Artificial Intelligence Problem: PLEASE ANSWER ALL PARTS OF THE QUESTIONS WITH F

Question

Artificial Intelligence Problem:

PLEASE ANSWER ALL PARTS OF THE QUESTIONS WITH FULL EXPLANATIONS

Consider the following "Rush Hour" puzzle. Recall that the rules for solving the puzzle are that vehicles can move only back or forward (no turning). The goal is to get the red car out of the parking lot through the exit at right. 2.1 (1 pt) Solve the problem and present your solution 2.2 (7 pts) Give as accurate an estimate as you can for the size of the problem space for this puzzle. (The estimate should be for this instance of the puzzle, not a "general" estimate 2.3 (7 pts) Suggest a plausible "h" function that would be appropriate for A* search for a general instance of the Rush Hour puzzle. (The function should be a non-trivial but easily computable underestimate of the number of moves required to solve the puzzle from a given position.) 2.4 (5 pts) Did your solution in 2.1 have features in common with (e.g.) depth-first search? Breadth-first search? Means-ends analysis? Would bidirectional search be a good idea for this puzzle? Why or why not?

Explanation / Answer

2.1

2.2 Problem space is the set of states from initial to final state and the connections between those states. Transition from one state to another state can be done by one of the operations which are predefined. Like in this case operations could be Move forward and move backward. In step 2.1 there are total 10 states thus problem space size is 10.

2.3 For rush hour puzzle consider following heuristics for A*:

all_hueristic: for total number of blocks

block_hueristic: At any particular state this will give us the number of cars blocking escape vehicle. This would be zero for goal state.

Operations:

mov_fwd: move forward

mov_bwd: move backward

Each state will have some heuristic value and transition between the states will be accomplished by above operations. Once a new state is achieved both the heuristics values will be calculated for that state where all_hueristic will be same for all the states but block heuristic will change and will dissolve to zero for goal state.

2.4 The solution resembles a depth first search algorithm. In a sense that we will start with the piece which must be moved before escape vehicle can exit,, in this case this would bbe the yellow piece. Now to move yellow piece one must move light blue piece. When this is done, next blocking piece is dark blue piece, in order to move this dark green should be moved, for that brown must be moved and so on.

            Bidirectional search is not good for this puzzle for following reasons:

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