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In hill climbing methods, at each step, the current solution is replaced with the best neighbour (that is, the neighbour with highest/smallest value). In simulated annealing, "downhills" moves are allowed.

What are the advantages of simulated annealing with respect to hill climbing approaches? How is simulated annealing better than hill climbing methods?

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In the least technical, most intuitive way possible: Simulated Annealing can be considered as a modification of Hill Climbing (or Hill Descent). Hill Climbing/Descent attempts to reach an optimum value by checking if its current state has the best cost/score in its neighborhood, this makes it prone to getting stuck in local optima.

Simulated Annealing attempts to overcome this problem by choosing a "bad" move every once in a while. The probability of choosing of a "bad" move decreases as time moves on, and eventually, Simulated Annealing becomes Hill Climbing/Descent.

If configured correctly, and under certain conditions, Simulated Annealing can guarantee finding the global optimum, whereas such a guarantee is available to Hill Climbing/Descent iff the all local optima in the search space have equal scores/costs.

For more, go through Wolfram Mathworld's entry here.

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