selection

Selection chooses which solutions survive and reproduce in evolutionary optimization. It creates selection pressure that drives the population toward better fitness.
If selection pressure is too weak, we suffer random drift and slow progress.
If it’s too strong, we get premature convergence to local optima.
Some of these strategies are commonly combined (e.g. always a little elitism to keep monotonic improvement / not loose progress).

Common selection methods

roulette wheel selection - Probability of selection proportional to fitness
Rank-based - Select based on fitness ranking, not absolute values, prevents premature convergence from extreme fitness values
Tournament - Randomly pick k individuals, select the best, simple, parallelizable, tunable pressure via k
Truncation - Select top n% of population; looses diversity
elitism (selection) - Always preserve best individuals. Guarantees monotonic improvement

Selection in ES $(\mu +\lambda )$, $(\mu ,\lambda )$

$\mu$ … elites, best performing individuals of a generation
$\lambda$ … population size (including elites)
$(\mu +\lambda )$ … give the parents a chance to compete with their children (elitist, best survive)
$(\mu ,\lambda )$ … replace parents by children (can help overcome local optimium through turnover/diversity→ advantage over gradient-based methods; bio inspo: death of old age)

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