after the line you quoted, the paper says "Species then reproduce by first eliminating the lowest performing members from the population. The entire population is then replaced by the offspring of the remaining organisms in each species." This could be implemented such that each species primarily replaces its own weakest organisms, which would make competition primarily occur within species. This is a technique called crowding (introduced in the Mahfoud, 1995 paper that this paper cites) and it can have similar effects to fitness sharing, especially if it were combined with certain other implementation decisions. However, it would be super weird for them to have done this, not mentioned it, and then said they were using fitness sharing rather than crowding. So I think this explanation is unlikely.

Regarding option B: Most computer science journal papers, like this one, are based off of groups of conference papers where the work was originally presented. The conference paper where most of the speciation research on NEAT was presented is here: https://pdfs.semanticscholar.org/78cc/6d52865d2eab817aaa3efd04fd8f46ca8b61.pdf. In the explanation of fitness sharing, that paper says: "Species then grow or shrink depending on whether their average adjusted fitness is above or below the population average" (emphasis mine). This is different than the sum of adjusted fitness referred to in the paper you linked to. If they were actually using the average (and mistakenly said sum), they'd effectively be dividing by the number of members of each species twice, which would make all of the other claims accurate, and make the data make sense.

Regarding option C: This one seems unlikely, since Figure 7 makes it look like there's definitely stable coexistence for longer than you'd expect without some sort of negative frequency dependence. Also, they clearly put a lot of effort into dissecting the effect of speciation, so I wouldn't expect them to miss something like that. Especially in such an impactful paper that so many people have built on.

So, on the whole, I'd say my money is on explanation B - that this is a one-word mistake that changes the meaning substantially. But it's hard to know for sure.