Genetic algorithms — what are the benefits of sexual, as opposed to asexual, genetic algorithms?

Question

Intuitively I'd think that if I want to find the "best" set of parameters, I can simply take the best performing 1 guy from a subset of lots of children, make that guy generate 100 children similar to himself, pick the best performer and repeat. What purpose does it serve to pick specifically the best 2 and crossbreed? For that matter, why not select 3, 4, or 10 parents ("orgy-derived" zygotes) from which to create each generation of children?

Answer 1

"from a subset of lots of children" - how were those children made, and what mechanism makes them different from each other? "generate 100 children similar to himself" - if not exactly like himself, then what mechanism makes them similar, yet not identical?

Sexual reproduction is a mechanism that answers these questions. Through sexual reproduction you create new combinations, made up of the genes of fit individuals. Just using random mutation alone as a mechanism for creating diversity and new combinations is what it says - random - a shot in the dark. Sexual reproduction creates new combinations using the genes of successful individuals, which is not simply random.

Questioning which is better, sexual vs. asexual is a good question, and there are a lot of articles on this topic of sexual vs. asexual, and not all favor sexual. There are successful asexual mechanisms, although I'm not sure if the alternative you proposed in your question is among them.

Answer 2

Think of it this way: your best performing guy is maybe better-than-average in, let's just say, 3 areas out of 10. Small variations of him (his asexually-reproduced kid) are probably going to have advantages in those same 3 areas: maybe 4 and maybe 2, depending on mutation. But the best performing guy and the best performing girl are better in perhaps 5 areas out of 10 (he's better-than-average in 3, she's better-than-average in 3, and maybe there's 1 where they overlap) and so if they had a good number of children one of them might be better-than-average in 5 areas (and perhaps one of them might inherit no advantages -- such are the breaks). And if that 5-areas-of-advantage kid mates with another 5-area-of-advantage kid, then while there's more chance of overlapping advantage, there's still a good chance (in our "10 gene" world) that the grand-child will have even more advantageous genes).

It's the recombination of several characteristics in a complex environment that's really at the heart of the genetic algorithm. It's not intuitive, because we don't generally think that twiddling every knob on the control panel at once is a good way to optimize, but if you have a lot of parameters and they're quite independent, it can be.

Answer 3

The fewer parents you have, the more likely you are to get caught in a local optimum-- potentially a not-very-good local optimum-- for a very long time. With only one parent, the only search mechanism left is individual mutation.

The more parents you have the less likely you are to capture whatever it was about the original parents that caused them to be selected for reproduction in the first place. The details will depend on exactly how your n-ary crossover works, but intuitively, the more parents you have, the less genetic material you are likely to have from any one particular parent, and the less likely the children are to inherit (and thus improve upon) any beneficial multi-chromosome traits of their parents.

This is related to the Schema Theorem.

Answer 4

Technically, you can have orgy-derived zygotes in your population, but there is no mathematical proof (at least to my knowledge) that they improve either diversity or the final result found by your algoritm. Besides, orgy operators (to use your term) are more complicated that the simple two parent kind, and are not easily prone to understanding by students. Hence, they are not advertised (does not mean that they are not allowed).

Actually, you can use a mix of both single and double parent in your GA. As one answer already pointed out, the single parent element is equivalent to a local search and technically you would be implementing a memetic algorithm, which is usually an improvement on the simple GA.