I used simulated annealing for my Master's thesis. I was trying to fit a differential equation to some experimental results. With small changes in the parameters, you could get huge changes in the solution of the DE. For some of the experiments, the parameters it chose fit almost perfectly. As a result, simulated annealing is one of the techniques I look at for highly non-linear optimization.
Simulated annealing is not required for non-linear optimization. It's useful for non-convex optimization. Non-linear but convex problems are trivial to solve with Newton's method - a simple example is finding the weights of an SVM.
