# What is the difference between Simulated Annealing and Monte-Carlo Simulations?

What is the difference between Simulated Annealing and Monte-Carlo Simulations? Is Simulated Annealing a specific type of Monte-Carlo simulation, or are they completely separate techniques?

In Monte Carlo simulation, we are aiming at computing some quantity $A$ by finding an easily samplable random variable $X$ whose expectation is $A$. We estimate $A$ by averaging many samples of $X$. More sophisticated versions of this are rejection sampling and MCMC.
Simulated annealing is a heuristic for optimizing an objective function $f$ over a domain $D$. We start with an arbitrary point $x \in D$, and then try making local changes which improve the value of $f$; this is local search. In simulated annealing, we also allow making local changes which worsen the value of $f$, with some small probability. The probability is smaller the more the change makes $f$ worse.