What is the difference between hill climbing and branch and bound search algorithms?

Hill search and branching are two heuristic search algorithms used in artificial intelligence. What is the difference between these two approaches?

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Hill search results start from the beginning with the initial guess of the solution, and then iteratively make local changes until a solution is found or the heuristic is stuck at a local maximum. There are many ways to avoid getting stuck at local maxima, such as performing many searches at the same time or probabilistic choice of successor state, etc. In many cases, mountain climbing algorithms will quickly converge on the correct answer. However, none of these approaches guarantees an optimal solution.

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