Given the high dimension of the search space, I think (b) is negligible and the linear model (a) of your first comment is better. In low dimension the boundary of the unit sphere is small and you can have a lot of copies on the inside, having to pass through the sphere to reach new terrain. Whereas, in high dimensions, the population will quickly thin out and all be unique, so what matters is the total volume of space explored, not how long it takes to get anywhere.
I’m not totally convinced this is the right way to think about it, any given useful mutation will depend on some constant number of coordinates flipping, so in this high-dimensional space you’re talking about, useful mutations would look like affine subspaces of low codimension. When you project down to the relevant few dimensions, there’s probably more copies of virus than points to fit in, and it takes a long time for them to spread out.
I guess it depends on the geometry of the problem, whether there are a small number of relevant mutations that make a difference, each with a reasonable chance of being reached, or a huge number of relevant mutations each of which is hard to reach.
Given the high dimension of the search space, I think (b) is negligible and the linear model (a) of your first comment is better. In low dimension the boundary of the unit sphere is small and you can have a lot of copies on the inside, having to pass through the sphere to reach new terrain. Whereas, in high dimensions, the population will quickly thin out and all be unique, so what matters is the total volume of space explored, not how long it takes to get anywhere.
I’m not totally convinced this is the right way to think about it, any given useful mutation will depend on some constant number of coordinates flipping, so in this high-dimensional space you’re talking about, useful mutations would look like affine subspaces of low codimension. When you project down to the relevant few dimensions, there’s probably more copies of virus than points to fit in, and it takes a long time for them to spread out.
I guess it depends on the geometry of the problem, whether there are a small number of relevant mutations that make a difference, each with a reasonable chance of being reached, or a huge number of relevant mutations each of which is hard to reach.