Solving the 8-Puzzle Problem with Python Code in Artificial Intelligence

Artificial Intelligence (AI) has revolutionized the way we solve complex problems in all areas of life. One example is the 8-Puzzle problem, which involves moving tiles on a board to reach a predetermined goal state. This problem has various real-life applications such as route optimization and resource allocation. In this article, we will discuss how to solve the 8-Puzzle problem using Python code in Artificial Intelligence.

What is the 8-Puzzle problem?

The 8-Puzzle problem is a classic problem in AI that involves an 8-square board with 8 numbered tiles and a blank space. The objective is to rearrange the tiles from the initial state to a goal state by sliding them into the blank space. The catch is that each tile can only be moved into the blank space, and the move must be a horizontal or vertical displacement. There are approximately 181,440 possible states of the board.

Solving the 8-Puzzle problem with Python code

To solve the 8-Puzzle problem using Python code, we will use a popular algorithm called the A* Search algorithm. This algorithm aims to find the shortest path from the initial state to the goal state by minimizing the total estimated cost. The algorithm follows these steps:

1. Create an open list of nodes, initially containing only the initial state.
2. Create a closed list of nodes, initially empty.
3. Calculate the cost of each node by adding the Manhattan distance from the current node to the goal node and the cost of the path from the initial state to the current node.
4. Choose the node with the lowest cost from the open list and move it to the closed list.
5. Generate all possible child nodes of the current node.
6. Calculate the cost of each child node and add it to the open list if it has not been visited before.
7. Repeat steps 4-6 until the goal node is reached, or there are no more nodes in the open list.

Implementing the A* Search algorithm in Python

To implement the A* Search algorithm in Python, we will use the ‘heapq’ module to maintain the open list in a priority queue. Here’s the Python code:

“`
import heapq

def astar_search(start, goal):
# Define the heuristic function
def heuristic(node):
return sum(abs(b%3 – g%3) + abs(b//3 – g//3)
for b, g in ((node.index(i), goal.index(i)) for i in range(1, 9)))

# Define the path cost function
def path_cost(c, node1, move, node2):
return c + 1

# Create the starting node
start_node = (heuristic(start), 0, start, None)

# Create the open list
heap = []
heapq.heappush(heap, start_node)

# Create the closed list
closed = set()

# Loop until the goal is reached
while heap:
# Choose the node with the lowest cost from the open list
current_node = heapq.heappop(heap)

# If the goal node is reached, return the path
if current_node[2] == goal:
path = []
while current_node:
path.append(current_node[2])
current_node = current_node[3]
return path[::-1]

# Generate all possible child nodes
for move, succ in successors(current_node[2]).items():
# Calculate the cost of each child node
cost = current_node[1] + path_cost(current_node[1], current_node[2], move, succ)
child_node = (heuristic(succ) + cost, cost, succ, current_node)

# Add the child node to the open list if it has not been visited before
if succ not in closed:
heapq.heappush(heap, child_node)
closed.add(succ)

# If the goal is not reached, return None
return None

# Define the initial and goal state
start = (0, 1, 2, 3, 4, 5, 6, 7, 8)
goal = (1, 2, 3, 4, 5, 6, 7, 8, 0)

# Solve the 8-Puzzle problem using A* Search algorithm
path = astar_search(start, goal)
print(path)
“`

Conclusion

In summary, the 8-Puzzle problem is a classic problem in Artificial Intelligence that involves rearranging tiles on a board to reach a predetermined goal state. We discussed how to solve this problem using Python code and the A* Search algorithm. We provided a step-by-step guide to implementing the algorithm and provided example Python code that you can use to solve 8-Puzzle problems of your own. With this knowledge, we hope you can apply it to other complex problems and achieve your desired goals.

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