Is there a metric that combines recall and precision other than the F1 score? I am looking for a machine learning optimization metric that combines recall and precision.
One such metric is the F1 score, which is the harmonic mean of the precision and the recall of a model. The problem with this metric is that it puts too much emphasis on the recall. For example:

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*A model with 5% recall and 90% precision has an F1 score of 9%.

*A model with 90% recall and 50% precision has an F1 score of 64%.

So for the F1 score, a model that makes lots of mediocre predictions is better than a model that makes a few great predictions.
Is there an alternative?

F1 score does not put importance on recall. It's a symmetric. So, both 90% recall + 50% precision and 90% precision + 50% recall yields the same F1 score , that is nearly 64%. F1 score gives importance to the lower of precision or recall, which is a property of the harmonic mean.
However, you can give more importance to one of the metrics via $F_\beta$ score, by setting $\beta$:
$$F_\beta=(1+\beta^2)\frac{pr}{\beta^2p + r}$$
A high $\beta$ would give more importance to recall, a low one gives more importance to precision. This is like a weighted harmonic mean. When $\beta=1$, it's the usual $F_1$ score.
