Simulated annealing and the (1+1) EA, a simple evolutionary algorithm, are both general randomized search heuristics that optimize any objective function with probability converging to 1. But they use very different techniques to achieve this global convergence. The (1+1) EA applies global mutations than can reach any point in the search space in one step together with an elitist selection mechanism. Simulated annealing restricts its search to a neighborhood but employs a randomized selection scheme where the probability for accepting a move to a new point in the search space depends on the difference in function values as well as on the current time step. Otherwise, the two algorithms are equal. It is known that the different philosophies of search implemented in the two heuristics can lead to exponential performance gaps between the two algorithms with respect to the expected optimization time. Even for very restricted classes of objective functions where the differences in function values between neighboring points are strictly limited the performance differences can be huge. Here, a more local point of view is taken. Considering obstacles in the fitness landscapes it is proven that the local performance of the two algorithms is remarkably similar in spite of their different search behaviors.
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