Why do low fitness individuals have a chance to survive to the next generation? I am currently reading and watching about genetic algorithm and I find it very interesting (I haven't had the chance to study it while I was at the university).

I understand that mutations are based on probability (randomness is the root of evolution) but I don't get why survival is.

From what I understand, an individual $I$ having a fitness $F(i)$ such as for another individual $J$ having a fitness $F(j)$ we have $F(i) &gt; F(j)$, then $I$ has a better probability than $J$ to survive to the next generation.

Probability implies that $J$ may survive and $I$ may not (with "bad luck"). I don't understand why this is good at all? If $I$ would always survive the selection, what would go wrong in the algorithm? My guess is that the algorithm would be similar to a greedy algorithm but I am not sure.
The main idea is that by allowing suboptimal individuals to survive, you can switch from one "peak" in the evolutionary landscape to another through a sequence of small incremental mutations. On the other hand, if you only are allowed to go uphill it requires a gigantic and massively unlikely mutation to switch peaks.

Here is a diagram showing the difference:



Practically, this globalization property is the main sellling point of evolutionary algorithms - if you just want to find a local maxima there exist more efficient specialized techniques. (eg., L-BFGS with finite difference gradient and line search)

In the real world of biological evolution, allowing suboptimal individuals to survive creates robustness when the evolutionary landscape changes. If everyone is concentrated at a peak, then if that peak becomes a valley the whole population dies (eg., dinosaurs were the most fit species until there was an asteroid strike and the evolutionary landscape changed). On the other hand, if there is some diversity in the population then when the landscape changes some will survive.