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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

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  • $\begingroup$ It's in the preliminaries of the very paper you provide. Read sections 2.2 and 2.3. $\endgroup$
    – Pål GD
    Commented Feb 13, 2022 at 14:27

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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.

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    $\begingroup$ 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. $\endgroup$
    – deong
    Commented Feb 13, 2022 at 15:57
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    $\begingroup$ @deong Care to make that (perhaps expanded a little) into an answer? I'd be happy to upvote. $\endgroup$
    – Juho
    Commented Feb 13, 2022 at 16:00

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