Gotcha with fitness function design

Typically, a genetic algorithm works by the notion of maximizing the fitness. Consider a function $y = x$, which is to be minimized in the interval $[-5, 5]$. One approach is use $\frac{1}{x}$ as the fitness function. Intuitively, by maximizing $\frac{1}{x}$, we are minimizing $y = x$. However, a plot of $\frac{1}{x}$ reveals some serious flaws.

If we move from the right, the maximum occurs at $x = 0$ instead of $x = -5$. Why? because $\frac{1}{x}$ is not differentiable at $x = 0$. Always make sure that the fitness/loss function is differentiable! In this case, it is better to use $y = -x$ as the fitness function.

In general, if we are seeking to minimize $y = f(x)$, where $f(x)$ is differentiable, then it is safer to use $y = -f(x)$ as the fitness function. Probably very obvious, but I got burned by this.