Problem 8 (10 points): Simulated annealing is an extension of hill climbing, which uses randomness to avoid getting stuck in local maxima and plateaux. a) For what types of problems will hill climbing work better than simulated annealing? In other words, when is the b) For what types of problems will randomly guessing the state work just as well as simulated annealing? In other c) Reasoning from your answers to parts (a) and (b) above, for what types of problems is simulated annealing a useful random part of simulated annealing not necessary? words, when is the hill-climbing part of simulated annealing not necessary? technique? In other terms, what assumptions about the shape of the value function are implicit in the design of simulated annealing? d) As defined in your textbook, simulated annealing returns the current state when the end of the annealing schedule is reached and if the annealing schedule is slow enough. Given that we know the value (measure of goodness) of each state we visit, is there anything smarter we could do? e) Simulated annealing requires a very small amount of memory, just enough to store two states: the current state and the proposed next state. Suppose we had enough memory to hold two million states. Propose a modification to simulated annealing that makes productive use of the additional memory. In particular, suggest something that will likely perform better than just running simulated annealing a million times consecutively with random restarts. [Note: There are multiple correct answers here.] Problem 8 (10 points): Simulated annealing is an extension of hill climbing, which uses randomness to avoid getting stuck in local maxima and plateaux. a) For what types of problems will hill climbing work better than simulated annealing? In other words, when is the b) For what types of problems will randomly guessing the state work just as well as simulated annealing? In other c) Reasoning from your answers to parts (a) and (b) above, for what types of problems is simulated annealing a useful random part of simulated annealing not necessary? words, when is the hill-climbing part of simulated annealing not necessary? technique? In other terms, what assumptions about the shape of the value function are implicit in the design of simulated annealing? d) As defined in your textbook, simulated annealing returns the current state when the end of the annealing schedule is reached and if the annealing schedule is slow enough. Given that we know the value (measure of goodness) of each state we visit, is there anything smarter we could do? e) Simulated annealing requires a very small amount of memory, just enough to store two states: the current state and the proposed next state. Suppose we had enough memory to hold two million states. Propose a modification to simulated annealing that makes productive use of the additional memory. In particular, suggest something that will likely perform better than just running simulated annealing a million times consecutively with random restarts. [Note: There are multiple correct answers here.]