Q19Principles of Artificial Intelligence
Question
Solve the 8-puzzle problem using Hill Climbing search. Explain the algorithm and its drawbacks.
Answer
Hill Climbing is a local search algorithm that can be applied to the 8-puzzle problem, but it suffers from local maxima, ridges, and plateau issues.
The 8-puzzle consists of a 3x3 grid with 8 numbered tiles and one blank space. The objective is to reach a specific goal configuration from an initial state by sliding tiles horizontally or vertically into the blank space.
Hill Climbing Search is a local search algorithm that continuously moves in the direction of increasing elevation (or decreasing cost) to find the peak of the mountain (the best state). For the 8-puzzle, a heuristic function h(n) is used, such as the Manhattan distance or the number of misplaced tiles. The algorithm evaluates all neighboring states (possible moves) and always moves to the neighbor that has the strictly lowest heuristic value.
Algorithm Steps:
1. Evaluate the initial state. If it is a goal state, return it.
2. Loop until a solution is found or no better neighbors exist: Select a neighboring state with the best heuristic value. If this value is worse than or equal to the current state, stop and return the current state.
Drawbacks:
- Local Maxima: A state that is better than all its neighbors but is not the global optimal goal. The algorithm gets stuck here.
- Ridges: A sequence of local maxima that is difficult for single-move algorithms to navigate.
- Plateaus: A flat area of the search space where all neighbors have the same value, causing the search to wander aimlessly.
