Hill climbing seems to be a very powerful tool for optimization. However, how to generate the "neighbors" of a solution always puzzles me.
For example, I am optimizing a solution $(x_1, x_2, x_3)$. Here $x_1$ is in range $(0, 0.1)$, $x_2$ is in range $(0, 100)$, $x_3$ is in range $(0, 1000000)$. What's the best way to generate "neighbors"? I can't really pick a "step size" here, because a step size of 1 is huge to $x_1$, but very minor to $x_3$.
What is the best generic way to generate "neighbors" in hill climbing algorithms?