# what does $(1 + (λ, λ))$ Genetic Algorithm mean?

I am discovering the topic of Genetic Algorithms, I read a bit about it on wikipedia and towardsdatascience. When I checked papers some papers, I found them using the notation "$$(1 + (λ, λ))$$" Genetic Algorithm. What does it mean exactly?

They also use the notation "(1 + 1)" evolutionary algorithm. Any idea what these notations mean?

Example paper: https://arxiv.org/pdf/2004.08664.pdf

Thanks

• It's in the preliminaries of the very paper you provide. Read sections 2.2 and 2.3. Feb 13, 2022 at 14:27

The very first sentence in the paper you link to says

The $$(1 + (\lambda, \lambda))$$ genetic algorithm (GA), proposed in [12], is a fairly recent algorithm with very interesting properties.

We search for the given citation, and see that it says in Section 1.3 that

We use a uniform crossover that takes bits from the parent with probability $$1 − c$$ and from the winning offspring with probability $$c$$ for some not too large crossover probability $$c$$. The outcome of such a crossover step will be close enough to the parent to give us a good chance of keeping the positive aspects of the parent. To give newly found positive genes of the winning offspring a reasonable chance to survive, we create again $$\lambda$$ offspring by this crossover. We call this algorithm the $$(1 + (\lambda, \lambda))$$ GA.

You can do a similar lookup for the (1+1) EA algorithm.

• Just to add on, $(\mu + \lambda)$ indicates a parent population size of $\mu$ generating $\lambda$ offspring each generation, with the plus indicating that the next generation comes from selecting from both parents and children (i.e., elitism). A $(\mu, \lambda)$ EA is the same except only offspring are sampled to form the next generation. Feb 13, 2022 at 15:57
• @deong Care to make that (perhaps expanded a little) into an answer? I'd be happy to upvote.
– Juho
Feb 13, 2022 at 16:00