15 Puzzle Problem Solving By Using Heuristic-Based Approaches

The 15-Puzzle is one of the most famous benchmarks to test heuristic search algorithms that are challenging both in efficient state space exploration and optimizing solutions. The task in this puzzle is to fit a 4x4 grid of numbered tiles in a disordered state to a target configuration with minimal moves. This paper covers heuristic-based approaches and works with Manhattan Distance, Misplaced Tile, and Linear Conflict heuristics under an A* search algorithm to come up with a solution for the problem. A* approximates the cost that has to be made to achieve the goal state by finding the best possible solution. Each heuristic was then measured on computation time and memory usage, by first solving the initial configurations of the puzzles with A*. Then each of them compared their performance regarding the nodes expanded, the actual time of computation, and path length. Analysis with techniques of visualization will involve node exploration graphs and the graphs of effectiveness in terms of heuristics used. The results indicate that there are instances when simpler heuristics provide faster less optimal solutions and advanced ones, such as Linear Conflict, prove to be more accurate path results but with higher computations. In this case, Manhattan Distance finds a kind of balance between accuracy and efficiency, and Linear Conflict reduces the search depth at nearly solved puzzles. Although less powerful for tile movement error, its simplicity also makes it a better alternative. Conclusion Manhattan distance and linear conflict heuristics are very effective for solving the 15-puzzle problem. Specifically, linear conflict is quite useful for configurations close to being solved. Hybrid approaches to applying heuristics can be quite valuable in improving performance but still retaining solution optimality. The combination of appropriate heuristics allows such a tradeoff between speed and accuracy, with significant implications for real world AI pathfinding and robotics.