Solving the 8 Puzzle Problem in Artificial Intelligence: Understanding the A* Algorithm

Solving the 8 Puzzle Problem in Artificial Intelligence: Understanding the A* Algorithm

If you are familiar with the 8 puzzle problem, you know it’s a common problem in artificial intelligence (AI). The puzzle includes arranging numbers 1-8 on a 3×3 grid, while considering the constraints of the single empty tile. Finding a solution to this problem involves searching all possible routes within an enormous search space, making it challenging to solve. But you can simplify such complexity with the A* algorithm.

The A* algorithm is among the most widely used search algorithms in AI for finding the shortest path from an initial state to a goal state. The algorithm uses a heuristic function that estimates the distance from the current state to the goal state, guiding the search towards the most promising path. Let’s dive deeper to explore how the A* algorithm works.

A* algorithm operation

The A* algorithm is a type of informed search technique that expands the nodes with the lowest cost value. The cost value includes the current state’s path cost plus an estimated cost from the current node to the goal node. The total cost is calculated using this formula f(n) = g(n) + h(n), where g(n) is the path cost from the source node to the current node, and h(n) is the estimated cost from the current node to the goal node.

For the 8 puzzle problem, the heuristic function (h(n)) considers Manhattan distance, which is the sum of the horizontal and vertical distances from the current state to the goal state. The algorithm’s initial state begins with the starting node, and it is expanded to its successors. The successor node that has the lowest total cost (f(n)) is chosen to be explored further until the goal state is reached.

Once the algorithm reaches the goal node, a path from the starting node to the goal node is generated by reversing the pointers along the path, which is the shortest path from the initial state to the goal state. The optimality of the algorithm makes it an attractive option for solving the 8 puzzle problem.

Code for A* algorithm

Here is the code implementation of the A* algorithm in Python:

def astar(start_node, goal_node):

# Initialize empty lists for open and closed nodes
open_nodes = []
closed_nodes = []

# Add the starting node to the open nodes
start_node.f = start_node.g + start_node.h
open_nodes.append(start_node)

# Loop until the goal node is found
while len(open_nodes) > 0:

# Choose the node with the lowest f value
current_node = min(open_nodes, key=lambda x: x.f)

# Exit if the goal node has been reached
if current_node == goal_node:
return current_node

# Move the current node from open to closed nodes
open_nodes.remove(current_node)
closed_nodes.append(current_node)

# Loop through the current node’s successors
for successor_node in current_node.successors:

# Skip the node if it is in closed nodes
if successor_node in closed_nodes:
continue

# Calculate the successor node’s f, g, and h values
successor_node.g = current_node.g + successor_node.move_cost
successor_node.h = manhattan_distance(successor_node,goal_node)
successor_node.f = successor_node.g + successor_node.h

# If the successor node is not in open nodes, add it
if successor_node not in open_nodes:
open_nodes.append(successor_node)

# Return None if no path is found
return None

Conclusion

The A* algorithm provides an efficient approach to solving the 8 puzzle problem by reducing the search space while finding the shortest path. It uses a heuristic function to guide the algorithm to the most promising path while maintaining optimality. Understanding the A* algorithm’s functionality enables developers to implement it in their projects successfully. With the right implementation, complex AI problems like the 8 puzzle problem can be solved with relative ease.